Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 72.9% → 82.0%

Time: 31.0s

Alternatives: 22

Speedup: 0.5×

• 57.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 72.9% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 82.0% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (pow (cbrt (* i (fma b t (* y (- j))))) 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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = pow(cbrt((i * fma(b, t, (y * -j)))), 3.0);
	}
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = cbrt(Float64(i * fma(b, t, Float64(y * Float64(-j))))) ^ 3.0;
	end
	return 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[Power[N[Power[N[(i * N[(b * t + N[(y * (-j)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 95.3%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 6.5%

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

      3. *-commutative 6.5%

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

      4. sub-neg 6.5%

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

      5. sub-neg 6.5%

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

      6. *-commutative 6.5%

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

   3. Simplified 6.5%

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

   4. Taylor expanded in y around 0 19.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 19.6%

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

      2. neg-mul-1 19.6%

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

      3. fma-neg 21.7%

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

      4. distribute-rgt-neg-in 21.7%

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

      5. neg-sub0 21.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 21.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 21.7%

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

      8. +-commutative 21.7%

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

      9. sub-neg 21.7%

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

   6. Simplified 21.7%

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

   7. Taylor expanded in i around inf 50.8%

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

      1. add-cube-cbrt 50.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \cdot \sqrt[3]{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}\right) \cdot \sqrt[3]{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}} \]

      2. pow3 50.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)}\right)}^{3}} \]

      3. +-commutative 50.8%

         \[\leadsto {\left(\sqrt[3]{i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)}}\right)}^{3} \]

      4. fma-def 53.0%

         \[\leadsto {\left(\sqrt[3]{i \cdot \color{blue}{\mathsf{fma}\left(b, t, -1 \cdot \left(j \cdot y\right)\right)}}\right)}^{3} \]

      5. mul-1-neg 53.0%

         \[\leadsto {\left(\sqrt[3]{i \cdot \mathsf{fma}\left(b, t, \color{blue}{-j \cdot y}\right)}\right)}^{3} \]

   9. Applied egg-rr 53.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{i \cdot \mathsf{fma}\left(b, t, -j \cdot y\right)}\right)}^{3}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

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

Alternative 2: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 95.3%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 6.5%

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

      3. *-commutative 6.5%

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

      4. sub-neg 6.5%

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

      5. sub-neg 6.5%

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

      6. *-commutative 6.5%

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

   3. Simplified 6.5%

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

   5. Applied egg-rr 2.2%

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

      1. count-2 2.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 2.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in t around inf 35.0%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 35.0%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(-a \cdot x\right)} + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      2. associate--l+ 35.0%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a \cdot x\right) + \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} \]

      3. distribute-lft-in 28.5%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      4. distribute-lft1-in 28.5%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot \left(b \cdot i\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      5. metadata-eval 28.5%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(\color{blue}{0} \cdot \left(b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. *-commutative 28.5%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(0 \cdot \color{blue}{\left(i \cdot b\right)}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. mul0-lft 41.6%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      8. metadata-eval 41.6%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(\color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. neg-sub0 41.6%

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

      10. mul-1-neg 41.6%

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

      11. *-commutative 41.6%

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

      12. remove-double-neg 41.6%

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

      13. *-commutative 41.6%

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

   10. Simplified 52.4%

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

4. Final simplification 87.6%

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

Alternative 3: 56.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 - a \cdot \left(x \cdot t\right)\\ t_3 := x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9.4 \cdot 10^{-206}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (- t_1 (* a (* x t))))
        (t_3 (+ (* x (* y z)) (* b (- (* t i) (* z c))))))
   (if (<= j -3.5e-44)
     t_2
     (if (<= j -9.4e-206)
       t_3
       (if (<= j -1.05e-298)
         (* x (- (* y z) (* t a)))
         (if (<= j 4.1e-53)
           (* t (- (* b i) (* x a)))
           (if (<= j 1.2e+148) t_2 (if (<= j 5.4e+210) t_3 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.5e-44) {
		tmp = t_2;
	} else if (j <= -9.4e-206) {
		tmp = t_3;
	} else if (j <= -1.05e-298) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 4.1e-53) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.2e+148) {
		tmp = t_2;
	} else if (j <= 5.4e+210) {
		tmp = t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 - (a * (x * t))
    t_3 = (x * (y * z)) + (b * ((t * i) - (z * c)))
    if (j <= (-3.5d-44)) then
        tmp = t_2
    else if (j <= (-9.4d-206)) then
        tmp = t_3
    else if (j <= (-1.05d-298)) then
        tmp = x * ((y * z) - (t * a))
    else if (j <= 4.1d-53) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 1.2d+148) then
        tmp = t_2
    else if (j <= 5.4d+210) then
        tmp = t_3
    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 = j * ((a * c) - (y * i));
	double t_2 = t_1 - (a * (x * t));
	double t_3 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.5e-44) {
		tmp = t_2;
	} else if (j <= -9.4e-206) {
		tmp = t_3;
	} else if (j <= -1.05e-298) {
		tmp = x * ((y * z) - (t * a));
	} else if (j <= 4.1e-53) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 1.2e+148) {
		tmp = t_2;
	} else if (j <= 5.4e+210) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 - (a * (x * t))
	t_3 = (x * (y * z)) + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -3.5e-44:
		tmp = t_2
	elif j <= -9.4e-206:
		tmp = t_3
	elif j <= -1.05e-298:
		tmp = x * ((y * z) - (t * a))
	elif j <= 4.1e-53:
		tmp = t * ((b * i) - (x * a))
	elif j <= 1.2e+148:
		tmp = t_2
	elif j <= 5.4e+210:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 - Float64(a * Float64(x * t)))
	t_3 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -3.5e-44)
		tmp = t_2;
	elseif (j <= -9.4e-206)
		tmp = t_3;
	elseif (j <= -1.05e-298)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (j <= 4.1e-53)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 1.2e+148)
		tmp = t_2;
	elseif (j <= 5.4e+210)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 - (a * (x * t));
	t_3 = (x * (y * z)) + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -3.5e-44)
		tmp = t_2;
	elseif (j <= -9.4e-206)
		tmp = t_3;
	elseif (j <= -1.05e-298)
		tmp = x * ((y * z) - (t * a));
	elseif (j <= 4.1e-53)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 1.2e+148)
		tmp = t_2;
	elseif (j <= 5.4e+210)
		tmp = t_3;
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.5e-44], t$95$2, If[LessEqual[j, -9.4e-206], t$95$3, If[LessEqual[j, -1.05e-298], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.1e-53], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e+148], t$95$2, If[LessEqual[j, 5.4e+210], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -3.4999999999999998e-44 or 4.1000000000000001e-53 < j < 1.19999999999999997e148

   1. Initial program 81.8%

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

      1. +-commutative 81.8%

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

      2. fma-def 84.5%

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

      3. *-commutative 84.5%

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

      4. sub-neg 84.5%

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

      5. sub-neg 84.5%

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

      6. *-commutative 84.5%

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

   3. Simplified 84.5%

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

   4. Taylor expanded in y around 0 77.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 77.0%

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

      2. neg-mul-1 77.0%

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

      3. fma-neg 77.0%

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

      4. distribute-rgt-neg-in 77.0%

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

      5. neg-sub0 77.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 77.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 77.0%

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

      8. +-commutative 77.0%

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

      9. sub-neg 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in b around 0 69.9%

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

      1. +-commutative 69.9%

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

      2. mul-1-neg 69.9%

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

      3. unsub-neg 69.9%

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

      4. sub-neg 69.9%

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

      5. *-commutative 69.9%

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

      6. sub-neg 69.9%

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

   9. Simplified 69.9%

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

   if -3.4999999999999998e-44 < j < -9.3999999999999997e-206 or 1.19999999999999997e148 < j < 5.3999999999999998e210

   1. Initial program 82.4%

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

   2. Taylor expanded in j around 0 77.1%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -9.3999999999999997e-206 < j < -1.05000000000000002e-298

   1. Initial program 56.4%

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

      1. +-commutative 56.4%

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

      2. fma-def 56.4%

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

      3. *-commutative 56.4%

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

      4. sub-neg 56.4%

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

      5. sub-neg 56.4%

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

      6. *-commutative 56.4%

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

   3. Simplified 56.4%

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

   5. Applied egg-rr 50.4%

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

      1. count-2 50.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 50.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in x around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

   10. Simplified 73.5%

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

   if -1.05000000000000002e-298 < j < 4.1000000000000001e-53

   1. Initial program 77.8%

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

      1. +-commutative 77.8%

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

      2. fma-def 77.8%

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

      3. *-commutative 77.8%

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

      4. sub-neg 77.8%

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

      5. sub-neg 77.8%

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

      6. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Applied egg-rr 61.1%

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

      1. count-2 61.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 49.8%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(-a \cdot x\right)} + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      2. associate--l+ 49.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a \cdot x\right) + \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} \]

      3. distribute-lft-in 48.0%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      4. distribute-lft1-in 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot \left(b \cdot i\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      5. metadata-eval 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(\color{blue}{0} \cdot \left(b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(0 \cdot \color{blue}{\left(i \cdot b\right)}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. mul0-lft 61.1%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      8. metadata-eval 61.1%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(\color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. neg-sub0 61.1%

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

      10. mul-1-neg 61.1%

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

      11. *-commutative 61.1%

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

      12. remove-double-neg 61.1%

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

      13. *-commutative 61.1%

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

   10. Simplified 64.8%

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

   if 5.3999999999999998e210 < j

   1. Initial program 68.2%

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

      1. +-commutative 68.2%

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

      2. fma-def 68.2%

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

      3. *-commutative 68.2%

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

      4. sub-neg 68.2%

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

      5. sub-neg 68.2%

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

      6. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   4. Taylor expanded in y around 0 63.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 63.6%

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

      2. neg-mul-1 63.6%

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

      3. fma-neg 63.6%

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

      4. distribute-rgt-neg-in 63.6%

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

      5. neg-sub0 63.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 63.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 63.6%

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

      8. +-commutative 63.6%

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

      9. sub-neg 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in j around inf 82.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   8. Step-by-step derivation

      1. sub-neg 82.2%

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

      2. *-commutative 82.2%

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

      3. sub-neg 82.2%

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

   9. Simplified 82.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.5 \cdot 10^{-44}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq -9.4 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-298}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.1 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{+148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 4: 67.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-35} \lor \neg \left(y \leq 2.7 \cdot 10^{-44}\right):\\ \;\;\;\;t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) - c \cdot \left(z \cdot b - a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= y -1.3e+229)
     (* y (- (* x z) (* i j)))
     (if (<= y -1.7e+166)
       t_1
       (if (or (<= y -7.5e-35) (not (<= y 2.7e-44)))
         (+ t_1 (* j (- (* a c) (* y i))))
         (- (* t (- (* b i) (* x a))) (* c (- (* z b) (* a j)))))))))

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 (y <= -1.3e+229) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.7e+166) {
		tmp = t_1;
	} else if ((y <= -7.5e-35) || !(y <= 2.7e-44)) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = (t * ((b * i) - (x * a))) - (c * ((z * b) - (a * j)));
	}
	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 (y <= (-1.3d+229)) then
        tmp = y * ((x * z) - (i * j))
    else if (y <= (-1.7d+166)) then
        tmp = t_1
    else if ((y <= (-7.5d-35)) .or. (.not. (y <= 2.7d-44))) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = (t * ((b * i) - (x * a))) - (c * ((z * b) - (a * j)))
    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 (y <= -1.3e+229) {
		tmp = y * ((x * z) - (i * j));
	} else if (y <= -1.7e+166) {
		tmp = t_1;
	} else if ((y <= -7.5e-35) || !(y <= 2.7e-44)) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = (t * ((b * i) - (x * a))) - (c * ((z * b) - (a * j)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if y <= -1.3e+229:
		tmp = y * ((x * z) - (i * j))
	elif y <= -1.7e+166:
		tmp = t_1
	elif (y <= -7.5e-35) or not (y <= 2.7e-44):
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = (t * ((b * i) - (x * a))) - (c * ((z * b) - (a * j)))
	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 (y <= -1.3e+229)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (y <= -1.7e+166)
		tmp = t_1;
	elseif ((y <= -7.5e-35) || !(y <= 2.7e-44))
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(Float64(t * Float64(Float64(b * i) - Float64(x * a))) - Float64(c * Float64(Float64(z * b) - Float64(a * j))));
	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 (y <= -1.3e+229)
		tmp = y * ((x * z) - (i * j));
	elseif (y <= -1.7e+166)
		tmp = t_1;
	elseif ((y <= -7.5e-35) || ~((y <= 2.7e-44)))
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = (t * ((b * i) - (x * a))) - (c * ((z * b) - (a * j)));
	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[y, -1.3e+229], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+166], t$95$1, If[Or[LessEqual[y, -7.5e-35], N[Not[LessEqual[y, 2.7e-44]], $MachinePrecision]], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(N[(z * b), $MachinePrecision] - N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3e229

   1. Initial program 64.9%

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

   2. Taylor expanded in y around inf 94.1%

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

      1. +-commutative 94.1%

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

      2. mul-1-neg 94.1%

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

      3. unsub-neg 94.1%

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

      4. *-commutative 94.1%

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

      5. *-commutative 94.1%

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

   4. Simplified 94.1%

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

   if -1.3e229 < y < -1.7e166

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. fma-def 68.4%

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

      3. *-commutative 68.4%

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

      4. sub-neg 68.4%

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

      5. sub-neg 68.4%

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

      6. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   5. Applied egg-rr 47.4%

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

      1. count-2 47.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 47.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in x around inf 84.7%

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

      1. *-commutative 84.7%

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

      2. *-commutative 84.7%

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

   10. Simplified 84.7%

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

   if -1.7e166 < y < -7.5e-35 or 2.6999999999999999e-44 < y

   1. Initial program 76.1%

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

   2. Taylor expanded in b around 0 75.2%

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

   if -7.5e-35 < y < 2.6999999999999999e-44

   1. Initial program 84.7%

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

      1. +-commutative 84.7%

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

      2. fma-def 85.6%

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

      3. *-commutative 85.6%

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

      4. sub-neg 85.6%

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

      5. sub-neg 85.6%

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

      6. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   4. Taylor expanded in y around 0 83.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 83.0%

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

      2. neg-mul-1 83.0%

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

      3. fma-neg 83.0%

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

      4. distribute-rgt-neg-in 83.0%

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

      5. neg-sub0 83.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 83.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 83.0%

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

      8. +-commutative 83.0%

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

      9. sub-neg 83.0%

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

   6. Simplified 83.0%

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

      1. fma-udef 82.1%

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

      2. *-commutative 82.1%

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

      3. *-commutative 82.1%

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

      4. *-commutative 82.1%

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

   8. Applied egg-rr 82.1%

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

   9. Taylor expanded in y around 0 78.3%

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

       1. associate-+r+ 78.3%

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

       2. mul-1-neg 78.3%

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

       3. distribute-rgt-neg-in 78.3%

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

       4. mul-1-neg 78.3%

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

       5. distribute-lft-in 79.2%

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

       6. fma-def 79.2%

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

       7. +-commutative 79.2%

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

       8. mul-1-neg 79.2%

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

       9. unsub-neg 79.2%

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

       10. *-commutative 79.2%

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

   11. Simplified 79.2%

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

   12. Taylor expanded in c around -inf 81.1%

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

       1. +-commutative 81.1%

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

       2. associate-+l+ 81.1%

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

       3. mul-1-neg 81.1%

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

       4. *-commutative 81.1%

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

       5. distribute-rgt-neg-in 81.1%

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

       6. +-commutative 81.1%

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

       7. mul-1-neg 81.1%

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

       8. unsub-neg 81.1%

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

       9. *-commutative 81.1%

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

       10. *-commutative 81.1%

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

       11. associate-*r* 80.3%

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

       12. mul-1-neg 80.3%

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

       13. *-commutative 80.3%

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

       14. associate-*r* 79.4%

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

       15. distribute-lft-neg-out 79.4%

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

       16. *-commutative 79.4%

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

       17. distribute-lft-in 79.4%

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

       18. unsub-neg 79.4%

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

   14. Simplified 79.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-35} \lor \neg \left(y \leq 2.7 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right) - c \cdot \left(z \cdot b - a \cdot j\right)\\ \end{array} \]

Alternative 5: 54.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.35 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.18 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* a (* x t))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.35e+128)
     t_2
     (if (<= i -2.2e-147)
       t_1
       (if (<= i 4.1e-140)
         (* x (- (* y z) (* t a)))
         (if (<= i 1.18e-58)
           (* c (- (* a j) (* z b)))
           (if (<= i 2.4e+61) 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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.35e+128) {
		tmp = t_2;
	} else if (i <= -2.2e-147) {
		tmp = t_1;
	} else if (i <= 4.1e-140) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.18e-58) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.4e+61) {
		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 = (j * ((a * c) - (y * i))) - (a * (x * t))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.35d+128)) then
        tmp = t_2
    else if (i <= (-2.2d-147)) then
        tmp = t_1
    else if (i <= 4.1d-140) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 1.18d-58) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 2.4d+61) 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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.35e+128) {
		tmp = t_2;
	} else if (i <= -2.2e-147) {
		tmp = t_1;
	} else if (i <= 4.1e-140) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 1.18e-58) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 2.4e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (a * (x * t))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.35e+128:
		tmp = t_2
	elif i <= -2.2e-147:
		tmp = t_1
	elif i <= 4.1e-140:
		tmp = x * ((y * z) - (t * a))
	elif i <= 1.18e-58:
		tmp = c * ((a * j) - (z * b))
	elif i <= 2.4e+61:
		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(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.35e+128)
		tmp = t_2;
	elseif (i <= -2.2e-147)
		tmp = t_1;
	elseif (i <= 4.1e-140)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 1.18e-58)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 2.4e+61)
		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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.35e+128)
		tmp = t_2;
	elseif (i <= -2.2e-147)
		tmp = t_1;
	elseif (i <= 4.1e-140)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 1.18e-58)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 2.4e+61)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.35e+128], t$95$2, If[LessEqual[i, -2.2e-147], t$95$1, If[LessEqual[i, 4.1e-140], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.18e-58], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e+61], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.35000000000000001e128 or 2.3999999999999999e61 < i

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. fma-def 69.3%

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

      3. *-commutative 69.3%

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

      4. sub-neg 69.3%

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

      5. sub-neg 69.3%

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

      6. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in y around 0 68.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.3%

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

      2. neg-mul-1 68.3%

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

      3. fma-neg 69.3%

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

      4. distribute-rgt-neg-in 69.3%

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

      5. neg-sub0 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 69.3%

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

      8. +-commutative 69.3%

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

      9. sub-neg 69.3%

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

   6. Simplified 69.3%

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

      1. fma-udef 66.2%

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

      2. *-commutative 66.2%

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

      3. *-commutative 66.2%

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

      4. *-commutative 66.2%

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

   8. Applied egg-rr 66.2%

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

   9. Taylor expanded in i around inf 68.2%

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

       1. neg-mul-1 68.2%

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

       2. +-commutative 68.2%

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

       3. unsub-neg 68.2%

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

   11. Simplified 68.2%

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

   if -1.35000000000000001e128 < i < -2.2000000000000001e-147 or 1.17999999999999996e-58 < i < 2.3999999999999999e61

   1. Initial program 82.5%

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

      1. +-commutative 82.5%

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

      2. fma-def 82.5%

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

      3. *-commutative 82.5%

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

      4. sub-neg 82.5%

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

      5. sub-neg 82.5%

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

      6. *-commutative 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in y around 0 78.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 78.1%

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

      2. neg-mul-1 78.1%

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

      3. fma-neg 78.1%

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

      4. distribute-rgt-neg-in 78.1%

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

      5. neg-sub0 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 78.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 78.1%

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

      8. +-commutative 78.1%

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

      9. sub-neg 78.1%

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

   6. Simplified 78.1%

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

   7. Taylor expanded in b around 0 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. sub-neg 71.0%

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

      5. *-commutative 71.0%

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

      6. sub-neg 71.0%

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

   9. Simplified 71.0%

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

   if -2.2000000000000001e-147 < i < 4.1000000000000001e-140

   1. Initial program 83.8%

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

      1. +-commutative 83.8%

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

      2. fma-def 85.6%

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

      3. *-commutative 85.6%

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

      4. sub-neg 85.6%

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

      5. sub-neg 85.6%

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

      6. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Applied egg-rr 76.6%

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

      1. count-2 76.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 76.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in x around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. *-commutative 61.6%

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

   10. Simplified 61.6%

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

   if 4.1000000000000001e-140 < i < 1.17999999999999996e-58

   1. Initial program 99.8%

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

   2. Taylor expanded in c around inf 58.7%

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

      1. *-commutative 58.7%

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

   4. Simplified 58.7%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{+128}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.1 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.18 \cdot 10^{-58}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 6: 50.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -0.00115:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-38}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -1.5e+31)
     t_2
     (if (<= a -0.00115)
       t_1
       (if (<= a -9.5e-38)
         (* j (- (* y i)))
         (if (<= a -7e-46)
           (* z (* x y))
           (if (<= a 2.2e-226)
             t_1
             (if (<= a 7.2e-169)
               (* i (* y (- j)))
               (if (<= a 7e-45) 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 * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+31) {
		tmp = t_2;
	} else if (a <= -0.00115) {
		tmp = t_1;
	} else if (a <= -9.5e-38) {
		tmp = j * -(y * i);
	} else if (a <= -7e-46) {
		tmp = z * (x * y);
	} else if (a <= 2.2e-226) {
		tmp = t_1;
	} else if (a <= 7.2e-169) {
		tmp = i * (y * -j);
	} else if (a <= 7e-45) {
		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 * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-1.5d+31)) then
        tmp = t_2
    else if (a <= (-0.00115d0)) then
        tmp = t_1
    else if (a <= (-9.5d-38)) then
        tmp = j * -(y * i)
    else if (a <= (-7d-46)) then
        tmp = z * (x * y)
    else if (a <= 2.2d-226) then
        tmp = t_1
    else if (a <= 7.2d-169) then
        tmp = i * (y * -j)
    else if (a <= 7d-45) 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 * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -1.5e+31) {
		tmp = t_2;
	} else if (a <= -0.00115) {
		tmp = t_1;
	} else if (a <= -9.5e-38) {
		tmp = j * -(y * i);
	} else if (a <= -7e-46) {
		tmp = z * (x * y);
	} else if (a <= 2.2e-226) {
		tmp = t_1;
	} else if (a <= 7.2e-169) {
		tmp = i * (y * -j);
	} else if (a <= 7e-45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -1.5e+31:
		tmp = t_2
	elif a <= -0.00115:
		tmp = t_1
	elif a <= -9.5e-38:
		tmp = j * -(y * i)
	elif a <= -7e-46:
		tmp = z * (x * y)
	elif a <= 2.2e-226:
		tmp = t_1
	elif a <= 7.2e-169:
		tmp = i * (y * -j)
	elif a <= 7e-45:
		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(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -1.5e+31)
		tmp = t_2;
	elseif (a <= -0.00115)
		tmp = t_1;
	elseif (a <= -9.5e-38)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (a <= -7e-46)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 2.2e-226)
		tmp = t_1;
	elseif (a <= 7.2e-169)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 7e-45)
		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 * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -1.5e+31)
		tmp = t_2;
	elseif (a <= -0.00115)
		tmp = t_1;
	elseif (a <= -9.5e-38)
		tmp = j * -(y * i);
	elseif (a <= -7e-46)
		tmp = z * (x * y);
	elseif (a <= 2.2e-226)
		tmp = t_1;
	elseif (a <= 7.2e-169)
		tmp = i * (y * -j);
	elseif (a <= 7e-45)
		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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e+31], t$95$2, If[LessEqual[a, -0.00115], t$95$1, If[LessEqual[a, -9.5e-38], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, -7e-46], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.2e-226], t$95$1, If[LessEqual[a, 7.2e-169], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-45], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.49999999999999995e31 or 7e-45 < a

   1. Initial program 71.9%

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

   2. Taylor expanded in a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

   4. Simplified 63.4%

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

   if -1.49999999999999995e31 < a < -0.00115 or -7.0000000000000004e-46 < a < 2.2e-226 or 7.20000000000000003e-169 < a < 7e-45

   1. Initial program 85.3%

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

   2. Taylor expanded in b around inf 51.0%

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

   if -0.00115 < a < -9.5000000000000009e-38

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-def 99.3%

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

      3. *-commutative 99.3%

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

      4. sub-neg 99.3%

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

      5. sub-neg 99.3%

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

      6. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 72.8%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 72.8%

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

      2. neg-mul-1 72.8%

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

      3. fma-neg 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

      5. neg-sub0 72.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 72.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 72.8%

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

      8. +-commutative 72.8%

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

      9. sub-neg 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in y around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. *-commutative 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

      4. *-commutative 45.9%

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

   9. Simplified 45.9%

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

   10. Taylor expanded in y around 0 45.9%

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

       1. associate-*r* 45.9%

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

       2. neg-mul-1 45.9%

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

       3. *-commutative 45.9%

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

       4. associate-*l* 58.0%

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

   12. Simplified 58.0%

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

   if -9.5000000000000009e-38 < a < -7.0000000000000004e-46

   1. Initial program 75.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.7%

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

   if 2.2e-226 < a < 7.20000000000000003e-169

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. fma-def 73.3%

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

      3. *-commutative 73.3%

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

      4. sub-neg 73.3%

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

      5. sub-neg 73.3%

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

      6. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in y around 0 60.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 60.4%

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

      2. neg-mul-1 60.4%

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

      3. fma-neg 60.4%

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

      4. distribute-rgt-neg-in 60.4%

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

      5. neg-sub0 60.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 60.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 60.4%

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

      8. +-commutative 60.4%

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

      9. sub-neg 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in y around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. *-commutative 48.2%

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

      3. distribute-rgt-neg-in 48.2%

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

      4. *-commutative 48.2%

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

   9. Simplified 48.2%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -0.00115:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-38}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-226}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-169}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-45}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 7: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-194}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -4.8e+28)
     t_2
     (if (<= a -8.2e-10)
       t_1
       (if (<= a -4.1e-37)
         (* j (- (* y i)))
         (if (<= a -4.8e-46)
           (* z (* x y))
           (if (<= a 8.4e-227)
             t_1
             (if (<= a 5.5e-194)
               (* i (* y (- j)))
               (if (<= a 5.2e+49) (* c (- (* a j) (* z b))) 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 * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.8e+28) {
		tmp = t_2;
	} else if (a <= -8.2e-10) {
		tmp = t_1;
	} else if (a <= -4.1e-37) {
		tmp = j * -(y * i);
	} else if (a <= -4.8e-46) {
		tmp = z * (x * y);
	} else if (a <= 8.4e-227) {
		tmp = t_1;
	} else if (a <= 5.5e-194) {
		tmp = i * (y * -j);
	} else if (a <= 5.2e+49) {
		tmp = c * ((a * j) - (z * b));
	} 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 * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-4.8d+28)) then
        tmp = t_2
    else if (a <= (-8.2d-10)) then
        tmp = t_1
    else if (a <= (-4.1d-37)) then
        tmp = j * -(y * i)
    else if (a <= (-4.8d-46)) then
        tmp = z * (x * y)
    else if (a <= 8.4d-227) then
        tmp = t_1
    else if (a <= 5.5d-194) then
        tmp = i * (y * -j)
    else if (a <= 5.2d+49) then
        tmp = c * ((a * j) - (z * b))
    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 * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.8e+28) {
		tmp = t_2;
	} else if (a <= -8.2e-10) {
		tmp = t_1;
	} else if (a <= -4.1e-37) {
		tmp = j * -(y * i);
	} else if (a <= -4.8e-46) {
		tmp = z * (x * y);
	} else if (a <= 8.4e-227) {
		tmp = t_1;
	} else if (a <= 5.5e-194) {
		tmp = i * (y * -j);
	} else if (a <= 5.2e+49) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.8e+28:
		tmp = t_2
	elif a <= -8.2e-10:
		tmp = t_1
	elif a <= -4.1e-37:
		tmp = j * -(y * i)
	elif a <= -4.8e-46:
		tmp = z * (x * y)
	elif a <= 8.4e-227:
		tmp = t_1
	elif a <= 5.5e-194:
		tmp = i * (y * -j)
	elif a <= 5.2e+49:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.8e+28)
		tmp = t_2;
	elseif (a <= -8.2e-10)
		tmp = t_1;
	elseif (a <= -4.1e-37)
		tmp = Float64(j * Float64(-Float64(y * i)));
	elseif (a <= -4.8e-46)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 8.4e-227)
		tmp = t_1;
	elseif (a <= 5.5e-194)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 5.2e+49)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.8e+28)
		tmp = t_2;
	elseif (a <= -8.2e-10)
		tmp = t_1;
	elseif (a <= -4.1e-37)
		tmp = j * -(y * i);
	elseif (a <= -4.8e-46)
		tmp = z * (x * y);
	elseif (a <= 8.4e-227)
		tmp = t_1;
	elseif (a <= 5.5e-194)
		tmp = i * (y * -j);
	elseif (a <= 5.2e+49)
		tmp = c * ((a * j) - (z * b));
	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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.8e+28], t$95$2, If[LessEqual[a, -8.2e-10], t$95$1, If[LessEqual[a, -4.1e-37], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], If[LessEqual[a, -4.8e-46], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-227], t$95$1, If[LessEqual[a, 5.5e-194], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.2e+49], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.79999999999999962e28 or 5.19999999999999977e49 < a

   1. Initial program 71.0%

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

   2. Taylor expanded in a around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. mul-1-neg 66.8%

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

      3. unsub-neg 66.8%

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

      4. *-commutative 66.8%

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

   4. Simplified 66.8%

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

   if -4.79999999999999962e28 < a < -8.1999999999999996e-10 or -4.80000000000000027e-46 < a < 8.3999999999999999e-227

   1. Initial program 84.6%

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

   2. Taylor expanded in b around inf 50.6%

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

   if -8.1999999999999996e-10 < a < -4.0999999999999998e-37

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-def 99.3%

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

      3. *-commutative 99.3%

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

      4. sub-neg 99.3%

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

      5. sub-neg 99.3%

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

      6. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 72.8%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 72.8%

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

      2. neg-mul-1 72.8%

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

      3. fma-neg 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

      5. neg-sub0 72.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 72.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 72.8%

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

      8. +-commutative 72.8%

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

      9. sub-neg 72.8%

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

   6. Simplified 72.8%

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

   7. Taylor expanded in y around inf 45.9%

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

      1. mul-1-neg 45.9%

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

      2. *-commutative 45.9%

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

      3. distribute-rgt-neg-in 45.9%

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

      4. *-commutative 45.9%

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

   9. Simplified 45.9%

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

   10. Taylor expanded in y around 0 45.9%

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

       1. associate-*r* 45.9%

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

       2. neg-mul-1 45.9%

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

       3. *-commutative 45.9%

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

       4. associate-*l* 58.0%

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

   12. Simplified 58.0%

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

   if -4.0999999999999998e-37 < a < -4.80000000000000027e-46

   1. Initial program 75.0%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.7%

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

   if 8.3999999999999999e-227 < a < 5.49999999999999941e-194

   1. Initial program 69.3%

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

      1. +-commutative 69.3%

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

      2. fma-def 69.3%

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

      3. *-commutative 69.3%

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

      4. sub-neg 69.3%

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

      5. sub-neg 69.3%

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

      6. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in y around 0 54.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

      3. fma-neg 54.5%

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

      4. distribute-rgt-neg-in 54.5%

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

      5. neg-sub0 54.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 54.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 54.5%

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

      8. +-commutative 54.5%

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

      9. sub-neg 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in y around inf 55.0%

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

      1. mul-1-neg 55.0%

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

      2. *-commutative 55.0%

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

      3. distribute-rgt-neg-in 55.0%

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

      4. *-commutative 55.0%

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

   9. Simplified 55.0%

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

   if 5.49999999999999941e-194 < a < 5.19999999999999977e49

   1. Initial program 84.2%

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

   2. Taylor expanded in c around inf 49.3%

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

      1. *-commutative 49.3%

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

   4. Simplified 49.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-37}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-46}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-194}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 8: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.7 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* a (* x t))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.7e+128)
     t_2
     (if (<= i -1.7e-147)
       t_1
       (if (<= i 1.9e-13)
         (- (* x (- (* y z) (* t a))) (* z (* b c)))
         (if (<= i 1.15e+51) 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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+128) {
		tmp = t_2;
	} else if (i <= -1.7e-147) {
		tmp = t_1;
	} else if (i <= 1.9e-13) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (i <= 1.15e+51) {
		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 = (j * ((a * c) - (y * i))) - (a * (x * t))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.7d+128)) then
        tmp = t_2
    else if (i <= (-1.7d-147)) then
        tmp = t_1
    else if (i <= 1.9d-13) then
        tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
    else if (i <= 1.15d+51) 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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.7e+128) {
		tmp = t_2;
	} else if (i <= -1.7e-147) {
		tmp = t_1;
	} else if (i <= 1.9e-13) {
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	} else if (i <= 1.15e+51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (a * (x * t))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.7e+128:
		tmp = t_2
	elif i <= -1.7e-147:
		tmp = t_1
	elif i <= 1.9e-13:
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c))
	elif i <= 1.15e+51:
		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(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(a * Float64(x * t)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.7e+128)
		tmp = t_2;
	elseif (i <= -1.7e-147)
		tmp = t_1;
	elseif (i <= 1.9e-13)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)));
	elseif (i <= 1.15e+51)
		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 = (j * ((a * c) - (y * i))) - (a * (x * t));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.7e+128)
		tmp = t_2;
	elseif (i <= -1.7e-147)
		tmp = t_1;
	elseif (i <= 1.9e-13)
		tmp = (x * ((y * z) - (t * a))) - (z * (b * c));
	elseif (i <= 1.15e+51)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.7e+128], t$95$2, If[LessEqual[i, -1.7e-147], t$95$1, If[LessEqual[i, 1.9e-13], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e+51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.6999999999999999e128 or 1.15000000000000003e51 < i

   1. Initial program 67.2%

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

      1. +-commutative 67.2%

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

      2. fma-def 69.3%

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

      3. *-commutative 69.3%

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

      4. sub-neg 69.3%

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

      5. sub-neg 69.3%

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

      6. *-commutative 69.3%

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

   3. Simplified 69.3%

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

   4. Taylor expanded in y around 0 68.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.3%

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

      2. neg-mul-1 68.3%

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

      3. fma-neg 69.3%

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

      4. distribute-rgt-neg-in 69.3%

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

      5. neg-sub0 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 69.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 69.3%

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

      8. +-commutative 69.3%

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

      9. sub-neg 69.3%

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

   6. Simplified 69.3%

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

      1. fma-udef 66.2%

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

      2. *-commutative 66.2%

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

      3. *-commutative 66.2%

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

      4. *-commutative 66.2%

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

   8. Applied egg-rr 66.2%

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

   9. Taylor expanded in i around inf 68.2%

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

       1. neg-mul-1 68.2%

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

       2. +-commutative 68.2%

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

       3. unsub-neg 68.2%

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

   11. Simplified 68.2%

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

   if -1.6999999999999999e128 < i < -1.69999999999999998e-147 or 1.9e-13 < i < 1.15000000000000003e51

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. fma-def 81.2%

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

      3. *-commutative 81.2%

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

      4. sub-neg 81.2%

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

      5. sub-neg 81.2%

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

      6. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 78.9%

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

      2. neg-mul-1 78.9%

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

      3. fma-neg 78.9%

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

      4. distribute-rgt-neg-in 78.9%

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

      5. neg-sub0 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 78.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 78.9%

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

      8. +-commutative 78.9%

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

      9. sub-neg 78.9%

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

   6. Simplified 78.9%

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

   7. Taylor expanded in b around 0 71.2%

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

      1. +-commutative 71.2%

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

      2. mul-1-neg 71.2%

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

      3. unsub-neg 71.2%

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

      4. sub-neg 71.2%

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

      5. *-commutative 71.2%

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

      6. sub-neg 71.2%

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

   9. Simplified 71.2%

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

   if -1.69999999999999998e-147 < i < 1.9e-13

   1. Initial program 88.5%

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

   2. Taylor expanded in j around 0 68.9%

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

   3. Taylor expanded in c around inf 68.1%

      \[\leadsto x \cdot \left(y \cdot z - a \cdot t\right) - \color{blue}{b \cdot \left(c \cdot z\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.7 \cdot 10^{+128}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-147}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+51}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 9: 63.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+127} \lor \neg \left(i \leq 2.8 \cdot 10^{+58}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -2.4e+127) (not (<= i 2.8e+58)))
   (* i (- (* t b) (* y j)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y 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 ((i <= -2.4e+127) || !(i <= 2.8e+58)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * 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 ((i <= (-2.4d+127)) .or. (.not. (i <= 2.8d+58))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * 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 ((i <= -2.4e+127) || !(i <= 2.8e+58)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -2.4e+127) or not (i <= 2.8e+58):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -2.4e+127) || !(i <= 2.8e+58))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -2.4e+127) || ~((i <= 2.8e+58)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -2.4e+127], N[Not[LessEqual[i, 2.8e+58]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -2.4000000000000002e127 or 2.7999999999999998e58 < i

   1. Initial program 66.5%

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

      1. +-commutative 66.5%

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

      2. fma-def 68.6%

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

      3. *-commutative 68.6%

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

      4. sub-neg 68.6%

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

      5. sub-neg 68.6%

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

      6. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in y around 0 68.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.6%

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

      2. neg-mul-1 68.6%

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

      3. fma-neg 69.7%

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

      4. distribute-rgt-neg-in 69.7%

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

      5. neg-sub0 69.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 69.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 69.7%

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

      8. +-commutative 69.7%

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

      9. sub-neg 69.7%

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

   6. Simplified 69.7%

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

      1. fma-udef 66.6%

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

      2. *-commutative 66.6%

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

      3. *-commutative 66.6%

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

      4. *-commutative 66.6%

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

   8. Applied egg-rr 66.6%

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

   9. Taylor expanded in i around inf 68.6%

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

       1. neg-mul-1 68.6%

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

       2. +-commutative 68.6%

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

       3. unsub-neg 68.6%

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

   11. Simplified 68.6%

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

   if -2.4000000000000002e127 < i < 2.7999999999999998e58

   1. Initial program 85.3%

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

   2. Taylor expanded in b around 0 76.4%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.4 \cdot 10^{+127} \lor \neg \left(i \leq 2.8 \cdot 10^{+58}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 10: 69.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -9.5 \cdot 10^{-38} \lor \neg \left(j \leq 3.55 \cdot 10^{-75}\right):\\ \;\;\;\;t_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (or (<= j -9.5e-38) (not (<= j 3.55e-75)))
     (+ t_1 (* j (- (* a c) (* y i))))
     (+ t_1 (* b (- (* t i) (* z c)))))))

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 ((j <= -9.5e-38) || !(j <= 3.55e-75)) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	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 ((j <= (-9.5d-38)) .or. (.not. (j <= 3.55d-75))) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = t_1 + (b * ((t * i) - (z * c)))
    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 ((j <= -9.5e-38) || !(j <= 3.55e-75)) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if (j <= -9.5e-38) or not (j <= 3.55e-75):
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	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 ((j <= -9.5e-38) || !(j <= 3.55e-75))
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	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 ((j <= -9.5e-38) || ~((j <= 3.55e-75)))
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = t_1 + (b * ((t * i) - (z * c)));
	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[Or[LessEqual[j, -9.5e-38], N[Not[LessEqual[j, 3.55e-75]], $MachinePrecision]], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if j < -9.5000000000000009e-38 or 3.5500000000000002e-75 < j

   1. Initial program 80.8%

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

   2. Taylor expanded in b around 0 75.8%

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

   if -9.5000000000000009e-38 < j < 3.5500000000000002e-75

   1. Initial program 74.2%

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

   2. Taylor expanded in j around 0 75.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.5 \cdot 10^{-38} \lor \neg \left(j \leq 3.55 \cdot 10^{-75}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 11: 51.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -4.8e+78)
     t_3
     (if (<= i -1.12e-88)
       t_2
       (if (<= i 2.5e-302)
         t_1
         (if (<= i 3.8e-140)
           t_2
           (if (<= i 8.8e-57) t_1 (if (<= i 1.75e+27) t_2 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 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+78) {
		tmp = t_3;
	} else if (i <= -1.12e-88) {
		tmp = t_2;
	} else if (i <= 2.5e-302) {
		tmp = t_1;
	} else if (i <= 3.8e-140) {
		tmp = t_2;
	} else if (i <= 8.8e-57) {
		tmp = t_1;
	} else if (i <= 1.75e+27) {
		tmp = t_2;
	} 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 = c * ((a * j) - (z * b))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-4.8d+78)) then
        tmp = t_3
    else if (i <= (-1.12d-88)) then
        tmp = t_2
    else if (i <= 2.5d-302) then
        tmp = t_1
    else if (i <= 3.8d-140) then
        tmp = t_2
    else if (i <= 8.8d-57) then
        tmp = t_1
    else if (i <= 1.75d+27) then
        tmp = t_2
    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 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+78) {
		tmp = t_3;
	} else if (i <= -1.12e-88) {
		tmp = t_2;
	} else if (i <= 2.5e-302) {
		tmp = t_1;
	} else if (i <= 3.8e-140) {
		tmp = t_2;
	} else if (i <= 8.8e-57) {
		tmp = t_1;
	} else if (i <= 1.75e+27) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.8e+78:
		tmp = t_3
	elif i <= -1.12e-88:
		tmp = t_2
	elif i <= 2.5e-302:
		tmp = t_1
	elif i <= 3.8e-140:
		tmp = t_2
	elif i <= 8.8e-57:
		tmp = t_1
	elif i <= 1.75e+27:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.8e+78)
		tmp = t_3;
	elseif (i <= -1.12e-88)
		tmp = t_2;
	elseif (i <= 2.5e-302)
		tmp = t_1;
	elseif (i <= 3.8e-140)
		tmp = t_2;
	elseif (i <= 8.8e-57)
		tmp = t_1;
	elseif (i <= 1.75e+27)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.8e+78)
		tmp = t_3;
	elseif (i <= -1.12e-88)
		tmp = t_2;
	elseif (i <= 2.5e-302)
		tmp = t_1;
	elseif (i <= 3.8e-140)
		tmp = t_2;
	elseif (i <= 8.8e-57)
		tmp = t_1;
	elseif (i <= 1.75e+27)
		tmp = t_2;
	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[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+78], t$95$3, If[LessEqual[i, -1.12e-88], t$95$2, If[LessEqual[i, 2.5e-302], t$95$1, If[LessEqual[i, 3.8e-140], t$95$2, If[LessEqual[i, 8.8e-57], t$95$1, If[LessEqual[i, 1.75e+27], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.7999999999999997e78 or 1.7500000000000001e27 < i

   1. Initial program 68.3%

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

      1. +-commutative 68.3%

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

      2. fma-def 70.0%

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

      3. *-commutative 70.0%

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

      4. sub-neg 70.0%

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

      5. sub-neg 70.0%

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

      6. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in y around 0 70.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 70.0%

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

      2. neg-mul-1 70.0%

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

      3. fma-neg 70.9%

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

      4. distribute-rgt-neg-in 70.9%

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

      5. neg-sub0 70.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 70.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 70.9%

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

      8. +-commutative 70.9%

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

      9. sub-neg 70.9%

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

   6. Simplified 70.9%

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

      1. fma-udef 68.3%

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

      2. *-commutative 68.3%

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

      3. *-commutative 68.3%

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

      4. *-commutative 68.3%

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

   8. Applied egg-rr 68.3%

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

   9. Taylor expanded in i around inf 65.8%

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

       1. neg-mul-1 65.8%

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

       2. +-commutative 65.8%

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

       3. unsub-neg 65.8%

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

   11. Simplified 65.8%

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

   if -4.7999999999999997e78 < i < -1.12e-88 or 2.50000000000000017e-302 < i < 3.79999999999999998e-140 or 8.79999999999999994e-57 < i < 1.7500000000000001e27

   1. Initial program 83.9%

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

   2. Taylor expanded in a around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   4. Simplified 59.9%

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

   if -1.12e-88 < i < 2.50000000000000017e-302 or 3.79999999999999998e-140 < i < 8.79999999999999994e-57

   1. Initial program 89.7%

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

   2. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   4. Simplified 56.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.12 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-302}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 8.8 \cdot 10^{-57}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 12: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 750000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= j -3.4e-20)
     (* a (* c j))
     (if (<= j -6.5e-195)
       (* b (* t i))
       (if (<= j 3.4e-273)
         t_1
         (if (<= j 2.55e-151)
           (* t (* b i))
           (if (<= j 750000.0)
             (* t (* a (- x)))
             (if (<= j 1.75e+29)
               t_1
               (if (<= j 2.7e+115) (* c (* a j)) (* j (- (* y i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (j <= -3.4e-20) {
		tmp = a * (c * j);
	} else if (j <= -6.5e-195) {
		tmp = b * (t * i);
	} else if (j <= 3.4e-273) {
		tmp = t_1;
	} else if (j <= 2.55e-151) {
		tmp = t * (b * i);
	} else if (j <= 750000.0) {
		tmp = t * (a * -x);
	} else if (j <= 1.75e+29) {
		tmp = t_1;
	} else if (j <= 2.7e+115) {
		tmp = c * (a * j);
	} else {
		tmp = j * -(y * 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) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (j <= (-3.4d-20)) then
        tmp = a * (c * j)
    else if (j <= (-6.5d-195)) then
        tmp = b * (t * i)
    else if (j <= 3.4d-273) then
        tmp = t_1
    else if (j <= 2.55d-151) then
        tmp = t * (b * i)
    else if (j <= 750000.0d0) then
        tmp = t * (a * -x)
    else if (j <= 1.75d+29) then
        tmp = t_1
    else if (j <= 2.7d+115) then
        tmp = c * (a * j)
    else
        tmp = j * -(y * 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 t_1 = z * (x * y);
	double tmp;
	if (j <= -3.4e-20) {
		tmp = a * (c * j);
	} else if (j <= -6.5e-195) {
		tmp = b * (t * i);
	} else if (j <= 3.4e-273) {
		tmp = t_1;
	} else if (j <= 2.55e-151) {
		tmp = t * (b * i);
	} else if (j <= 750000.0) {
		tmp = t * (a * -x);
	} else if (j <= 1.75e+29) {
		tmp = t_1;
	} else if (j <= 2.7e+115) {
		tmp = c * (a * j);
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if j <= -3.4e-20:
		tmp = a * (c * j)
	elif j <= -6.5e-195:
		tmp = b * (t * i)
	elif j <= 3.4e-273:
		tmp = t_1
	elif j <= 2.55e-151:
		tmp = t * (b * i)
	elif j <= 750000.0:
		tmp = t * (a * -x)
	elif j <= 1.75e+29:
		tmp = t_1
	elif j <= 2.7e+115:
		tmp = c * (a * j)
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (j <= -3.4e-20)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -6.5e-195)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 3.4e-273)
		tmp = t_1;
	elseif (j <= 2.55e-151)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 750000.0)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (j <= 1.75e+29)
		tmp = t_1;
	elseif (j <= 2.7e+115)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (j <= -3.4e-20)
		tmp = a * (c * j);
	elseif (j <= -6.5e-195)
		tmp = b * (t * i);
	elseif (j <= 3.4e-273)
		tmp = t_1;
	elseif (j <= 2.55e-151)
		tmp = t * (b * i);
	elseif (j <= 750000.0)
		tmp = t * (a * -x);
	elseif (j <= 1.75e+29)
		tmp = t_1;
	elseif (j <= 2.7e+115)
		tmp = c * (a * j);
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e-20], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-195], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-273], t$95$1, If[LessEqual[j, 2.55e-151], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 750000.0], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.75e+29], t$95$1, If[LessEqual[j, 2.7e+115], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if j < -3.3999999999999997e-20

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in j around inf 48.4%

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

   if -3.3999999999999997e-20 < j < -6.50000000000000004e-195

   1. Initial program 73.4%

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

   2. Taylor expanded in j around 0 76.4%

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

   3. Taylor expanded in i around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 38.3%

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

   5. Simplified 38.3%

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

   if -6.50000000000000004e-195 < j < 3.39999999999999991e-273 or 7.5e5 < j < 1.74999999999999989e29

   1. Initial program 69.0%

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

   2. Taylor expanded in z around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. *-commutative 61.1%

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

   4. Simplified 61.1%

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

   5. Taylor expanded in y around inf 41.5%

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

   if 3.39999999999999991e-273 < j < 2.5499999999999999e-151

   1. Initial program 77.8%

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

   2. Taylor expanded in j around 0 78.0%

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

   3. Taylor expanded in i around inf 51.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if 2.5499999999999999e-151 < j < 7.5e5

   1. Initial program 82.4%

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

      1. +-commutative 82.4%

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

      2. fma-def 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. sub-neg 82.4%

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

      6. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 68.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. fma-neg 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. neg-sub0 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 68.1%

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

      8. +-commutative 68.1%

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

      9. sub-neg 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in t around inf 51.2%

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

   8. Taylor expanded in a around inf 31.3%

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

      1. mul-1-neg 31.3%

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

      2. *-commutative 31.3%

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

      3. associate-*r* 36.8%

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

      4. distribute-lft-neg-out 36.8%

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

      5. *-commutative 36.8%

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

      6. *-commutative 36.8%

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

      7. distribute-rgt-neg-in 36.8%

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

   10. Simplified 36.8%

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

   if 1.74999999999999989e29 < j < 2.70000000000000004e115

   1. Initial program 87.3%

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

      1. +-commutative 87.3%

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

      2. fma-def 93.6%

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

      3. *-commutative 93.6%

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

      4. sub-neg 93.6%

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

      5. sub-neg 93.6%

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

      6. *-commutative 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 81.8%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 81.8%

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

      2. neg-mul-1 81.8%

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

      3. fma-neg 81.8%

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

      4. distribute-rgt-neg-in 81.8%

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

      5. neg-sub0 81.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 81.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 81.8%

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

      8. +-commutative 81.8%

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

      9. sub-neg 81.8%

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

   6. Simplified 81.8%

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

      1. fma-udef 75.6%

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

      2. *-commutative 75.6%

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

      3. *-commutative 75.6%

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

      4. *-commutative 75.6%

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

   8. Applied egg-rr 75.6%

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

   9. Taylor expanded in y around 0 69.9%

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

       1. associate-+r+ 69.9%

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

       2. mul-1-neg 69.9%

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

       3. distribute-rgt-neg-in 69.9%

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

       4. mul-1-neg 69.9%

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

       5. distribute-lft-in 69.9%

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

       6. fma-def 69.9%

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

       7. +-commutative 69.9%

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

       8. mul-1-neg 69.9%

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

       9. unsub-neg 69.9%

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

       10. *-commutative 69.9%

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

   11. Simplified 69.9%

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

   12. Taylor expanded in j around inf 44.8%

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

       1. associate-*r* 50.6%

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

       2. *-commutative 50.6%

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

       3. associate-*r* 50.7%

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

   14. Simplified 50.7%

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

   if 2.70000000000000004e115 < j

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. fma-def 82.1%

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

      3. *-commutative 82.1%

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

      4. sub-neg 82.1%

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

      5. sub-neg 82.1%

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

      6. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in y around 0 71.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 71.4%

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

      2. neg-mul-1 71.4%

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

      3. fma-neg 73.6%

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

      4. distribute-rgt-neg-in 73.6%

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

      5. neg-sub0 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 73.6%

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

      8. +-commutative 73.6%

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

      9. sub-neg 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in y around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. *-commutative 47.8%

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

      3. distribute-rgt-neg-in 47.8%

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

      4. *-commutative 47.8%

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

   9. Simplified 47.8%

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

   10. Taylor expanded in y around 0 47.8%

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

       1. associate-*r* 47.8%

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

       2. neg-mul-1 47.8%

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

       3. *-commutative 47.8%

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

       4. associate-*l* 47.8%

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

   12. Simplified 47.8%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{-20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.55 \cdot 10^{-151}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 750000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+115}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]

Alternative 13: 29.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 450000000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+115}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.35e-31)
   (* a (* c j))
   (if (<= j -9.2e-191)
     (* b (* t i))
     (if (<= j 3.1e-273)
       (* z (* x y))
       (if (<= j 2.95e-154)
         (* t (* b i))
         (if (<= j 450000000000.0)
           (* t (* a (- x)))
           (if (<= j 5.4e+28)
             (* z (- (* b c)))
             (if (<= j 3.8e+115) (* c (* a j)) (* j (- (* y 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 (j <= -1.35e-31) {
		tmp = a * (c * j);
	} else if (j <= -9.2e-191) {
		tmp = b * (t * i);
	} else if (j <= 3.1e-273) {
		tmp = z * (x * y);
	} else if (j <= 2.95e-154) {
		tmp = t * (b * i);
	} else if (j <= 450000000000.0) {
		tmp = t * (a * -x);
	} else if (j <= 5.4e+28) {
		tmp = z * -(b * c);
	} else if (j <= 3.8e+115) {
		tmp = c * (a * j);
	} else {
		tmp = j * -(y * 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 (j <= (-1.35d-31)) then
        tmp = a * (c * j)
    else if (j <= (-9.2d-191)) then
        tmp = b * (t * i)
    else if (j <= 3.1d-273) then
        tmp = z * (x * y)
    else if (j <= 2.95d-154) then
        tmp = t * (b * i)
    else if (j <= 450000000000.0d0) then
        tmp = t * (a * -x)
    else if (j <= 5.4d+28) then
        tmp = z * -(b * c)
    else if (j <= 3.8d+115) then
        tmp = c * (a * j)
    else
        tmp = j * -(y * 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 (j <= -1.35e-31) {
		tmp = a * (c * j);
	} else if (j <= -9.2e-191) {
		tmp = b * (t * i);
	} else if (j <= 3.1e-273) {
		tmp = z * (x * y);
	} else if (j <= 2.95e-154) {
		tmp = t * (b * i);
	} else if (j <= 450000000000.0) {
		tmp = t * (a * -x);
	} else if (j <= 5.4e+28) {
		tmp = z * -(b * c);
	} else if (j <= 3.8e+115) {
		tmp = c * (a * j);
	} else {
		tmp = j * -(y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.35e-31:
		tmp = a * (c * j)
	elif j <= -9.2e-191:
		tmp = b * (t * i)
	elif j <= 3.1e-273:
		tmp = z * (x * y)
	elif j <= 2.95e-154:
		tmp = t * (b * i)
	elif j <= 450000000000.0:
		tmp = t * (a * -x)
	elif j <= 5.4e+28:
		tmp = z * -(b * c)
	elif j <= 3.8e+115:
		tmp = c * (a * j)
	else:
		tmp = j * -(y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.35e-31)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -9.2e-191)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 3.1e-273)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2.95e-154)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 450000000000.0)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (j <= 5.4e+28)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (j <= 3.8e+115)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(j * Float64(-Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.35e-31)
		tmp = a * (c * j);
	elseif (j <= -9.2e-191)
		tmp = b * (t * i);
	elseif (j <= 3.1e-273)
		tmp = z * (x * y);
	elseif (j <= 2.95e-154)
		tmp = t * (b * i);
	elseif (j <= 450000000000.0)
		tmp = t * (a * -x);
	elseif (j <= 5.4e+28)
		tmp = z * -(b * c);
	elseif (j <= 3.8e+115)
		tmp = c * (a * j);
	else
		tmp = j * -(y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.35e-31], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -9.2e-191], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-273], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.95e-154], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 450000000000.0], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.4e+28], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 3.8e+115], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -1.35000000000000007e-31

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in j around inf 48.4%

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

   if -1.35000000000000007e-31 < j < -9.20000000000000042e-191

   1. Initial program 73.4%

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

   2. Taylor expanded in j around 0 76.4%

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

   3. Taylor expanded in i around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 38.3%

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

   5. Simplified 38.3%

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

   if -9.20000000000000042e-191 < j < 3.09999999999999988e-273

   1. Initial program 68.4%

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

   2. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in y around inf 44.1%

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

   if 3.09999999999999988e-273 < j < 2.9500000000000001e-154

   1. Initial program 77.8%

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

   2. Taylor expanded in j around 0 78.0%

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

   3. Taylor expanded in i around inf 51.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if 2.9500000000000001e-154 < j < 4.5e11

   1. Initial program 82.4%

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

      1. +-commutative 82.4%

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

      2. fma-def 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. sub-neg 82.4%

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

      6. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 68.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. fma-neg 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. neg-sub0 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 68.1%

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

      8. +-commutative 68.1%

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

      9. sub-neg 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in t around inf 51.2%

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

   8. Taylor expanded in a around inf 31.3%

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

      1. mul-1-neg 31.3%

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

      2. *-commutative 31.3%

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

      3. associate-*r* 36.8%

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

      4. distribute-lft-neg-out 36.8%

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

      5. *-commutative 36.8%

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

      6. *-commutative 36.8%

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

      7. distribute-rgt-neg-in 36.8%

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

   10. Simplified 36.8%

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

   if 4.5e11 < j < 5.4000000000000003e28

   1. Initial program 66.7%

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

   2. Taylor expanded in z around inf 53.1%

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

      1. *-commutative 53.1%

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

      2. *-commutative 53.1%

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

   4. Simplified 53.1%

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

   5. Taylor expanded in y around 0 36.5%

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

      1. mul-1-neg 36.5%

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

      2. *-commutative 36.5%

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

      3. distribute-rgt-neg-in 36.5%

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

   7. Simplified 36.5%

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

   if 5.4000000000000003e28 < j < 3.8000000000000001e115

   1. Initial program 88.1%

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

      1. +-commutative 88.1%

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

      2. fma-def 93.9%

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

      3. *-commutative 93.9%

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

      4. sub-neg 93.9%

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

      5. sub-neg 93.9%

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

      6. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 77.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 77.3%

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

      2. neg-mul-1 77.3%

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

      3. fma-neg 77.3%

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

      4. distribute-rgt-neg-in 77.3%

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

      5. neg-sub0 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 77.3%

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

      8. +-commutative 77.3%

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

      9. sub-neg 77.3%

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

   6. Simplified 77.3%

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

      1. fma-udef 71.4%

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

      2. *-commutative 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

   8. Applied egg-rr 71.4%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. associate-+r+ 65.8%

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

       2. mul-1-neg 65.8%

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

       3. distribute-rgt-neg-in 65.8%

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

       4. mul-1-neg 65.8%

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

       5. distribute-lft-in 65.8%

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

       6. fma-def 65.8%

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

       7. +-commutative 65.8%

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

       8. mul-1-neg 65.8%

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

       9. unsub-neg 65.8%

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

       10. *-commutative 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in j around inf 42.4%

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

       1. associate-*r* 47.8%

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

       2. *-commutative 47.8%

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

       3. associate-*r* 47.9%

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

   14. Simplified 47.9%

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

   if 3.8000000000000001e115 < j

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. fma-def 82.1%

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

      3. *-commutative 82.1%

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

      4. sub-neg 82.1%

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

      5. sub-neg 82.1%

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

      6. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in y around 0 71.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 71.4%

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

      2. neg-mul-1 71.4%

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

      3. fma-neg 73.6%

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

      4. distribute-rgt-neg-in 73.6%

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

      5. neg-sub0 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 73.6%

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

      8. +-commutative 73.6%

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

      9. sub-neg 73.6%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in y around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. *-commutative 47.8%

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

      3. distribute-rgt-neg-in 47.8%

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

      4. *-commutative 47.8%

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

   9. Simplified 47.8%

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

   10. Taylor expanded in y around 0 47.8%

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

       1. associate-*r* 47.8%

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

       2. neg-mul-1 47.8%

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

       3. *-commutative 47.8%

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

       4. associate-*l* 47.8%

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

   12. Simplified 47.8%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{-31}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -9.2 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.95 \cdot 10^{-154}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 450000000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 5.4 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+115}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \end{array} \]

Alternative 14: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -8.4 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 190000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4.8e-38)
   (* a (* c j))
   (if (<= j -8.4e-191)
     (* b (* t i))
     (if (<= j 3.4e-273)
       (* z (* x y))
       (if (<= j 2.05e-153)
         (* t (* b i))
         (if (<= j 190000000.0)
           (* t (* a (- x)))
           (if (<= j 6e+28)
             (* z (- (* b c)))
             (if (<= j 4.6e+116) (* c (* a j)) (* i (* y (- j)))))))))))

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 <= -4.8e-38) {
		tmp = a * (c * j);
	} else if (j <= -8.4e-191) {
		tmp = b * (t * i);
	} else if (j <= 3.4e-273) {
		tmp = z * (x * y);
	} else if (j <= 2.05e-153) {
		tmp = t * (b * i);
	} else if (j <= 190000000.0) {
		tmp = t * (a * -x);
	} else if (j <= 6e+28) {
		tmp = z * -(b * c);
	} else if (j <= 4.6e+116) {
		tmp = c * (a * j);
	} else {
		tmp = i * (y * -j);
	}
	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 <= (-4.8d-38)) then
        tmp = a * (c * j)
    else if (j <= (-8.4d-191)) then
        tmp = b * (t * i)
    else if (j <= 3.4d-273) then
        tmp = z * (x * y)
    else if (j <= 2.05d-153) then
        tmp = t * (b * i)
    else if (j <= 190000000.0d0) then
        tmp = t * (a * -x)
    else if (j <= 6d+28) then
        tmp = z * -(b * c)
    else if (j <= 4.6d+116) then
        tmp = c * (a * j)
    else
        tmp = i * (y * -j)
    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 <= -4.8e-38) {
		tmp = a * (c * j);
	} else if (j <= -8.4e-191) {
		tmp = b * (t * i);
	} else if (j <= 3.4e-273) {
		tmp = z * (x * y);
	} else if (j <= 2.05e-153) {
		tmp = t * (b * i);
	} else if (j <= 190000000.0) {
		tmp = t * (a * -x);
	} else if (j <= 6e+28) {
		tmp = z * -(b * c);
	} else if (j <= 4.6e+116) {
		tmp = c * (a * j);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4.8e-38:
		tmp = a * (c * j)
	elif j <= -8.4e-191:
		tmp = b * (t * i)
	elif j <= 3.4e-273:
		tmp = z * (x * y)
	elif j <= 2.05e-153:
		tmp = t * (b * i)
	elif j <= 190000000.0:
		tmp = t * (a * -x)
	elif j <= 6e+28:
		tmp = z * -(b * c)
	elif j <= 4.6e+116:
		tmp = c * (a * j)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4.8e-38)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= -8.4e-191)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 3.4e-273)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2.05e-153)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 190000000.0)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (j <= 6e+28)
		tmp = Float64(z * Float64(-Float64(b * c)));
	elseif (j <= 4.6e+116)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -4.8e-38)
		tmp = a * (c * j);
	elseif (j <= -8.4e-191)
		tmp = b * (t * i);
	elseif (j <= 3.4e-273)
		tmp = z * (x * y);
	elseif (j <= 2.05e-153)
		tmp = t * (b * i);
	elseif (j <= 190000000.0)
		tmp = t * (a * -x);
	elseif (j <= 6e+28)
		tmp = z * -(b * c);
	elseif (j <= 4.6e+116)
		tmp = c * (a * j);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4.8e-38], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.4e-191], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.4e-273], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.05e-153], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 190000000.0], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e+28], N[(z * (-N[(b * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 4.6e+116], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -4.80000000000000044e-38

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

      4. *-commutative 54.6%

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

   4. Simplified 54.6%

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

   5. Taylor expanded in j around inf 48.4%

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

   if -4.80000000000000044e-38 < j < -8.39999999999999941e-191

   1. Initial program 73.4%

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

   2. Taylor expanded in j around 0 76.4%

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

   3. Taylor expanded in i around inf 38.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 38.3%

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

   5. Simplified 38.3%

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

   if -8.39999999999999941e-191 < j < 3.39999999999999991e-273

   1. Initial program 68.4%

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

   2. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

      2. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in y around inf 44.1%

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

   if 3.39999999999999991e-273 < j < 2.05e-153

   1. Initial program 77.8%

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

   2. Taylor expanded in j around 0 78.0%

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

   3. Taylor expanded in i around inf 51.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 58.8%

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

      2. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if 2.05e-153 < j < 1.9e8

   1. Initial program 82.4%

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

      1. +-commutative 82.4%

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

      2. fma-def 82.4%

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

      3. *-commutative 82.4%

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

      4. sub-neg 82.4%

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

      5. sub-neg 82.4%

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

      6. *-commutative 82.4%

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

   3. Simplified 82.4%

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

   4. Taylor expanded in y around 0 68.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.1%

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

      2. neg-mul-1 68.1%

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

      3. fma-neg 68.1%

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

      4. distribute-rgt-neg-in 68.1%

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

      5. neg-sub0 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 68.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 68.1%

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

      8. +-commutative 68.1%

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

      9. sub-neg 68.1%

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

   6. Simplified 68.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in t around inf 51.2%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]

   8. Taylor expanded in a around inf 31.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 31.3%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

      2. *-commutative 31.3%

         \[\leadsto -a \cdot \color{blue}{\left(x \cdot t\right)} \]

      3. associate-*r* 36.8%

         \[\leadsto -\color{blue}{\left(a \cdot x\right) \cdot t} \]

      4. distribute-lft-neg-out 36.8%

         \[\leadsto \color{blue}{\left(-a \cdot x\right) \cdot t} \]

      5. *-commutative 36.8%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right)} \]

      6. *-commutative 36.8%

         \[\leadsto t \cdot \left(-\color{blue}{x \cdot a}\right) \]

      7. distribute-rgt-neg-in 36.8%

         \[\leadsto t \cdot \color{blue}{\left(x \cdot \left(-a\right)\right)} \]

   10. Simplified 36.8%

       \[\leadsto \color{blue}{t \cdot \left(x \cdot \left(-a\right)\right)} \]

   if 1.9e8 < j < 6.0000000000000002e28

   1. Initial program 66.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in z around inf 53.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   3. Step-by-step derivation

      1. *-commutative 53.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 53.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   4. Simplified 53.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   5. Taylor expanded in y around 0 36.5%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. *-commutative 36.5%

         \[\leadsto z \cdot \left(-\color{blue}{c \cdot b}\right) \]

      3. distribute-rgt-neg-in 36.5%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   7. Simplified 36.5%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if 6.0000000000000002e28 < j < 4.5999999999999999e116

   1. Initial program 88.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 88.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 93.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 93.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 93.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 93.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 93.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 77.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 77.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 77.3%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]
   7. Step-by-step derivation

      1. fma-udef 71.4%

         \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right) + \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

      2. *-commutative 71.4%

         \[\leadsto j \cdot \left(a \cdot c - y \cdot i\right) + \mathsf{fma}\left(-a, \color{blue}{x \cdot t}, b \cdot \left(i \cdot t - c \cdot z\right)\right) \]

      3. *-commutative 71.4%

         \[\leadsto j \cdot \left(a \cdot c - y \cdot i\right) + \mathsf{fma}\left(-a, x \cdot t, b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right)\right) \]

      4. *-commutative 71.4%

         \[\leadsto j \cdot \left(a \cdot c - y \cdot i\right) + \mathsf{fma}\left(-a, x \cdot t, b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right)\right) \]

   8. Applied egg-rr 71.4%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right) + \mathsf{fma}\left(-a, x \cdot t, b \cdot \left(t \cdot i - z \cdot c\right)\right)} \]

   9. Taylor expanded in y around 0 65.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(a \cdot \left(c \cdot j\right) + b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]
   10. Step-by-step derivation

       1. associate-+r+ 65.8%

          \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)\right) + b \cdot \left(i \cdot t - c \cdot z\right)} \]

       2. mul-1-neg 65.8%

          \[\leadsto \left(\color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(c \cdot j\right)\right) + b \cdot \left(i \cdot t - c \cdot z\right) \]

       3. distribute-rgt-neg-in 65.8%

          \[\leadsto \left(\color{blue}{a \cdot \left(-t \cdot x\right)} + a \cdot \left(c \cdot j\right)\right) + b \cdot \left(i \cdot t - c \cdot z\right) \]

       4. mul-1-neg 65.8%

          \[\leadsto \left(a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} + a \cdot \left(c \cdot j\right)\right) + b \cdot \left(i \cdot t - c \cdot z\right) \]

       5. distribute-lft-in 65.8%

          \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} + b \cdot \left(i \cdot t - c \cdot z\right) \]

       6. fma-def 65.8%

          \[\leadsto \color{blue}{\mathsf{fma}\left(a, -1 \cdot \left(t \cdot x\right) + c \cdot j, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

       7. +-commutative 65.8%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{c \cdot j + -1 \cdot \left(t \cdot x\right)}, b \cdot \left(i \cdot t - c \cdot z\right)\right) \]

       8. mul-1-neg 65.8%

          \[\leadsto \mathsf{fma}\left(a, c \cdot j + \color{blue}{\left(-t \cdot x\right)}, b \cdot \left(i \cdot t - c \cdot z\right)\right) \]

       9. unsub-neg 65.8%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{c \cdot j - t \cdot x}, b \cdot \left(i \cdot t - c \cdot z\right)\right) \]

       10. *-commutative 65.8%

           \[\leadsto \mathsf{fma}\left(a, \color{blue}{j \cdot c} - t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right) \]

   11. Simplified 65.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(a, j \cdot c - t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)} \]

   12. Taylor expanded in j around inf 42.4%

       \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   13. Step-by-step derivation

       1. associate-*r* 47.8%

          \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

       2. *-commutative 47.8%

          \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

       3. associate-*r* 47.9%

          \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   14. Simplified 47.9%

       \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if 4.5999999999999999e116 < j

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 82.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 82.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 82.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 82.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 82.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 71.4%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 71.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 71.4%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 73.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 73.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in y around inf 47.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 47.8%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 47.8%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

      4. *-commutative 47.8%

         \[\leadsto \color{blue}{\left(y \cdot j\right)} \cdot \left(-i\right) \]

   9. Simplified 47.8%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.8 \cdot 10^{-38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -8.4 \cdot 10^{-191}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{-273}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2.05 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 190000000:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(-b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.6 \cdot 10^{+116}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 15: 52.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.3 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -3.3e-34)
     t_2
     (if (<= j -5.2e-194)
       (* b (- (* t i) (* z c)))
       (if (<= j -1.55e-304)
         t_1
         (if (<= j 5.5e-128)
           (* t (- (* b i) (* x a)))
           (if (<= j 5.8e+52) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.3e-34) {
		tmp = t_2;
	} else if (j <= -5.2e-194) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -1.55e-304) {
		tmp = t_1;
	} else if (j <= 5.5e-128) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 5.8e+52) {
		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))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-3.3d-34)) then
        tmp = t_2
    else if (j <= (-5.2d-194)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= (-1.55d-304)) then
        tmp = t_1
    else if (j <= 5.5d-128) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 5.8d+52) 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));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -3.3e-34) {
		tmp = t_2;
	} else if (j <= -5.2e-194) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -1.55e-304) {
		tmp = t_1;
	} else if (j <= 5.5e-128) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 5.8e+52) {
		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))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -3.3e-34:
		tmp = t_2
	elif j <= -5.2e-194:
		tmp = b * ((t * i) - (z * c))
	elif j <= -1.55e-304:
		tmp = t_1
	elif j <= 5.5e-128:
		tmp = t * ((b * i) - (x * a))
	elif j <= 5.8e+52:
		tmp = t_1
	else:
		tmp = t_2
	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)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.3e-34)
		tmp = t_2;
	elseif (j <= -5.2e-194)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= -1.55e-304)
		tmp = t_1;
	elseif (j <= 5.5e-128)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 5.8e+52)
		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));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.3e-34)
		tmp = t_2;
	elseif (j <= -5.2e-194)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= -1.55e-304)
		tmp = t_1;
	elseif (j <= 5.5e-128)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 5.8e+52)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.3e-34], t$95$2, If[LessEqual[j, -5.2e-194], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.55e-304], t$95$1, If[LessEqual[j, 5.5e-128], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.8e+52], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.29999999999999983e-34 or 5.8e52 < j

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 83.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 83.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 74.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 74.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 74.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 75.0%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 75.0%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in j around inf 66.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   8. Step-by-step derivation

      1. sub-neg 66.8%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 66.8%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 66.8%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   9. Simplified 66.8%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -3.29999999999999983e-34 < j < -5.20000000000000003e-194

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 64.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.20000000000000003e-194 < j < -1.54999999999999992e-304 or 5.5000000000000004e-128 < j < 5.8e52

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 75.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 75.3%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 75.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   5. Applied egg-rr 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \left(\mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right) + \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. count-2 61.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in x around inf 65.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   9. Step-by-step derivation

      1. *-commutative 65.3%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

      2. *-commutative 65.3%

         \[\leadsto x \cdot \left(z \cdot y - \color{blue}{t \cdot a}\right) \]

   10. Simplified 65.3%

       \[\leadsto \color{blue}{x \cdot \left(z \cdot y - t \cdot a\right)} \]

   if -1.54999999999999992e-304 < j < 5.5000000000000004e-128

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 77.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 77.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   5. Applied egg-rr 60.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \left(\mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right) + \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. count-2 60.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 60.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in t around inf 49.5%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 49.5%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(-a \cdot x\right)} + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      2. associate--l+ 49.5%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a \cdot x\right) + \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} \]

      3. distribute-lft-in 46.7%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      4. distribute-lft1-in 46.7%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot \left(b \cdot i\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      5. metadata-eval 46.7%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(\color{blue}{0} \cdot \left(b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. *-commutative 46.7%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(0 \cdot \color{blue}{\left(i \cdot b\right)}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. mul0-lft 60.6%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      8. metadata-eval 60.6%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(\color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. neg-sub0 60.6%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(--1 \cdot \left(b \cdot i\right)\right)} \]

      10. mul-1-neg 60.6%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(-\color{blue}{\left(-b \cdot i\right)}\right) \]

      11. *-commutative 60.6%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(-\left(-\color{blue}{i \cdot b}\right)\right) \]

      12. remove-double-neg 60.6%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(i \cdot b\right)} \]

      13. *-commutative 60.6%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(b \cdot i\right)} \]

   10. Simplified 66.2%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.3 \cdot 10^{-34}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 16: 41.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -1.55 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= i -1.55e+121)
     (* b (* t i))
     (if (<= i 4e+27)
       t_1
       (if (<= i 8.5e+140)
         (* i (* y (- j)))
         (if (<= i 1.5e+190) t_1 (* t (* b i))))))))

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 * ((c * j) - (x * t));
	double tmp;
	if (i <= -1.55e+121) {
		tmp = b * (t * i);
	} else if (i <= 4e+27) {
		tmp = t_1;
	} else if (i <= 8.5e+140) {
		tmp = i * (y * -j);
	} else if (i <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = t * (b * 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) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (i <= (-1.55d+121)) then
        tmp = b * (t * i)
    else if (i <= 4d+27) then
        tmp = t_1
    else if (i <= 8.5d+140) then
        tmp = i * (y * -j)
    else if (i <= 1.5d+190) then
        tmp = t_1
    else
        tmp = t * (b * 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 t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -1.55e+121) {
		tmp = b * (t * i);
	} else if (i <= 4e+27) {
		tmp = t_1;
	} else if (i <= 8.5e+140) {
		tmp = i * (y * -j);
	} else if (i <= 1.5e+190) {
		tmp = t_1;
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if i <= -1.55e+121:
		tmp = b * (t * i)
	elif i <= 4e+27:
		tmp = t_1
	elif i <= 8.5e+140:
		tmp = i * (y * -j)
	elif i <= 1.5e+190:
		tmp = t_1
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (i <= -1.55e+121)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 4e+27)
		tmp = t_1;
	elseif (i <= 8.5e+140)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (i <= 1.5e+190)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (i <= -1.55e+121)
		tmp = b * (t * i);
	elseif (i <= 4e+27)
		tmp = t_1;
	elseif (i <= 8.5e+140)
		tmp = i * (y * -j);
	elseif (i <= 1.5e+190)
		tmp = t_1;
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.55e+121], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+27], t$95$1, If[LessEqual[i, 8.5e+140], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+190], t$95$1, N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.55000000000000004e121

   1. Initial program 61.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 60.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 45.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 45.1%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   5. Simplified 45.1%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.55000000000000004e121 < i < 4.0000000000000001e27 or 8.4999999999999996e140 < i < 1.49999999999999991e190

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 50.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 50.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 50.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 4.0000000000000001e27 < i < 8.4999999999999996e140

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 68.6%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 68.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 68.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 68.6%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 68.6%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in y around inf 43.1%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 43.1%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 43.1%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 43.1%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

      4. *-commutative 43.1%

         \[\leadsto \color{blue}{\left(y \cdot j\right)} \cdot \left(-i\right) \]

   9. Simplified 43.1%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]

   if 1.49999999999999991e190 < i

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 61.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 59.2%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+27}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{+140}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+190}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 17: 50.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -8.5 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -8.5e+147)
     t_2
     (if (<= b -2.6e-209)
       t_1
       (if (<= b 1.65e-253)
         (* a (- (* c j) (* x t)))
         (if (<= b 4.2e-47) 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 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.5e+147) {
		tmp = t_2;
	} else if (b <= -2.6e-209) {
		tmp = t_1;
	} else if (b <= 1.65e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 4.2e-47) {
		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 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-8.5d+147)) then
        tmp = t_2
    else if (b <= (-2.6d-209)) then
        tmp = t_1
    else if (b <= 1.65d-253) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 4.2d-47) 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 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -8.5e+147) {
		tmp = t_2;
	} else if (b <= -2.6e-209) {
		tmp = t_1;
	} else if (b <= 1.65e-253) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 4.2e-47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -8.5e+147:
		tmp = t_2
	elif b <= -2.6e-209:
		tmp = t_1
	elif b <= 1.65e-253:
		tmp = a * ((c * j) - (x * t))
	elif b <= 4.2e-47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -8.5e+147)
		tmp = t_2;
	elseif (b <= -2.6e-209)
		tmp = t_1;
	elseif (b <= 1.65e-253)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 4.2e-47)
		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 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -8.5e+147)
		tmp = t_2;
	elseif (b <= -2.6e-209)
		tmp = t_1;
	elseif (b <= 1.65e-253)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 4.2e-47)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.5e+147], t$95$2, If[LessEqual[b, -2.6e-209], t$95$1, If[LessEqual[b, 1.65e-253], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.2e-47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.5000000000000007e147 or 4.2000000000000001e-47 < b

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 62.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -8.5000000000000007e147 < b < -2.59999999999999984e-209 or 1.65e-253 < b < 4.2000000000000001e-47

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 80.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 81.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 81.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 81.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 81.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 81.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 68.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 68.7%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 68.7%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in j around inf 57.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   8. Step-by-step derivation

      1. sub-neg 57.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 57.7%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 57.7%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   9. Simplified 57.7%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -2.59999999999999984e-209 < b < 1.65e-253

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 57.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 57.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 57.7%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 57.7%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 57.7%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 57.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-209}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-47}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 18: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-234}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.8e-33)
     t_1
     (if (<= j -6e-234)
       (* b (- (* t i) (* z c)))
       (if (<= j -3.8e-298)
         (* z (* x y))
         (if (<= j 6e-53) (* t (- (* b i) (* 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.8e-33) {
		tmp = t_1;
	} else if (j <= -6e-234) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -3.8e-298) {
		tmp = z * (x * y);
	} else if (j <= 6e-53) {
		tmp = t * ((b * i) - (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 = j * ((a * c) - (y * i))
    if (j <= (-1.8d-33)) then
        tmp = t_1
    else if (j <= (-6d-234)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= (-3.8d-298)) then
        tmp = z * (x * y)
    else if (j <= 6d-53) then
        tmp = t * ((b * i) - (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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.8e-33) {
		tmp = t_1;
	} else if (j <= -6e-234) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= -3.8e-298) {
		tmp = z * (x * y);
	} else if (j <= 6e-53) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.8e-33:
		tmp = t_1
	elif j <= -6e-234:
		tmp = b * ((t * i) - (z * c))
	elif j <= -3.8e-298:
		tmp = z * (x * y)
	elif j <= 6e-53:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.8e-33)
		tmp = t_1;
	elseif (j <= -6e-234)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= -3.8e-298)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 6e-53)
		tmp = Float64(t * Float64(Float64(b * i) - 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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.8e-33)
		tmp = t_1;
	elseif (j <= -6e-234)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= -3.8e-298)
		tmp = z * (x * y);
	elseif (j <= 6e-53)
		tmp = t * ((b * i) - (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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.8e-33], t$95$1, If[LessEqual[j, -6e-234], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.8e-298], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-53], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.80000000000000017e-33 or 6.0000000000000004e-53 < j

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 81.1%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 83.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 74.2%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 74.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 74.2%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 74.9%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in j around inf 62.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   8. Step-by-step derivation

      1. sub-neg 62.6%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 62.6%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 62.6%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   9. Simplified 62.6%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -1.80000000000000017e-33 < j < -5.99999999999999975e-234

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 61.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.99999999999999975e-234 < j < -3.8e-298

   1. Initial program 61.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in z around inf 74.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   3. Step-by-step derivation

      1. *-commutative 74.1%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 74.1%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   4. Simplified 74.1%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   5. Taylor expanded in y around inf 60.6%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if -3.8e-298 < j < 6.0000000000000004e-53

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 77.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 77.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 77.8%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   5. Applied egg-rr 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \left(\mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right) + \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)\right)}\right) \]
   6. Step-by-step derivation

      1. count-2 61.1%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   7. Simplified 61.1%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) + 2 \cdot \mathsf{fma}\left(-\left(c \cdot z - i \cdot t\right), b, b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

   8. Taylor expanded in t around inf 49.8%

      \[\leadsto \color{blue}{t \cdot \left(\left(-1 \cdot \left(a \cdot x\right) + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   9. Step-by-step derivation

      1. neg-mul-1 49.8%

         \[\leadsto t \cdot \left(\left(\color{blue}{\left(-a \cdot x\right)} + 2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      2. associate--l+ 49.8%

         \[\leadsto t \cdot \color{blue}{\left(\left(-a \cdot x\right) + \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)\right)} \]

      3. distribute-lft-in 48.0%

         \[\leadsto \color{blue}{t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(-1 \cdot \left(b \cdot i\right) + b \cdot i\right) - -1 \cdot \left(b \cdot i\right)\right)} \]

      4. distribute-lft1-in 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{\left(\left(-1 + 1\right) \cdot \left(b \cdot i\right)\right)} - -1 \cdot \left(b \cdot i\right)\right) \]

      5. metadata-eval 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(\color{blue}{0} \cdot \left(b \cdot i\right)\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      6. *-commutative 48.0%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \left(0 \cdot \color{blue}{\left(i \cdot b\right)}\right) - -1 \cdot \left(b \cdot i\right)\right) \]

      7. mul0-lft 61.1%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(2 \cdot \color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      8. metadata-eval 61.1%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(\color{blue}{0} - -1 \cdot \left(b \cdot i\right)\right) \]

      9. neg-sub0 61.1%

         \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(--1 \cdot \left(b \cdot i\right)\right)} \]

      10. mul-1-neg 61.1%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(-\color{blue}{\left(-b \cdot i\right)}\right) \]

      11. *-commutative 61.1%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \left(-\left(-\color{blue}{i \cdot b}\right)\right) \]

      12. remove-double-neg 61.1%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(i \cdot b\right)} \]

      13. *-commutative 61.1%

          \[\leadsto t \cdot \left(-a \cdot x\right) + t \cdot \color{blue}{\left(b \cdot i\right)} \]

   10. Simplified 64.8%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.8 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-234}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.8 \cdot 10^{-298}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 19: 30.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.4e+57)
   (* b (* t i))
   (if (<= i -5e-145)
     (* a (* c j))
     (if (<= i 4.8e-72)
       (* z (* x y))
       (if (<= i 1.85e+48) (* a (* t (- x))) (* t (* b 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 (i <= -5.4e+57) {
		tmp = b * (t * i);
	} else if (i <= -5e-145) {
		tmp = a * (c * j);
	} else if (i <= 4.8e-72) {
		tmp = z * (x * y);
	} else if (i <= 1.85e+48) {
		tmp = a * (t * -x);
	} else {
		tmp = t * (b * 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 (i <= (-5.4d+57)) then
        tmp = b * (t * i)
    else if (i <= (-5d-145)) then
        tmp = a * (c * j)
    else if (i <= 4.8d-72) then
        tmp = z * (x * y)
    else if (i <= 1.85d+48) then
        tmp = a * (t * -x)
    else
        tmp = t * (b * 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 (i <= -5.4e+57) {
		tmp = b * (t * i);
	} else if (i <= -5e-145) {
		tmp = a * (c * j);
	} else if (i <= 4.8e-72) {
		tmp = z * (x * y);
	} else if (i <= 1.85e+48) {
		tmp = a * (t * -x);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.4e+57:
		tmp = b * (t * i)
	elif i <= -5e-145:
		tmp = a * (c * j)
	elif i <= 4.8e-72:
		tmp = z * (x * y)
	elif i <= 1.85e+48:
		tmp = a * (t * -x)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.4e+57)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= -5e-145)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 4.8e-72)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.85e+48)
		tmp = Float64(a * Float64(t * Float64(-x)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.4e+57)
		tmp = b * (t * i);
	elseif (i <= -5e-145)
		tmp = a * (c * j);
	elseif (i <= 4.8e-72)
		tmp = z * (x * y);
	elseif (i <= 1.85e+48)
		tmp = a * (t * -x);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.4e+57], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5e-145], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.8e-72], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.85e+48], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.3999999999999997e57

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 63.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   5. Simplified 47.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -5.3999999999999997e57 < i < -4.9999999999999998e-145

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   5. Taylor expanded in j around inf 34.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -4.9999999999999998e-145 < i < 4.8e-72

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in z around inf 51.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 51.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   4. Simplified 51.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   5. Taylor expanded in y around inf 35.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if 4.8e-72 < i < 1.85e48

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 53.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 53.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 53.6%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 53.6%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   5. Taylor expanded in j around 0 32.3%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 32.3%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 32.3%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 32.3%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   7. Simplified 32.3%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   if 1.85e48 < i

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 57.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 42.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 43.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 43.4%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   5. Simplified 43.4%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-145}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.85 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 20: 29.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4.9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.3 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -4.9e+57)
   (* b (* t i))
   (if (<= i -1.35e-144)
     (* a (* c j))
     (if (<= i 5.3e-78)
       (* z (* x y))
       (if (<= i 3e+192) (* j (- (* y i))) (* t (* b 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 (i <= -4.9e+57) {
		tmp = b * (t * i);
	} else if (i <= -1.35e-144) {
		tmp = a * (c * j);
	} else if (i <= 5.3e-78) {
		tmp = z * (x * y);
	} else if (i <= 3e+192) {
		tmp = j * -(y * i);
	} else {
		tmp = t * (b * 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 (i <= (-4.9d+57)) then
        tmp = b * (t * i)
    else if (i <= (-1.35d-144)) then
        tmp = a * (c * j)
    else if (i <= 5.3d-78) then
        tmp = z * (x * y)
    else if (i <= 3d+192) then
        tmp = j * -(y * i)
    else
        tmp = t * (b * 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 (i <= -4.9e+57) {
		tmp = b * (t * i);
	} else if (i <= -1.35e-144) {
		tmp = a * (c * j);
	} else if (i <= 5.3e-78) {
		tmp = z * (x * y);
	} else if (i <= 3e+192) {
		tmp = j * -(y * i);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -4.9e+57:
		tmp = b * (t * i)
	elif i <= -1.35e-144:
		tmp = a * (c * j)
	elif i <= 5.3e-78:
		tmp = z * (x * y)
	elif i <= 3e+192:
		tmp = j * -(y * i)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -4.9e+57)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= -1.35e-144)
		tmp = Float64(a * Float64(c * j));
	elseif (i <= 5.3e-78)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3e+192)
		tmp = Float64(j * Float64(-Float64(y * i)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -4.9e+57)
		tmp = b * (t * i);
	elseif (i <= -1.35e-144)
		tmp = a * (c * j);
	elseif (i <= 5.3e-78)
		tmp = z * (x * y);
	elseif (i <= 3e+192)
		tmp = j * -(y * i);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -4.9e+57], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.35e-144], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.3e-78], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+192], N[(j * (-N[(y * i), $MachinePrecision])), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.8999999999999999e57

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 63.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 47.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   5. Simplified 47.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -4.8999999999999999e57 < i < -1.34999999999999988e-144

   1. Initial program 88.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 54.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   5. Taylor expanded in j around inf 34.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.34999999999999988e-144 < i < 5.29999999999999957e-78

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in z around inf 51.8%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.8%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 51.8%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   4. Simplified 51.8%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   5. Taylor expanded in y around inf 35.8%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if 5.29999999999999957e-78 < i < 3e192

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. +-commutative 75.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot a - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      2. fma-def 75.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot a - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right)} \]

      3. *-commutative 75.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{a \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) \]

      4. sub-neg 75.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z + \left(-t \cdot i\right)\right)}\right) \]

      5. sub-neg 75.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(c \cdot z - t \cdot i\right)}\right) \]

      6. *-commutative 75.9%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)\right) \]

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - t \cdot i\right)\right)} \]

   4. Taylor expanded in y around 0 73.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - b \cdot \left(c \cdot z - i \cdot t\right)}\right) \]
   5. Step-by-step derivation

      1. associate-*r* 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      2. neg-mul-1 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) - b \cdot \left(c \cdot z - i \cdot t\right)\right) \]

      3. fma-neg 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, -b \cdot \left(c \cdot z - i \cdot t\right)\right)}\right) \]

      4. distribute-rgt-neg-in 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      5. neg-sub0 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(0 - \left(c \cdot z - i \cdot t\right)\right)}\right)\right) \]

      6. associate--r- 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)}\right)\right) \]

      7. neg-sub0 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right)\right)\right) \]

      8. +-commutative 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)}\right)\right) \]

      9. sub-neg 73.5%

         \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \mathsf{fma}\left(-a, t \cdot x, b \cdot \color{blue}{\left(i \cdot t - c \cdot z\right)}\right)\right) \]

   6. Simplified 73.5%

      \[\leadsto \mathsf{fma}\left(j, a \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(-a, t \cdot x, b \cdot \left(i \cdot t - c \cdot z\right)\right)}\right) \]

   7. Taylor expanded in y around inf 31.0%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 31.0%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 31.0%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 31.0%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

      4. *-commutative 31.0%

         \[\leadsto \color{blue}{\left(y \cdot j\right)} \cdot \left(-i\right) \]

   9. Simplified 31.0%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]

   10. Taylor expanded in y around 0 31.0%

       \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 31.0%

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

       2. neg-mul-1 31.0%

          \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

       3. *-commutative 31.0%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*l* 30.7%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   12. Simplified 30.7%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   if 3e192 < i

   1. Initial program 67.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 61.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 56.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 59.2%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. *-commutative 59.2%

         \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   5. Simplified 59.2%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.9 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-144}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq 5.3 \cdot 10^{-78}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+192}:\\ \;\;\;\;j \cdot \left(-y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 21: 31.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+22} \lor \neg \left(t \leq 27500000\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -5.1e+22) (not (<= t 27500000.0))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -5.1e+22) || !(t <= 27500000.0)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	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 ((t <= (-5.1d+22)) .or. (.not. (t <= 27500000.0d0))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    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 ((t <= -5.1e+22) || !(t <= 27500000.0)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -5.1e+22) or not (t <= 27500000.0):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -5.1e+22) || !(t <= 27500000.0))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -5.1e+22) || ~((t <= 27500000.0)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -5.1e+22], N[Not[LessEqual[t, 27500000.0]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1000000000000002e22 or 2.75e7 < t

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in j around 0 70.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   3. Taylor expanded in i around inf 39.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.6%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   5. Simplified 39.6%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -5.1000000000000002e22 < t < 2.75e7

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 43.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   3. Step-by-step derivation

      1. +-commutative 43.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.2%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   4. Simplified 43.2%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   5. Taylor expanded in j around inf 34.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{+22} \lor \neg \left(t \leq 27500000\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 22: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

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 * (c * j)
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 * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in a around inf 40.9%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
3. Step-by-step derivation

   1. +-commutative 40.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.9%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 40.9%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

4. Simplified 40.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

5. Taylor expanded in j around inf 24.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

6. Final simplification 24.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))