Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.3% → 83.3%

Time: 21.6s

Alternatives: 21

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \sqrt[3]{{\left(c \cdot j - x \cdot a\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (* j (- (* t c) (* y i)))
          (+ (* b (- (* z c) (* a i))) (* x (- (* t a) (* y z)))))))
   (if (<= t_1 INFINITY) t_1 (* t (cbrt (pow (- (* c j) (* x a)) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * cbrt(pow(((c * j) - (x * a)), 3.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * Math.cbrt(Math.pow(((c * j) - (x * a)), 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * cbrt((Float64(Float64(c * j) - Float64(x * a)) ^ 3.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[Power[N[Power[N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 94.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 0.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 8.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 12.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 51.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 51.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 51.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 51.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 51.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
   7. Step-by-step derivation

      1. add-cbrt-cube 55.5%

         \[\leadsto t \cdot \color{blue}{\sqrt[3]{\left(\left(c \cdot j - a \cdot x\right) \cdot \left(c \cdot j - a \cdot x\right)\right) \cdot \left(c \cdot j - a \cdot x\right)}} \]

      2. pow3 55.5%

         \[\leadsto t \cdot \sqrt[3]{\color{blue}{{\left(c \cdot j - a \cdot x\right)}^{3}}} \]

   8. Applied egg-rr 55.5%

      \[\leadsto t \cdot \color{blue}{\sqrt[3]{{\left(c \cdot j - a \cdot x\right)}^{3}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \sqrt[3]{{\left(c \cdot j - x \cdot a\right)}^{3}}\\ \end{array} \]

Alternative 2: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (* j (- (* t c) (* y i)))
          (+ (* b (- (* z c) (* a i))) (* x (- (* t a) (* y z)))))))
   (if (<= t_1 INFINITY) t_1 (* a (- (* b i) (* x t))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - ((b * ((z * c) - (a * i))) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 94.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 0.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 8.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 8.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 10.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 12.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 53.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 53.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right) \leq \infty:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 3: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -7 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -7e+78)
     t_1
     (if (<= x -4.7e-14)
       (* i (- (* a b) (* y j)))
       (if (<= x -4.3e-29)
         (- (* y (* x z)) (* a (* x t)))
         (if (<= x 6e+56)
           (+ (* j (- (* t c) (* y i))) (* b (- (* a i) (* z c))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+78) {
		tmp = t_1;
	} else if (x <= -4.7e-14) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= -4.3e-29) {
		tmp = (y * (x * z)) - (a * (x * t));
	} else if (x <= 6e+56) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-7d+78)) then
        tmp = t_1
    else if (x <= (-4.7d-14)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= (-4.3d-29)) then
        tmp = (y * (x * z)) - (a * (x * t))
    else if (x <= 6d+56) then
        tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -7e+78) {
		tmp = t_1;
	} else if (x <= -4.7e-14) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= -4.3e-29) {
		tmp = (y * (x * z)) - (a * (x * t));
	} else if (x <= 6e+56) {
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -7e+78:
		tmp = t_1
	elif x <= -4.7e-14:
		tmp = i * ((a * b) - (y * j))
	elif x <= -4.3e-29:
		tmp = (y * (x * z)) - (a * (x * t))
	elif x <= 6e+56:
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -7e+78)
		tmp = t_1;
	elseif (x <= -4.7e-14)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= -4.3e-29)
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(x * t)));
	elseif (x <= 6e+56)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -7e+78)
		tmp = t_1;
	elseif (x <= -4.7e-14)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= -4.3e-29)
		tmp = (y * (x * z)) - (a * (x * t));
	elseif (x <= 6e+56)
		tmp = (j * ((t * c) - (y * i))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7e+78], t$95$1, If[LessEqual[x, -4.7e-14], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.3e-29], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+56], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.0000000000000003e78 or 6.00000000000000012e56 < x

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 75.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -7.0000000000000003e78 < x < -4.7000000000000002e-14

   1. Initial program 81.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 81.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 81.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 81.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 81.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 81.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 81.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 81.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around -inf 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   if -4.7000000000000002e-14 < x < -4.2999999999999998e-29

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 85.6%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around 0 85.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)} \]

   if -4.2999999999999998e-29 < x < 6.00000000000000012e56

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 77.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 77.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 77.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around 0 70.5%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j - b \cdot \left(c \cdot z - a \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-14}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+56}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 4: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -65000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-250}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -3.2e+62)
     t_3
     (if (<= t -3.3e+24)
       t_1
       (if (<= t -65000.0)
         (* x (- (* y z) (* t a)))
         (if (<= t -7.2e-238)
           t_2
           (if (<= t -6.6e-292)
             (* z (- (* x y) (* b c)))
             (if (<= t 1.25e-250)
               t_2
               (if (<= t 4.3e-101)
                 (* y (- (* x z) (* i j)))
                 (if (<= t 4.2e-63) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.2e+62) {
		tmp = t_3;
	} else if (t <= -3.3e+24) {
		tmp = t_1;
	} else if (t <= -65000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -7.2e-238) {
		tmp = t_2;
	} else if (t <= -6.6e-292) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.25e-250) {
		tmp = t_2;
	} else if (t <= 4.3e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.2e-63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = i * ((a * b) - (y * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-3.2d+62)) then
        tmp = t_3
    else if (t <= (-3.3d+24)) then
        tmp = t_1
    else if (t <= (-65000.0d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= (-7.2d-238)) then
        tmp = t_2
    else if (t <= (-6.6d-292)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.25d-250) then
        tmp = t_2
    else if (t <= 4.3d-101) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.2d-63) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.2e+62) {
		tmp = t_3;
	} else if (t <= -3.3e+24) {
		tmp = t_1;
	} else if (t <= -65000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -7.2e-238) {
		tmp = t_2;
	} else if (t <= -6.6e-292) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.25e-250) {
		tmp = t_2;
	} else if (t <= 4.3e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.2e-63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = i * ((a * b) - (y * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.2e+62:
		tmp = t_3
	elif t <= -3.3e+24:
		tmp = t_1
	elif t <= -65000.0:
		tmp = x * ((y * z) - (t * a))
	elif t <= -7.2e-238:
		tmp = t_2
	elif t <= -6.6e-292:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.25e-250:
		tmp = t_2
	elif t <= 4.3e-101:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.2e-63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.2e+62)
		tmp = t_3;
	elseif (t <= -3.3e+24)
		tmp = t_1;
	elseif (t <= -65000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= -7.2e-238)
		tmp = t_2;
	elseif (t <= -6.6e-292)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.25e-250)
		tmp = t_2;
	elseif (t <= 4.3e-101)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.2e-63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = i * ((a * b) - (y * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.2e+62)
		tmp = t_3;
	elseif (t <= -3.3e+24)
		tmp = t_1;
	elseif (t <= -65000.0)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= -7.2e-238)
		tmp = t_2;
	elseif (t <= -6.6e-292)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.25e-250)
		tmp = t_2;
	elseif (t <= 4.3e-101)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.2e-63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+62], t$95$3, If[LessEqual[t, -3.3e+24], t$95$1, If[LessEqual[t, -65000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.2e-238], t$95$2, If[LessEqual[t, -6.6e-292], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-250], t$95$2, If[LessEqual[t, 4.3e-101], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-63], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.19999999999999984e62 or 4.2e-63 < t

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.19999999999999984e62 < t < -3.2999999999999999e24 or 4.2999999999999997e-101 < t < 4.2e-63

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -3.2999999999999999e24 < t < -65000

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -65000 < t < -7.20000000000000021e-238 or -6.59999999999999989e-292 < t < 1.25000000000000007e-250

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around -inf 64.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   if -7.20000000000000021e-238 < t < -6.59999999999999989e-292

   1. Initial program 93.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 93.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 93.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if 1.25000000000000007e-250 < t < 4.2999999999999997e-101

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 65.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 65.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -65000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-238}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-250}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 5: 51.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -230000:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -2.9e+62)
     t_3
     (if (<= t -4.5e+24)
       t_1
       (if (<= t -230000.0)
         (- (* y (* x z)) (* a (* x t)))
         (if (<= t -8.5e-232)
           t_2
           (if (<= t -5.2e-292)
             (* z (- (* x y) (* b c)))
             (if (<= t 5.3e-251)
               t_2
               (if (<= t 9e-101)
                 (* y (- (* x z) (* i j)))
                 (if (<= t 4.7e-63) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.9e+62) {
		tmp = t_3;
	} else if (t <= -4.5e+24) {
		tmp = t_1;
	} else if (t <= -230000.0) {
		tmp = (y * (x * z)) - (a * (x * t));
	} else if (t <= -8.5e-232) {
		tmp = t_2;
	} else if (t <= -5.2e-292) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 5.3e-251) {
		tmp = t_2;
	} else if (t <= 9e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.7e-63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = i * ((a * b) - (y * j))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-2.9d+62)) then
        tmp = t_3
    else if (t <= (-4.5d+24)) then
        tmp = t_1
    else if (t <= (-230000.0d0)) then
        tmp = (y * (x * z)) - (a * (x * t))
    else if (t <= (-8.5d-232)) then
        tmp = t_2
    else if (t <= (-5.2d-292)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 5.3d-251) then
        tmp = t_2
    else if (t <= 9d-101) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.7d-63) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.9e+62) {
		tmp = t_3;
	} else if (t <= -4.5e+24) {
		tmp = t_1;
	} else if (t <= -230000.0) {
		tmp = (y * (x * z)) - (a * (x * t));
	} else if (t <= -8.5e-232) {
		tmp = t_2;
	} else if (t <= -5.2e-292) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 5.3e-251) {
		tmp = t_2;
	} else if (t <= 9e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.7e-63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = i * ((a * b) - (y * j))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.9e+62:
		tmp = t_3
	elif t <= -4.5e+24:
		tmp = t_1
	elif t <= -230000.0:
		tmp = (y * (x * z)) - (a * (x * t))
	elif t <= -8.5e-232:
		tmp = t_2
	elif t <= -5.2e-292:
		tmp = z * ((x * y) - (b * c))
	elif t <= 5.3e-251:
		tmp = t_2
	elif t <= 9e-101:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.7e-63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.9e+62)
		tmp = t_3;
	elseif (t <= -4.5e+24)
		tmp = t_1;
	elseif (t <= -230000.0)
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(a * Float64(x * t)));
	elseif (t <= -8.5e-232)
		tmp = t_2;
	elseif (t <= -5.2e-292)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 5.3e-251)
		tmp = t_2;
	elseif (t <= 9e-101)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.7e-63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = i * ((a * b) - (y * j));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.9e+62)
		tmp = t_3;
	elseif (t <= -4.5e+24)
		tmp = t_1;
	elseif (t <= -230000.0)
		tmp = (y * (x * z)) - (a * (x * t));
	elseif (t <= -8.5e-232)
		tmp = t_2;
	elseif (t <= -5.2e-292)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 5.3e-251)
		tmp = t_2;
	elseif (t <= 9e-101)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.7e-63)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e+62], t$95$3, If[LessEqual[t, -4.5e+24], t$95$1, If[LessEqual[t, -230000.0], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-232], t$95$2, If[LessEqual[t, -5.2e-292], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e-251], t$95$2, If[LessEqual[t, 9e-101], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e-63], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.89999999999999984e62 or 4.7000000000000001e-63 < t

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.89999999999999984e62 < t < -4.50000000000000019e24 or 8.9999999999999997e-101 < t < 4.7000000000000001e-63

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -4.50000000000000019e24 < t < -2.3e5

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around 0 86.4%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + y \cdot \left(z \cdot x\right)} \]

   if -2.3e5 < t < -8.5e-232 or -5.20000000000000027e-292 < t < 5.29999999999999963e-251

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around -inf 64.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j - a \cdot b\right)\right)} \]

   if -8.5e-232 < t < -5.20000000000000027e-292

   1. Initial program 93.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 93.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 93.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 93.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if 5.29999999999999963e-251 < t < 8.9999999999999997e-101

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 85.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 85.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 65.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 65.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 65.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 65.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 65.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -230000:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-232}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-292}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{-251}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 6: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -7.4 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -21000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -7.4e+62)
     t_2
     (if (<= t -3.5e+23)
       t_1
       (if (<= t -21000.0)
         t_2
         (if (<= t -1.15e-101)
           (* j (- (* t c) (* y i)))
           (if (<= t 5.5e-256)
             t_1
             (if (<= t 2.55e-101)
               (* y (- (* x z) (* i j)))
               (if (<= t 4.6e-63) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.4e+62) {
		tmp = t_2;
	} else if (t <= -3.5e+23) {
		tmp = t_1;
	} else if (t <= -21000.0) {
		tmp = t_2;
	} else if (t <= -1.15e-101) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 5.5e-256) {
		tmp = t_1;
	} else if (t <= 2.55e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-7.4d+62)) then
        tmp = t_2
    else if (t <= (-3.5d+23)) then
        tmp = t_1
    else if (t <= (-21000.0d0)) then
        tmp = t_2
    else if (t <= (-1.15d-101)) then
        tmp = j * ((t * c) - (y * i))
    else if (t <= 5.5d-256) then
        tmp = t_1
    else if (t <= 2.55d-101) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.6d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -7.4e+62) {
		tmp = t_2;
	} else if (t <= -3.5e+23) {
		tmp = t_1;
	} else if (t <= -21000.0) {
		tmp = t_2;
	} else if (t <= -1.15e-101) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 5.5e-256) {
		tmp = t_1;
	} else if (t <= 2.55e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -7.4e+62:
		tmp = t_2
	elif t <= -3.5e+23:
		tmp = t_1
	elif t <= -21000.0:
		tmp = t_2
	elif t <= -1.15e-101:
		tmp = j * ((t * c) - (y * i))
	elif t <= 5.5e-256:
		tmp = t_1
	elif t <= 2.55e-101:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.6e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -7.4e+62)
		tmp = t_2;
	elseif (t <= -3.5e+23)
		tmp = t_1;
	elseif (t <= -21000.0)
		tmp = t_2;
	elseif (t <= -1.15e-101)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (t <= 5.5e-256)
		tmp = t_1;
	elseif (t <= 2.55e-101)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -7.4e+62)
		tmp = t_2;
	elseif (t <= -3.5e+23)
		tmp = t_1;
	elseif (t <= -21000.0)
		tmp = t_2;
	elseif (t <= -1.15e-101)
		tmp = j * ((t * c) - (y * i));
	elseif (t <= 5.5e-256)
		tmp = t_1;
	elseif (t <= 2.55e-101)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.4e+62], t$95$2, If[LessEqual[t, -3.5e+23], t$95$1, If[LessEqual[t, -21000.0], t$95$2, If[LessEqual[t, -1.15e-101], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-256], t$95$1, If[LessEqual[t, 2.55e-101], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e-63], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.40000000000000028e62 or -3.5000000000000002e23 < t < -21000 or 4.6e-63 < t

   1. Initial program 69.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -7.40000000000000028e62 < t < -3.5000000000000002e23 or -1.15e-101 < t < 5.4999999999999998e-256 or 2.5500000000000001e-101 < t < 4.6e-63

   1. Initial program 84.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 62.5%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -21000 < t < -1.15e-101

   1. Initial program 84.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 88.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 58.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if 5.4999999999999998e-256 < t < 2.5500000000000001e-101

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 64.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 64.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -21000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 51.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -95000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -5.2e+62)
     t_2
     (if (<= t -1.2e+24)
       t_1
       (if (<= t -95000.0)
         (* x (- (* y z) (* t a)))
         (if (<= t -6.2e-102)
           (* j (- (* t c) (* y i)))
           (if (<= t 1.35e-255)
             t_1
             (if (<= t 3.1e-101)
               (* y (- (* x z) (* i j)))
               (if (<= t 4.8e-63) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.2e+62) {
		tmp = t_2;
	} else if (t <= -1.2e+24) {
		tmp = t_1;
	} else if (t <= -95000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -6.2e-102) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 1.35e-255) {
		tmp = t_1;
	} else if (t <= 3.1e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.8e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-5.2d+62)) then
        tmp = t_2
    else if (t <= (-1.2d+24)) then
        tmp = t_1
    else if (t <= (-95000.0d0)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= (-6.2d-102)) then
        tmp = j * ((t * c) - (y * i))
    else if (t <= 1.35d-255) then
        tmp = t_1
    else if (t <= 3.1d-101) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.8d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.2e+62) {
		tmp = t_2;
	} else if (t <= -1.2e+24) {
		tmp = t_1;
	} else if (t <= -95000.0) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= -6.2e-102) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 1.35e-255) {
		tmp = t_1;
	} else if (t <= 3.1e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.8e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.2e+62:
		tmp = t_2
	elif t <= -1.2e+24:
		tmp = t_1
	elif t <= -95000.0:
		tmp = x * ((y * z) - (t * a))
	elif t <= -6.2e-102:
		tmp = j * ((t * c) - (y * i))
	elif t <= 1.35e-255:
		tmp = t_1
	elif t <= 3.1e-101:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.8e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.2e+62)
		tmp = t_2;
	elseif (t <= -1.2e+24)
		tmp = t_1;
	elseif (t <= -95000.0)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= -6.2e-102)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (t <= 1.35e-255)
		tmp = t_1;
	elseif (t <= 3.1e-101)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.8e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.2e+62)
		tmp = t_2;
	elseif (t <= -1.2e+24)
		tmp = t_1;
	elseif (t <= -95000.0)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= -6.2e-102)
		tmp = j * ((t * c) - (y * i));
	elseif (t <= 1.35e-255)
		tmp = t_1;
	elseif (t <= 3.1e-101)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.8e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+62], t$95$2, If[LessEqual[t, -1.2e+24], t$95$1, If[LessEqual[t, -95000.0], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.2e-102], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-255], t$95$1, If[LessEqual[t, 3.1e-101], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-63], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.19999999999999968e62 or 4.8000000000000001e-63 < t

   1. Initial program 69.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.19999999999999968e62 < t < -1.2e24 or -6.20000000000000026e-102 < t < 1.35000000000000008e-255 or 3.09999999999999973e-101 < t < 4.8000000000000001e-63

   1. Initial program 83.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 83.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 83.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 83.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 83.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 62.0%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -1.2e24 < t < -95000

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 71.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 71.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 86.4%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -95000 < t < -6.20000000000000026e-102

   1. Initial program 84.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around -inf 88.4%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(z \cdot \left(-1 \cdot \left(y \cdot x\right) - -1 \cdot \left(c \cdot b\right)\right)\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right) - -1 \cdot \left(a \cdot \left(i \cdot b\right)\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 88.4%

      \[\leadsto \color{blue}{\left(a \cdot \left(i \cdot b - t \cdot x\right) + \left(c \cdot b - y \cdot x\right) \cdot \left(-z\right)\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in j around inf 58.9%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   if 1.35000000000000008e-255 < t < 3.09999999999999973e-101

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 64.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 64.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -95000:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-255}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 8: 50.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -0.7:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -3.2e+62)
     t_2
     (if (<= t -1.6e+23)
       t_1
       (if (<= t -0.7)
         t_2
         (if (<= t 4.2e-256)
           t_1
           (if (<= t 6e-101)
             (* y (- (* x z) (* i j)))
             (if (<= t 6.6e-63) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.2e+62) {
		tmp = t_2;
	} else if (t <= -1.6e+23) {
		tmp = t_1;
	} else if (t <= -0.7) {
		tmp = t_2;
	} else if (t <= 4.2e-256) {
		tmp = t_1;
	} else if (t <= 6e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 6.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-3.2d+62)) then
        tmp = t_2
    else if (t <= (-1.6d+23)) then
        tmp = t_1
    else if (t <= (-0.7d0)) then
        tmp = t_2
    else if (t <= 4.2d-256) then
        tmp = t_1
    else if (t <= 6d-101) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 6.6d-63) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -3.2e+62) {
		tmp = t_2;
	} else if (t <= -1.6e+23) {
		tmp = t_1;
	} else if (t <= -0.7) {
		tmp = t_2;
	} else if (t <= 4.2e-256) {
		tmp = t_1;
	} else if (t <= 6e-101) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 6.6e-63) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -3.2e+62:
		tmp = t_2
	elif t <= -1.6e+23:
		tmp = t_1
	elif t <= -0.7:
		tmp = t_2
	elif t <= 4.2e-256:
		tmp = t_1
	elif t <= 6e-101:
		tmp = y * ((x * z) - (i * j))
	elif t <= 6.6e-63:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -3.2e+62)
		tmp = t_2;
	elseif (t <= -1.6e+23)
		tmp = t_1;
	elseif (t <= -0.7)
		tmp = t_2;
	elseif (t <= 4.2e-256)
		tmp = t_1;
	elseif (t <= 6e-101)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 6.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -3.2e+62)
		tmp = t_2;
	elseif (t <= -1.6e+23)
		tmp = t_1;
	elseif (t <= -0.7)
		tmp = t_2;
	elseif (t <= 4.2e-256)
		tmp = t_1;
	elseif (t <= 6e-101)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 6.6e-63)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.2e+62], t$95$2, If[LessEqual[t, -1.6e+23], t$95$1, If[LessEqual[t, -0.7], t$95$2, If[LessEqual[t, 4.2e-256], t$95$1, If[LessEqual[t, 6e-101], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e-63], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.19999999999999984e62 or -1.6e23 < t < -0.69999999999999996 or 6.59999999999999987e-63 < t

   1. Initial program 69.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 69.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 69.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 70.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 70.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 71.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 71.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 68.9%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 68.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 68.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 68.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 68.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.19999999999999984e62 < t < -1.6e23 or -0.69999999999999996 < t < 4.20000000000000005e-256 or 6.0000000000000006e-101 < t < 6.59999999999999987e-63

   1. Initial program 84.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 57.9%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if 4.20000000000000005e-256 < t < 6.0000000000000006e-101

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 85.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 85.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 64.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 64.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 64.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+23}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -0.7:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-256}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-63}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 9: 29.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x \cdot a\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -33000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* x a)))))
   (if (<= a -2.25e+27)
     (* i (* a b))
     (if (<= a -33000.0)
       t_1
       (if (<= a -8e-269)
         (* t (* c j))
         (if (<= a 7.5e-200)
           (* b (* z (- c)))
           (if (<= a 4.9e-136)
             (* i (* y (- j)))
             (if (<= a 9e+73) (* y (* x z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * -(x * a);
	double tmp;
	if (a <= -2.25e+27) {
		tmp = i * (a * b);
	} else if (a <= -33000.0) {
		tmp = t_1;
	} else if (a <= -8e-269) {
		tmp = t * (c * j);
	} else if (a <= 7.5e-200) {
		tmp = b * (z * -c);
	} else if (a <= 4.9e-136) {
		tmp = i * (y * -j);
	} else if (a <= 9e+73) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * -(x * a)
    if (a <= (-2.25d+27)) then
        tmp = i * (a * b)
    else if (a <= (-33000.0d0)) then
        tmp = t_1
    else if (a <= (-8d-269)) then
        tmp = t * (c * j)
    else if (a <= 7.5d-200) then
        tmp = b * (z * -c)
    else if (a <= 4.9d-136) then
        tmp = i * (y * -j)
    else if (a <= 9d+73) then
        tmp = y * (x * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * -(x * a);
	double tmp;
	if (a <= -2.25e+27) {
		tmp = i * (a * b);
	} else if (a <= -33000.0) {
		tmp = t_1;
	} else if (a <= -8e-269) {
		tmp = t * (c * j);
	} else if (a <= 7.5e-200) {
		tmp = b * (z * -c);
	} else if (a <= 4.9e-136) {
		tmp = i * (y * -j);
	} else if (a <= 9e+73) {
		tmp = y * (x * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * -(x * a)
	tmp = 0
	if a <= -2.25e+27:
		tmp = i * (a * b)
	elif a <= -33000.0:
		tmp = t_1
	elif a <= -8e-269:
		tmp = t * (c * j)
	elif a <= 7.5e-200:
		tmp = b * (z * -c)
	elif a <= 4.9e-136:
		tmp = i * (y * -j)
	elif a <= 9e+73:
		tmp = y * (x * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(-Float64(x * a)))
	tmp = 0.0
	if (a <= -2.25e+27)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= -33000.0)
		tmp = t_1;
	elseif (a <= -8e-269)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 7.5e-200)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 4.9e-136)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 9e+73)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * -(x * a);
	tmp = 0.0;
	if (a <= -2.25e+27)
		tmp = i * (a * b);
	elseif (a <= -33000.0)
		tmp = t_1;
	elseif (a <= -8e-269)
		tmp = t * (c * j);
	elseif (a <= 7.5e-200)
		tmp = b * (z * -c);
	elseif (a <= 4.9e-136)
		tmp = i * (y * -j);
	elseif (a <= 9e+73)
		tmp = y * (x * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * (-N[(x * a), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[a, -2.25e+27], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -33000.0], t$95$1, If[LessEqual[a, -8e-269], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-200], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-136], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+73], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -2.25e27

   1. Initial program 73.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 73.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 73.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 78.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 64.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 64.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 64.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 64.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 37.1%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 41.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -2.25e27 < a < -33000 or 8.99999999999999969e73 < a

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 72.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 72.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 72.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 72.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 72.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 73.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 69.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 69.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 69.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around 0 58.8%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.8%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-rgt-neg-out 58.8%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 58.8%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   if -33000 < a < -7.9999999999999997e-269

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 44.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 44.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 44.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 42.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -7.9999999999999997e-269 < a < 7.49999999999999958e-200

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 56.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around 0 49.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \cdot b \]
   6. Step-by-step derivation

      1. neg-mul-1 49.4%

         \[\leadsto \color{blue}{\left(-c \cdot z\right)} \cdot b \]

      2. distribute-rgt-neg-in 49.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-z\right)\right)} \cdot b \]

   7. Simplified 49.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(-z\right)\right)} \cdot b \]

   if 7.49999999999999958e-200 < a < 4.9e-136

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 83.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 83.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 40.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 40.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 40.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 40.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 40.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]

   if 4.9e-136 < a < 8.99999999999999969e73

   1. Initial program 84.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 84.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 84.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 84.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 86.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 86.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 48.0%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 48.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 48.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 48.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 48.0%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 48.0%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 48.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 36.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{+27}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -33000:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-269}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-200}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-136}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \end{array} \]

Alternative 10: 42.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3100:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.02 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -3100.0)
     t_1
     (if (<= a -1.15e-272)
       (* t (* c j))
       (if (<= a 1.25e-199)
         (* b (* z (- c)))
         (if (<= a 2.02e-135) (* i (* y (- j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3100.0) {
		tmp = t_1;
	} else if (a <= -1.15e-272) {
		tmp = t * (c * j);
	} else if (a <= 1.25e-199) {
		tmp = b * (z * -c);
	} else if (a <= 2.02e-135) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-3100.0d0)) then
        tmp = t_1
    else if (a <= (-1.15d-272)) then
        tmp = t * (c * j)
    else if (a <= 1.25d-199) then
        tmp = b * (z * -c)
    else if (a <= 2.02d-135) then
        tmp = i * (y * -j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3100.0) {
		tmp = t_1;
	} else if (a <= -1.15e-272) {
		tmp = t * (c * j);
	} else if (a <= 1.25e-199) {
		tmp = b * (z * -c);
	} else if (a <= 2.02e-135) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3100.0:
		tmp = t_1
	elif a <= -1.15e-272:
		tmp = t * (c * j)
	elif a <= 1.25e-199:
		tmp = b * (z * -c)
	elif a <= 2.02e-135:
		tmp = i * (y * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3100.0)
		tmp = t_1;
	elseif (a <= -1.15e-272)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 1.25e-199)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (a <= 2.02e-135)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3100.0)
		tmp = t_1;
	elseif (a <= -1.15e-272)
		tmp = t * (c * j);
	elseif (a <= 1.25e-199)
		tmp = b * (z * -c);
	elseif (a <= 2.02e-135)
		tmp = i * (y * -j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3100.0], t$95$1, If[LessEqual[a, -1.15e-272], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e-199], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.02e-135], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3100 or 2.02000000000000013e-135 < a

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 62.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -3100 < a < -1.14999999999999994e-272

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 77.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 44.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 44.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 44.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 44.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 44.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 42.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -1.14999999999999994e-272 < a < 1.2499999999999999e-199

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 74.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 56.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around 0 49.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \cdot b \]
   6. Step-by-step derivation

      1. neg-mul-1 49.4%

         \[\leadsto \color{blue}{\left(-c \cdot z\right)} \cdot b \]

      2. distribute-rgt-neg-in 49.4%

         \[\leadsto \color{blue}{\left(c \cdot \left(-z\right)\right)} \cdot b \]

   7. Simplified 49.4%

      \[\leadsto \color{blue}{\left(c \cdot \left(-z\right)\right)} \cdot b \]

   if 1.2499999999999999e-199 < a < 2.02000000000000013e-135

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 83.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 83.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 40.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 40.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 40.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 40.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 40.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 40.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3100:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-272}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-199}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 2.02 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 11: 50.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -175000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 880000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -175000.0)
     t_2
     (if (<= a 1.15e-161)
       t_1
       (if (<= a 1.48e-90) (* i (* y (- j))) (if (<= a 880000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -175000.0) {
		tmp = t_2;
	} else if (a <= 1.15e-161) {
		tmp = t_1;
	} else if (a <= 1.48e-90) {
		tmp = i * (y * -j);
	} else if (a <= 880000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-175000.0d0)) then
        tmp = t_2
    else if (a <= 1.15d-161) then
        tmp = t_1
    else if (a <= 1.48d-90) then
        tmp = i * (y * -j)
    else if (a <= 880000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -175000.0) {
		tmp = t_2;
	} else if (a <= 1.15e-161) {
		tmp = t_1;
	} else if (a <= 1.48e-90) {
		tmp = i * (y * -j);
	} else if (a <= 880000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -175000.0:
		tmp = t_2
	elif a <= 1.15e-161:
		tmp = t_1
	elif a <= 1.48e-90:
		tmp = i * (y * -j)
	elif a <= 880000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -175000.0)
		tmp = t_2;
	elseif (a <= 1.15e-161)
		tmp = t_1;
	elseif (a <= 1.48e-90)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 880000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -175000.0)
		tmp = t_2;
	elseif (a <= 1.15e-161)
		tmp = t_1;
	elseif (a <= 1.48e-90)
		tmp = i * (y * -j);
	elseif (a <= 880000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -175000.0], t$95$2, If[LessEqual[a, 1.15e-161], t$95$1, If[LessEqual[a, 1.48e-90], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 880000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -175000 or 8.8e5 < a

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 76.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 69.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 69.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 69.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 69.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 69.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -175000 < a < 1.15e-161 or 1.4800000000000001e-90 < a < 8.8e5

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 78.4%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 79.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 79.5%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 79.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 79.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 79.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 79.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 56.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if 1.15e-161 < a < 1.4800000000000001e-90

   1. Initial program 76.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 76.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 80.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 49.6%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 49.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 49.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 49.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 49.6%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 49.6%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 49.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in i around inf 39.9%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -175000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-161}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.48 \cdot 10^{-90}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 880000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 12: 50.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -1550000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -1550000.0)
     t_1
     (if (<= a 3.4e-170)
       (* c (- (* t j) (* z b)))
       (if (<= a 1.75e-135)
         (* i (* y (- j)))
         (if (<= a 4.5e+15) (* t (- (* c j) (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1550000.0) {
		tmp = t_1;
	} else if (a <= 3.4e-170) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.75e-135) {
		tmp = i * (y * -j);
	} else if (a <= 4.5e+15) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-1550000.0d0)) then
        tmp = t_1
    else if (a <= 3.4d-170) then
        tmp = c * ((t * j) - (z * b))
    else if (a <= 1.75d-135) then
        tmp = i * (y * -j)
    else if (a <= 4.5d+15) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -1550000.0) {
		tmp = t_1;
	} else if (a <= 3.4e-170) {
		tmp = c * ((t * j) - (z * b));
	} else if (a <= 1.75e-135) {
		tmp = i * (y * -j);
	} else if (a <= 4.5e+15) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -1550000.0:
		tmp = t_1
	elif a <= 3.4e-170:
		tmp = c * ((t * j) - (z * b))
	elif a <= 1.75e-135:
		tmp = i * (y * -j)
	elif a <= 4.5e+15:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1550000.0)
		tmp = t_1;
	elseif (a <= 3.4e-170)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (a <= 1.75e-135)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 4.5e+15)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -1550000.0)
		tmp = t_1;
	elseif (a <= 3.4e-170)
		tmp = c * ((t * j) - (z * b));
	elseif (a <= 1.75e-135)
		tmp = i * (y * -j);
	elseif (a <= 4.5e+15)
		tmp = t * ((c * j) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1550000.0], t$95$1, If[LessEqual[a, 3.4e-170], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-135], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+15], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e6 or 4.5e15 < a

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 76.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 70.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 70.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 70.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 70.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   if -1.55e6 < a < 3.40000000000000013e-170

   1. Initial program 76.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 54.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if 3.40000000000000013e-170 < a < 1.7499999999999999e-135

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 42.3%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 42.3%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 42.3%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 42.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 42.3%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 42.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 42.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in i around inf 70.3%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(y \cdot j\right)\right)} \]

   if 1.7499999999999999e-135 < a < 4.5e15

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 83.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 83.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 83.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 86.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 42.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 42.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 42.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 42.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 42.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1550000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-170}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-135}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+15}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 13: 50.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -2.2e+51)
     t_2
     (if (<= t -1.65e-140)
       t_1
       (if (<= t -2.4e-217)
         (* a (- (* b i) (* x t)))
         (if (<= t 1.7e-101) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.2e+51) {
		tmp = t_2;
	} else if (t <= -1.65e-140) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 1.7e-101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-2.2d+51)) then
        tmp = t_2
    else if (t <= (-1.65d-140)) then
        tmp = t_1
    else if (t <= (-2.4d-217)) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= 1.7d-101) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.2e+51) {
		tmp = t_2;
	} else if (t <= -1.65e-140) {
		tmp = t_1;
	} else if (t <= -2.4e-217) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= 1.7e-101) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.2e+51:
		tmp = t_2
	elif t <= -1.65e-140:
		tmp = t_1
	elif t <= -2.4e-217:
		tmp = a * ((b * i) - (x * t))
	elif t <= 1.7e-101:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.2e+51)
		tmp = t_2;
	elseif (t <= -1.65e-140)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= 1.7e-101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.2e+51)
		tmp = t_2;
	elseif (t <= -1.65e-140)
		tmp = t_1;
	elseif (t <= -2.4e-217)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= 1.7e-101)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+51], t$95$2, If[LessEqual[t, -1.65e-140], t$95$1, If[LessEqual[t, -2.4e-217], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e-101], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.19999999999999992e51 or 1.69999999999999995e-101 < t

   1. Initial program 71.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 72.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 72.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 73.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 64.8%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 64.8%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 64.8%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 64.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.19999999999999992e51 < t < -1.64999999999999994e-140 or -2.3999999999999999e-217 < t < 1.69999999999999995e-101

   1. Initial program 82.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 84.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 84.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 84.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 54.7%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 54.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 54.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 54.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 54.7%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 54.7%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 54.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -1.64999999999999994e-140 < t < -2.3999999999999999e-217

   1. Initial program 84.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 84.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 84.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 84.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 84.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 84.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 62.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 62.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 62.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 62.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-217}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-101}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 14: 30.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.18 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* x a)))) (t_2 (* x (* y z))))
   (if (<= y -1.18e+111)
     t_2
     (if (<= y -2.7e-240)
       t_1
       (if (<= y 8e-65) (* i (* a b)) (if (<= y 4.6e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * -(x * a);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.18e+111) {
		tmp = t_2;
	} else if (y <= -2.7e-240) {
		tmp = t_1;
	} else if (y <= 8e-65) {
		tmp = i * (a * b);
	} else if (y <= 4.6e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -(x * a)
    t_2 = x * (y * z)
    if (y <= (-1.18d+111)) then
        tmp = t_2
    else if (y <= (-2.7d-240)) then
        tmp = t_1
    else if (y <= 8d-65) then
        tmp = i * (a * b)
    else if (y <= 4.6d+75) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * -(x * a);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.18e+111) {
		tmp = t_2;
	} else if (y <= -2.7e-240) {
		tmp = t_1;
	} else if (y <= 8e-65) {
		tmp = i * (a * b);
	} else if (y <= 4.6e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * -(x * a)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -1.18e+111:
		tmp = t_2
	elif y <= -2.7e-240:
		tmp = t_1
	elif y <= 8e-65:
		tmp = i * (a * b)
	elif y <= 4.6e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(-Float64(x * a)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.18e+111)
		tmp = t_2;
	elseif (y <= -2.7e-240)
		tmp = t_1;
	elseif (y <= 8e-65)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 4.6e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * -(x * a);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.18e+111)
		tmp = t_2;
	elseif (y <= -2.7e-240)
		tmp = t_1;
	elseif (y <= 8e-65)
		tmp = i * (a * b);
	elseif (y <= 4.6e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * (-N[(x * a), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.18e+111], t$95$2, If[LessEqual[y, -2.7e-240], t$95$1, If[LessEqual[y, 8e-65], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1799999999999999e111 or 4.5999999999999997e75 < y

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 61.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 61.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 66.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 47.7%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   6. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 47.7%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if -1.1799999999999999e111 < y < -2.70000000000000018e-240 or 7.99999999999999939e-65 < y < 4.5999999999999997e75

   1. Initial program 82.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 82.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 82.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 82.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 82.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 58.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 58.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 58.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 58.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 58.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around 0 39.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 39.4%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-rgt-neg-out 39.4%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 39.4%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   if -2.70000000000000018e-240 < y < 7.99999999999999939e-65

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 88.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 88.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 34.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 37.9%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+111}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-240}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-65}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 15: 30.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= y -5.5e+109)
     t_1
     (if (<= y -9.8e-241)
       (* a (* t (- x)))
       (if (<= y 2.3e-58)
         (* i (* a b))
         (if (<= y 4.2e+75) (* t (- (* x a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -5.5e+109) {
		tmp = t_1;
	} else if (y <= -9.8e-241) {
		tmp = a * (t * -x);
	} else if (y <= 2.3e-58) {
		tmp = i * (a * b);
	} else if (y <= 4.2e+75) {
		tmp = t * -(x * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (y <= (-5.5d+109)) then
        tmp = t_1
    else if (y <= (-9.8d-241)) then
        tmp = a * (t * -x)
    else if (y <= 2.3d-58) then
        tmp = i * (a * b)
    else if (y <= 4.2d+75) then
        tmp = t * -(x * a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -5.5e+109) {
		tmp = t_1;
	} else if (y <= -9.8e-241) {
		tmp = a * (t * -x);
	} else if (y <= 2.3e-58) {
		tmp = i * (a * b);
	} else if (y <= 4.2e+75) {
		tmp = t * -(x * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if y <= -5.5e+109:
		tmp = t_1
	elif y <= -9.8e-241:
		tmp = a * (t * -x)
	elif y <= 2.3e-58:
		tmp = i * (a * b)
	elif y <= 4.2e+75:
		tmp = t * -(x * a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -5.5e+109)
		tmp = t_1;
	elseif (y <= -9.8e-241)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (y <= 2.3e-58)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 4.2e+75)
		tmp = Float64(t * Float64(-Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -5.5e+109)
		tmp = t_1;
	elseif (y <= -9.8e-241)
		tmp = a * (t * -x);
	elseif (y <= 2.3e-58)
		tmp = i * (a * b);
	elseif (y <= 4.2e+75)
		tmp = t * -(x * a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+109], t$95$1, If[LessEqual[y, -9.8e-241], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-58], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+75], N[(t * (-N[(x * a), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4999999999999998e109 or 4.19999999999999997e75 < y

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 61.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 61.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 65.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 65.6%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 66.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 66.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 51.1%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 47.7%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   6. Step-by-step derivation

      1. *-commutative 47.7%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 47.7%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if -5.4999999999999998e109 < y < -9.7999999999999997e-241

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 55.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.1%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 55.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around 0 40.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 40.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 40.3%

         \[\leadsto -\color{blue}{\left(t \cdot x\right) \cdot a} \]

      3. distribute-rgt-neg-in 40.3%

         \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

   9. Simplified 40.3%

      \[\leadsto \color{blue}{\left(t \cdot x\right) \cdot \left(-a\right)} \]

   if -9.7999999999999997e-241 < y < 2.2999999999999999e-58

   1. Initial program 88.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 88.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 88.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 88.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 88.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 52.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 52.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 34.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 37.9%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 2.2999999999999999e-58 < y < 4.19999999999999997e75

   1. Initial program 90.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 90.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 90.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 90.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 90.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 90.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 49.7%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 49.7%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 49.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 49.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around 0 37.4%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 37.4%

         \[\leadsto t \cdot \color{blue}{\left(-a \cdot x\right)} \]

      2. distribute-rgt-neg-out 37.4%

         \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]

   9. Simplified 37.4%

      \[\leadsto t \cdot \color{blue}{\left(a \cdot \left(-x\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-241}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \left(-x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 16: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -9 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= j -9e-50)
     t_1
     (if (<= j -7.8e-304)
       (* y (* x z))
       (if (<= j 1.45e+88) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -9e-50) {
		tmp = t_1;
	} else if (j <= -7.8e-304) {
		tmp = y * (x * z);
	} else if (j <= 1.45e+88) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (j <= (-9d-50)) then
        tmp = t_1
    else if (j <= (-7.8d-304)) then
        tmp = y * (x * z)
    else if (j <= 1.45d+88) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -9e-50) {
		tmp = t_1;
	} else if (j <= -7.8e-304) {
		tmp = y * (x * z);
	} else if (j <= 1.45e+88) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if j <= -9e-50:
		tmp = t_1
	elif j <= -7.8e-304:
		tmp = y * (x * z)
	elif j <= 1.45e+88:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (j <= -9e-50)
		tmp = t_1;
	elseif (j <= -7.8e-304)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.45e+88)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (j <= -9e-50)
		tmp = t_1;
	elseif (j <= -7.8e-304)
		tmp = y * (x * z);
	elseif (j <= 1.45e+88)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -9e-50], t$95$1, If[LessEqual[j, -7.8e-304], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e+88], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.99999999999999924e-50 or 1.45e88 < j

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 56.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 56.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 56.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 56.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 40.2%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -8.99999999999999924e-50 < j < -7.79999999999999949e-304

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 73.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 73.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 45.2%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 45.2%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 45.2%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 45.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 45.2%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 45.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 45.2%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 37.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if -7.79999999999999949e-304 < j < 1.45e88

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 55.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 35.2%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 37.3%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{+88}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 17: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -14500000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -14500000.0)
   (* i (* a b))
   (if (<= a 2.6e-51)
     (* t (* c j))
     (if (<= a 6e+58) (* y (* x z)) (* b (* a i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -14500000.0) {
		tmp = i * (a * b);
	} else if (a <= 2.6e-51) {
		tmp = t * (c * j);
	} else if (a <= 6e+58) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-14500000.0d0)) then
        tmp = i * (a * b)
    else if (a <= 2.6d-51) then
        tmp = t * (c * j)
    else if (a <= 6d+58) then
        tmp = y * (x * z)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -14500000.0) {
		tmp = i * (a * b);
	} else if (a <= 2.6e-51) {
		tmp = t * (c * j);
	} else if (a <= 6e+58) {
		tmp = y * (x * z);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -14500000.0:
		tmp = i * (a * b)
	elif a <= 2.6e-51:
		tmp = t * (c * j)
	elif a <= 6e+58:
		tmp = y * (x * z)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -14500000.0)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 2.6e-51)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 6e+58)
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -14500000.0)
		tmp = i * (a * b);
	elseif (a <= 2.6e-51)
		tmp = t * (c * j);
	elseif (a <= 6e+58)
		tmp = y * (x * z);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -14500000.0], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e-51], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+58], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.45e7

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 75.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 75.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 79.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 79.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 79.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 65.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 65.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 65.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 65.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 65.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 34.3%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 38.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.45e7 < a < 2.6e-51

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 76.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 76.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 77.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 78.6%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 78.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 39.0%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 39.0%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 39.0%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 39.0%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 39.0%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 32.6%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if 2.6e-51 < a < 6.0000000000000005e58

   1. Initial program 86.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 86.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 86.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 86.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 86.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 86.2%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in y around inf 55.5%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]
   5. Step-by-step derivation

      1. +-commutative 55.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \cdot y \]

      2. *-commutative 55.5%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + z \cdot x\right)} \]

      3. +-commutative 55.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right)} \]

      4. mul-1-neg 55.5%

         \[\leadsto y \cdot \left(z \cdot x + \color{blue}{\left(-i \cdot j\right)}\right) \]

      5. unsub-neg 55.5%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x - i \cdot j\right)} \]

   6. Simplified 55.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around inf 50.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 6.0000000000000005e58 < a

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 53.7%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   5. Taylor expanded in a around inf 48.1%

      \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -14500000:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 18: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -5 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= j -5e-50)
     t_1
     (if (<= j -6e-298) (* x (* y z)) (if (<= j 1.3e+85) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -5e-50) {
		tmp = t_1;
	} else if (j <= -6e-298) {
		tmp = x * (y * z);
	} else if (j <= 1.3e+85) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (j <= (-5d-50)) then
        tmp = t_1
    else if (j <= (-6d-298)) then
        tmp = x * (y * z)
    else if (j <= 1.3d+85) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -5e-50) {
		tmp = t_1;
	} else if (j <= -6e-298) {
		tmp = x * (y * z);
	} else if (j <= 1.3e+85) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if j <= -5e-50:
		tmp = t_1
	elif j <= -6e-298:
		tmp = x * (y * z)
	elif j <= 1.3e+85:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (j <= -5e-50)
		tmp = t_1;
	elseif (j <= -6e-298)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 1.3e+85)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (j <= -5e-50)
		tmp = t_1;
	elseif (j <= -6e-298)
		tmp = x * (y * z);
	elseif (j <= 1.3e+85)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5e-50], t$95$1, If[LessEqual[j, -6e-298], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e+85], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -4.99999999999999968e-50 or 1.30000000000000005e85 < j

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.6%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 81.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 81.5%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 81.5%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 56.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 56.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 56.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 56.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 40.2%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -4.99999999999999968e-50 < j < -5.9999999999999999e-298

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 73.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 73.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 73.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 73.9%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 75.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 75.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in x around inf 66.5%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   5. Taylor expanded in y around inf 41.9%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]
   6. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   7. Simplified 41.9%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

   if -5.9999999999999999e-298 < j < 1.30000000000000005e85

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 76.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 76.3%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 76.3%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 55.3%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 55.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.3%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.3%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 55.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 35.2%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 37.3%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{+85}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 19: 29.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{-28} \lor \neg \left(j \leq 6.5 \cdot 10^{+81}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3.2e-28) (not (<= j 6.5e+81))) (* t (* c j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.2e-28) || !(j <= 6.5e+81)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-3.2d-28)) .or. (.not. (j <= 6.5d+81))) then
        tmp = t * (c * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3.2e-28) || !(j <= 6.5e+81)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3.2e-28) or not (j <= 6.5e+81):
		tmp = t * (c * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3.2e-28) || !(j <= 6.5e+81))
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -3.2e-28) || ~((j <= 6.5e+81)))
		tmp = t * (c * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3.2e-28], N[Not[LessEqual[j, 6.5e+81]], $MachinePrecision]], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.19999999999999982e-28 or 6.4999999999999996e81 < j

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 79.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 79.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 81.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 81.8%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 81.8%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in t around inf 56.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 56.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 56.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 56.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   6. Simplified 56.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   7. Taylor expanded in c around inf 41.8%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -3.19999999999999982e-28 < j < 6.4999999999999996e81

   1. Initial program 74.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 74.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 74.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 75.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. sub-neg 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. +-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. *-commutative 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      9. distribute-rgt-neg-in 75.2%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      10. fma-def 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      11. *-commutative 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      12. distribute-rgt-neg-in 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      13. sub-neg 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      14. distribute-neg-in 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

      15. unsub-neg 75.9%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

   3. Simplified 76.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

   4. Taylor expanded in a around inf 51.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
   5. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 51.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 51.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   7. Taylor expanded in i around inf 30.4%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

   8. Taylor expanded in a around 0 32.9%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{-28} \lor \neg \left(j \leq 6.5 \cdot 10^{+81}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 20: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. sub-neg 76.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-+l+ 76.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   3. fma-def 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   4. +-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   5. fma-def 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   6. sub-neg 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   7. +-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   8. *-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   9. distribute-rgt-neg-in 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   10. fma-def 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   11. *-commutative 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   12. distribute-rgt-neg-in 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

   13. sub-neg 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

   14. distribute-neg-in 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

   15. unsub-neg 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

3. Simplified 78.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

4. Taylor expanded in a around inf 44.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
5. Step-by-step derivation

   1. +-commutative 44.8%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 44.8%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 44.8%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

6. Simplified 44.8%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

7. Taylor expanded in i around inf 25.2%

   \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Final simplification 25.2%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 21: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ i \cdot \left(a \cdot b\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* i (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return i * (a * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = i * (a * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return i * (a * b);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return i * (a * b)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(i * Float64(a * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = i * (a * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.2%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. sub-neg 76.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. associate-+l+ 76.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   3. fma-def 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

   4. +-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   5. fma-def 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

   6. sub-neg 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{c \cdot t + \left(-i \cdot y\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   7. +-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\left(-i \cdot y\right) + c \cdot t}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   8. *-commutative 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \left(-\color{blue}{y \cdot i}\right) + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   9. distribute-rgt-neg-in 77.8%

      \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{y \cdot \left(-i\right)} + c \cdot t, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   10. fma-def 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{\mathsf{fma}\left(y, -i, c \cdot t\right)}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   11. *-commutative 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, \color{blue}{t \cdot c}\right), -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

   12. distribute-rgt-neg-in 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

   13. sub-neg 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

   14. distribute-neg-in 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) + \left(-\left(-i \cdot a\right)\right)\right)}\right)\right) \]

   15. unsub-neg 78.2%

       \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \color{blue}{\left(\left(-c \cdot z\right) - \left(-i \cdot a\right)\right)}\right)\right) \]

3. Simplified 78.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \mathsf{fma}\left(y, -i, t \cdot c\right), b \cdot \mathsf{fma}\left(c, -z, a \cdot i\right)\right)\right)} \]

4. Taylor expanded in a around inf 44.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]
5. Step-by-step derivation

   1. +-commutative 44.8%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 44.8%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 44.8%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

6. Simplified 44.8%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

7. Taylor expanded in i around inf 25.2%

   \[\leadsto a \cdot \color{blue}{\left(i \cdot b\right)} \]

8. Taylor expanded in a around 0 26.7%

   \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

9. Final simplification 26.7%

   \[\leadsto i \cdot \left(a \cdot b\right) \]

Developer target: 68.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))