Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.5% → 82.9%

Time: 36.2s

Alternatives: 26

Speedup: 0.5×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \cdot t\_2 + \left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (- (* t c) (* y i))))
   (if (<= (+ (* j t_2) (+ (* x (- (* y z) (* t a))) t_1)) INFINITY)
     (fma j t_2 (+ (* x (fma y z (* t (- a)))) t_1))
     (* y (- (* x z) (* i 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 = b * ((a * i) - (z * c));
	double t_2 = (t * c) - (y * i);
	double tmp;
	if (((j * t_2) + ((x * ((y * z) - (t * a))) + t_1)) <= ((double) INFINITY)) {
		tmp = fma(j, t_2, ((x * fma(y, z, (t * -a))) + t_1));
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (Float64(Float64(j * t_2) + Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)) <= Inf)
		tmp = fma(j, t_2, Float64(Float64(x * fma(y, z, Float64(t * Float64(-a)))) + t_1));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(j * t$95$2), $MachinePrecision] + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + N[(N[(x * N[(y * z + N[(t * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 91.6%

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

      3. *-commutative 91.6%

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

      4. *-commutative 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. cancel-sign-sub 91.6%

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

      7. *-commutative 91.6%

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

      8. fma-neg 91.6%

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

      9. *-commutative 91.6%

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

      10. distribute-rgt-neg-out 91.6%

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

      11. remove-double-neg 91.6%

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

      12. *-commutative 91.6%

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

      13. *-commutative 91.6%

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

   3. Simplified 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 87.0%

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

Alternative 2: 82.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (* j (- (* t c) (* y i)))
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c)))))))
   (if (<= t_1 INFINITY) t_1 (* y (- (* x z) (* i 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 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * ((x * z) - (i * j));
	}
	return tmp;
}

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   5. Simplified 60.0%

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

4. Final simplification 87.0%

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

Alternative 3: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) - t\_1\\ \mathbf{if}\;j \leq -6.9 \cdot 10^{+16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-116}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - t\_1\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{-97}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+227}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+280}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b c)))
        (t_2 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_3 (- (* x (- (* y z) (* t a))) t_1)))
   (if (<= j -6.9e+16)
     t_2
     (if (<= j -4.6e-116)
       t_3
       (if (<= j -7.2e-168)
         (- (* i (* a b)) t_1)
         (if (<= j 8.8e-97)
           t_3
           (if (<= j 4.2e+37)
             t_2
             (if (<= j 1.12e+101)
               t_3
               (if (<= j 2e+227)
                 (* y (- (* x z) (* i j)))
                 (if (<= j 2.45e+280) (* c (- (* t 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 = z * (b * c);
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = (x * ((y * z) - (t * a))) - t_1;
	double tmp;
	if (j <= -6.9e+16) {
		tmp = t_2;
	} else if (j <= -4.6e-116) {
		tmp = t_3;
	} else if (j <= -7.2e-168) {
		tmp = (i * (a * b)) - t_1;
	} else if (j <= 8.8e-97) {
		tmp = t_3;
	} else if (j <= 4.2e+37) {
		tmp = t_2;
	} else if (j <= 1.12e+101) {
		tmp = t_3;
	} else if (j <= 2e+227) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.45e+280) {
		tmp = c * ((t * 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) :: t_3
    real(8) :: tmp
    t_1 = z * (b * c)
    t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_3 = (x * ((y * z) - (t * a))) - t_1
    if (j <= (-6.9d+16)) then
        tmp = t_2
    else if (j <= (-4.6d-116)) then
        tmp = t_3
    else if (j <= (-7.2d-168)) then
        tmp = (i * (a * b)) - t_1
    else if (j <= 8.8d-97) then
        tmp = t_3
    else if (j <= 4.2d+37) then
        tmp = t_2
    else if (j <= 1.12d+101) then
        tmp = t_3
    else if (j <= 2d+227) then
        tmp = y * ((x * z) - (i * j))
    else if (j <= 2.45d+280) then
        tmp = c * ((t * 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 = z * (b * c);
	double t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	double t_3 = (x * ((y * z) - (t * a))) - t_1;
	double tmp;
	if (j <= -6.9e+16) {
		tmp = t_2;
	} else if (j <= -4.6e-116) {
		tmp = t_3;
	} else if (j <= -7.2e-168) {
		tmp = (i * (a * b)) - t_1;
	} else if (j <= 8.8e-97) {
		tmp = t_3;
	} else if (j <= 4.2e+37) {
		tmp = t_2;
	} else if (j <= 1.12e+101) {
		tmp = t_3;
	} else if (j <= 2e+227) {
		tmp = y * ((x * z) - (i * j));
	} else if (j <= 2.45e+280) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * c)
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_3 = (x * ((y * z) - (t * a))) - t_1
	tmp = 0
	if j <= -6.9e+16:
		tmp = t_2
	elif j <= -4.6e-116:
		tmp = t_3
	elif j <= -7.2e-168:
		tmp = (i * (a * b)) - t_1
	elif j <= 8.8e-97:
		tmp = t_3
	elif j <= 4.2e+37:
		tmp = t_2
	elif j <= 1.12e+101:
		tmp = t_3
	elif j <= 2e+227:
		tmp = y * ((x * z) - (i * j))
	elif j <= 2.45e+280:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * c))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1)
	tmp = 0.0
	if (j <= -6.9e+16)
		tmp = t_2;
	elseif (j <= -4.6e-116)
		tmp = t_3;
	elseif (j <= -7.2e-168)
		tmp = Float64(Float64(i * Float64(a * b)) - t_1);
	elseif (j <= 8.8e-97)
		tmp = t_3;
	elseif (j <= 4.2e+37)
		tmp = t_2;
	elseif (j <= 1.12e+101)
		tmp = t_3;
	elseif (j <= 2e+227)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (j <= 2.45e+280)
		tmp = Float64(c * Float64(Float64(t * 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 = z * (b * c);
	t_2 = (j * ((t * c) - (y * i))) + (x * (y * z));
	t_3 = (x * ((y * z) - (t * a))) - t_1;
	tmp = 0.0;
	if (j <= -6.9e+16)
		tmp = t_2;
	elseif (j <= -4.6e-116)
		tmp = t_3;
	elseif (j <= -7.2e-168)
		tmp = (i * (a * b)) - t_1;
	elseif (j <= 8.8e-97)
		tmp = t_3;
	elseif (j <= 4.2e+37)
		tmp = t_2;
	elseif (j <= 1.12e+101)
		tmp = t_3;
	elseif (j <= 2e+227)
		tmp = y * ((x * z) - (i * j));
	elseif (j <= 2.45e+280)
		tmp = c * ((t * 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[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[j, -6.9e+16], t$95$2, If[LessEqual[j, -4.6e-116], t$95$3, If[LessEqual[j, -7.2e-168], N[(N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 8.8e-97], t$95$3, If[LessEqual[j, 4.2e+37], t$95$2, If[LessEqual[j, 1.12e+101], t$95$3, If[LessEqual[j, 2e+227], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.45e+280], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -6.9e16 or 8.7999999999999996e-97 < j < 4.2000000000000002e37 or 2.45000000000000016e280 < j

   1. Initial program 80.9%

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

   3. Taylor expanded in b around 0 75.8%

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

   4. Taylor expanded in a around 0 75.6%

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

   if -6.9e16 < j < -4.60000000000000003e-116 or -7.1999999999999998e-168 < j < 8.7999999999999996e-97 or 4.2000000000000002e37 < j < 1.1199999999999999e101

   1. Initial program 78.7%

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

   3. Taylor expanded in j around 0 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in c around inf 67.4%

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

      1. associate-*r* 70.0%

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

   8. Simplified 70.0%

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

   if -4.60000000000000003e-116 < j < -7.1999999999999998e-168

   1. Initial program 65.9%

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

   3. Taylor expanded in b around inf 71.2%

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

   4. Taylor expanded in a around 0 65.8%

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

      1. mul-1-neg 65.8%

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

      2. +-commutative 65.8%

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

      3. unsub-neg 65.8%

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

      4. associate-*r* 71.2%

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

      5. associate-*r* 76.8%

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

   6. Simplified 76.8%

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

   if 1.1199999999999999e101 < j < 2.0000000000000002e227

   1. Initial program 75.7%

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

   3. Taylor expanded in y around inf 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if 2.0000000000000002e227 < j < 2.45000000000000016e280

   1. Initial program 76.7%

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

   3. Taylor expanded in c around inf 77.9%

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

      1. *-commutative 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.9 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq -4.6 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-168}:\\ \;\;\;\;i \cdot \left(a \cdot b\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 8.8 \cdot 10^{-97}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+37}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.12 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+227}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;j \leq 2.45 \cdot 10^{+280}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 30.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+76}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -0.114:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= y -2.5e+76)
     (* (* y i) (- j))
     (if (<= y -0.114)
       t_1
       (if (<= y -1.75e-106)
         (* a (* b i))
         (if (<= y -2.3e-227)
           t_1
           (if (<= y 2.9e-303)
             (* c (* t j))
             (if (<= y 4.2e-192)
               (* a (- (* x t)))
               (if (<= y 5e-151)
                 (* j (* t c))
                 (if (<= y 1.8e-63)
                   (* i (* a b))
                   (if (<= y 9.6e+86)
                     (* y (* i (- j)))
                     (* x (* y z)))))))))))))

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 * (z * -c);
	double tmp;
	if (y <= -2.5e+76) {
		tmp = (y * i) * -j;
	} else if (y <= -0.114) {
		tmp = t_1;
	} else if (y <= -1.75e-106) {
		tmp = a * (b * i);
	} else if (y <= -2.3e-227) {
		tmp = t_1;
	} else if (y <= 2.9e-303) {
		tmp = c * (t * j);
	} else if (y <= 4.2e-192) {
		tmp = a * -(x * t);
	} else if (y <= 5e-151) {
		tmp = j * (t * c);
	} else if (y <= 1.8e-63) {
		tmp = i * (a * b);
	} else if (y <= 9.6e+86) {
		tmp = y * (i * -j);
	} else {
		tmp = x * (y * z);
	}
	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 = b * (z * -c)
    if (y <= (-2.5d+76)) then
        tmp = (y * i) * -j
    else if (y <= (-0.114d0)) then
        tmp = t_1
    else if (y <= (-1.75d-106)) then
        tmp = a * (b * i)
    else if (y <= (-2.3d-227)) then
        tmp = t_1
    else if (y <= 2.9d-303) then
        tmp = c * (t * j)
    else if (y <= 4.2d-192) then
        tmp = a * -(x * t)
    else if (y <= 5d-151) then
        tmp = j * (t * c)
    else if (y <= 1.8d-63) then
        tmp = i * (a * b)
    else if (y <= 9.6d+86) then
        tmp = y * (i * -j)
    else
        tmp = x * (y * z)
    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 * (z * -c);
	double tmp;
	if (y <= -2.5e+76) {
		tmp = (y * i) * -j;
	} else if (y <= -0.114) {
		tmp = t_1;
	} else if (y <= -1.75e-106) {
		tmp = a * (b * i);
	} else if (y <= -2.3e-227) {
		tmp = t_1;
	} else if (y <= 2.9e-303) {
		tmp = c * (t * j);
	} else if (y <= 4.2e-192) {
		tmp = a * -(x * t);
	} else if (y <= 5e-151) {
		tmp = j * (t * c);
	} else if (y <= 1.8e-63) {
		tmp = i * (a * b);
	} else if (y <= 9.6e+86) {
		tmp = y * (i * -j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if y <= -2.5e+76:
		tmp = (y * i) * -j
	elif y <= -0.114:
		tmp = t_1
	elif y <= -1.75e-106:
		tmp = a * (b * i)
	elif y <= -2.3e-227:
		tmp = t_1
	elif y <= 2.9e-303:
		tmp = c * (t * j)
	elif y <= 4.2e-192:
		tmp = a * -(x * t)
	elif y <= 5e-151:
		tmp = j * (t * c)
	elif y <= 1.8e-63:
		tmp = i * (a * b)
	elif y <= 9.6e+86:
		tmp = y * (i * -j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (y <= -2.5e+76)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (y <= -0.114)
		tmp = t_1;
	elseif (y <= -1.75e-106)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= -2.3e-227)
		tmp = t_1;
	elseif (y <= 2.9e-303)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 4.2e-192)
		tmp = Float64(a * Float64(-Float64(x * t)));
	elseif (y <= 5e-151)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 1.8e-63)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 9.6e+86)
		tmp = Float64(y * Float64(i * Float64(-j)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (y <= -2.5e+76)
		tmp = (y * i) * -j;
	elseif (y <= -0.114)
		tmp = t_1;
	elseif (y <= -1.75e-106)
		tmp = a * (b * i);
	elseif (y <= -2.3e-227)
		tmp = t_1;
	elseif (y <= 2.9e-303)
		tmp = c * (t * j);
	elseif (y <= 4.2e-192)
		tmp = a * -(x * t);
	elseif (y <= 5e-151)
		tmp = j * (t * c);
	elseif (y <= 1.8e-63)
		tmp = i * (a * b);
	elseif (y <= 9.6e+86)
		tmp = y * (i * -j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+76], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[y, -0.114], t$95$1, If[LessEqual[y, -1.75e-106], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-227], t$95$1, If[LessEqual[y, 2.9e-303], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-192], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 5e-151], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-63], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+86], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -2.49999999999999996e76

   1. Initial program 70.7%

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

   3. Taylor expanded in j around inf 69.9%

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

   4. Taylor expanded in c around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-lft-neg-out 64.2%

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

      3. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   if -2.49999999999999996e76 < y < -0.114000000000000004 or -1.75e-106 < y < -2.30000000000000012e-227

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 70.8%

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

   4. Taylor expanded in a around 0 55.2%

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

      1. associate-*r* 55.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 55.2%

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

   6. Simplified 55.2%

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

   if -0.114000000000000004 < y < -1.75e-106

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 45.3%

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

      3. associate-*r* 48.6%

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

      4. associate-*r* 48.6%

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

      5. distribute-rgt-in 48.6%

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

      6. +-commutative 48.6%

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

      7. mul-1-neg 48.6%

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

      8. unsub-neg 48.6%

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

      9. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in a around inf 36.3%

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

   if -2.30000000000000012e-227 < y < 2.90000000000000014e-303

   1. Initial program 72.3%

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

   3. Taylor expanded in t around -inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. *-commutative 49.1%

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

      3. distribute-rgt-neg-in 49.1%

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

      4. +-commutative 49.1%

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

      5. mul-1-neg 49.1%

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

      6. unsub-neg 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around 0 40.3%

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

   if 2.90000000000000014e-303 < y < 4.19999999999999986e-192

   1. Initial program 78.7%

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

   3. Taylor expanded in t around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. *-commutative 61.1%

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

      3. distribute-rgt-neg-in 61.1%

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

      4. +-commutative 61.1%

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

      5. mul-1-neg 61.1%

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

      6. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. mul-1-neg 41.7%

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

      2. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 4.19999999999999986e-192 < y < 5.00000000000000003e-151

   1. Initial program 75.7%

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

   3. Taylor expanded in t around -inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. *-commutative 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

      4. +-commutative 75.4%

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

      5. mul-1-neg 75.4%

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

      6. unsub-neg 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around 0 64.3%

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

   7. Taylor expanded in a around 0 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 50.9%

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

   9. Simplified 50.9%

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

   if 5.00000000000000003e-151 < y < 1.80000000000000004e-63

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-*r* 65.2%

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

      3. associate-*r* 65.2%

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

      4. associate-*r* 65.2%

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

      5. distribute-rgt-in 65.2%

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

      6. +-commutative 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. *-commutative 65.2%

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

   5. Simplified 65.2%

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

      1. cancel-sign-sub-inv 65.2%

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

      2. *-commutative 65.2%

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

      3. fma-define 65.3%

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

      4. *-commutative 65.3%

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

      5. *-commutative 65.3%

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

   7. Applied egg-rr 65.3%

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

   8. Taylor expanded in a around inf 57.9%

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

      1. associate-*r* 64.8%

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

      2. *-commutative 64.8%

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

   10. Simplified 64.8%

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

   if 1.80000000000000004e-63 < y < 9.6000000000000001e86

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. distribute-lft-neg-out 36.8%

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

      3. *-commutative 36.8%

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

   8. Simplified 36.8%

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

   if 9.6000000000000001e86 < y

   1. Initial program 73.9%

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

   3. Taylor expanded in t around 0 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*r* 51.8%

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

      3. associate-*r* 63.2%

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

      4. associate-*r* 63.2%

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

      5. distribute-rgt-in 74.3%

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

      6. +-commutative 74.3%

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

      7. mul-1-neg 74.3%

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

      8. unsub-neg 74.3%

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

      9. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in x around inf 39.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+76}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -0.114:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-106}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+73}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -25.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-191}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+87}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= y -7e+73)
     (* (* y i) (- j))
     (if (<= y -25.5)
       t_1
       (if (<= y -1.26e-105)
         (* a (* b i))
         (if (<= y -1.75e-227)
           t_1
           (if (<= y 2.3e-303)
             (* c (* t j))
             (if (<= y 3.4e-191)
               (* a (- (* x t)))
               (if (<= y 4.5e-151)
                 (* j (* t c))
                 (if (<= y 1.95e-63)
                   (* i (* a b))
                   (if (<= y 7e+87) (* i (* y (- j))) (* x (* y z)))))))))))))

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 * (z * -c);
	double tmp;
	if (y <= -7e+73) {
		tmp = (y * i) * -j;
	} else if (y <= -25.5) {
		tmp = t_1;
	} else if (y <= -1.26e-105) {
		tmp = a * (b * i);
	} else if (y <= -1.75e-227) {
		tmp = t_1;
	} else if (y <= 2.3e-303) {
		tmp = c * (t * j);
	} else if (y <= 3.4e-191) {
		tmp = a * -(x * t);
	} else if (y <= 4.5e-151) {
		tmp = j * (t * c);
	} else if (y <= 1.95e-63) {
		tmp = i * (a * b);
	} else if (y <= 7e+87) {
		tmp = i * (y * -j);
	} else {
		tmp = x * (y * z);
	}
	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 = b * (z * -c)
    if (y <= (-7d+73)) then
        tmp = (y * i) * -j
    else if (y <= (-25.5d0)) then
        tmp = t_1
    else if (y <= (-1.26d-105)) then
        tmp = a * (b * i)
    else if (y <= (-1.75d-227)) then
        tmp = t_1
    else if (y <= 2.3d-303) then
        tmp = c * (t * j)
    else if (y <= 3.4d-191) then
        tmp = a * -(x * t)
    else if (y <= 4.5d-151) then
        tmp = j * (t * c)
    else if (y <= 1.95d-63) then
        tmp = i * (a * b)
    else if (y <= 7d+87) then
        tmp = i * (y * -j)
    else
        tmp = x * (y * z)
    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 * (z * -c);
	double tmp;
	if (y <= -7e+73) {
		tmp = (y * i) * -j;
	} else if (y <= -25.5) {
		tmp = t_1;
	} else if (y <= -1.26e-105) {
		tmp = a * (b * i);
	} else if (y <= -1.75e-227) {
		tmp = t_1;
	} else if (y <= 2.3e-303) {
		tmp = c * (t * j);
	} else if (y <= 3.4e-191) {
		tmp = a * -(x * t);
	} else if (y <= 4.5e-151) {
		tmp = j * (t * c);
	} else if (y <= 1.95e-63) {
		tmp = i * (a * b);
	} else if (y <= 7e+87) {
		tmp = i * (y * -j);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if y <= -7e+73:
		tmp = (y * i) * -j
	elif y <= -25.5:
		tmp = t_1
	elif y <= -1.26e-105:
		tmp = a * (b * i)
	elif y <= -1.75e-227:
		tmp = t_1
	elif y <= 2.3e-303:
		tmp = c * (t * j)
	elif y <= 3.4e-191:
		tmp = a * -(x * t)
	elif y <= 4.5e-151:
		tmp = j * (t * c)
	elif y <= 1.95e-63:
		tmp = i * (a * b)
	elif y <= 7e+87:
		tmp = i * (y * -j)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (y <= -7e+73)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (y <= -25.5)
		tmp = t_1;
	elseif (y <= -1.26e-105)
		tmp = Float64(a * Float64(b * i));
	elseif (y <= -1.75e-227)
		tmp = t_1;
	elseif (y <= 2.3e-303)
		tmp = Float64(c * Float64(t * j));
	elseif (y <= 3.4e-191)
		tmp = Float64(a * Float64(-Float64(x * t)));
	elseif (y <= 4.5e-151)
		tmp = Float64(j * Float64(t * c));
	elseif (y <= 1.95e-63)
		tmp = Float64(i * Float64(a * b));
	elseif (y <= 7e+87)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (y <= -7e+73)
		tmp = (y * i) * -j;
	elseif (y <= -25.5)
		tmp = t_1;
	elseif (y <= -1.26e-105)
		tmp = a * (b * i);
	elseif (y <= -1.75e-227)
		tmp = t_1;
	elseif (y <= 2.3e-303)
		tmp = c * (t * j);
	elseif (y <= 3.4e-191)
		tmp = a * -(x * t);
	elseif (y <= 4.5e-151)
		tmp = j * (t * c);
	elseif (y <= 1.95e-63)
		tmp = i * (a * b);
	elseif (y <= 7e+87)
		tmp = i * (y * -j);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+73], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[y, -25.5], t$95$1, If[LessEqual[y, -1.26e-105], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-227], t$95$1, If[LessEqual[y, 2.3e-303], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-191], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, 4.5e-151], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-63], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+87], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if y < -7.00000000000000004e73

   1. Initial program 70.7%

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

   3. Taylor expanded in j around inf 69.9%

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

   4. Taylor expanded in c around 0 64.2%

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

      1. mul-1-neg 64.2%

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

      2. distribute-lft-neg-out 64.2%

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

      3. *-commutative 64.2%

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

   6. Simplified 64.2%

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

   if -7.00000000000000004e73 < y < -25.5 or -1.2600000000000001e-105 < y < -1.75000000000000005e-227

   1. Initial program 86.4%

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

   3. Taylor expanded in b around inf 70.8%

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

   4. Taylor expanded in a around 0 55.2%

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

      1. associate-*r* 55.2%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 55.2%

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

   6. Simplified 55.2%

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

   if -25.5 < y < -1.2600000000000001e-105

   1. Initial program 88.3%

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

   3. Taylor expanded in t around 0 48.8%

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

      1. *-commutative 48.8%

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

      2. associate-*r* 45.3%

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

      3. associate-*r* 48.6%

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

      4. associate-*r* 48.6%

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

      5. distribute-rgt-in 48.6%

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

      6. +-commutative 48.6%

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

      7. mul-1-neg 48.6%

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

      8. unsub-neg 48.6%

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

      9. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in a around inf 36.3%

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

   if -1.75000000000000005e-227 < y < 2.29999999999999995e-303

   1. Initial program 72.3%

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

   3. Taylor expanded in t around -inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. *-commutative 49.1%

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

      3. distribute-rgt-neg-in 49.1%

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

      4. +-commutative 49.1%

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

      5. mul-1-neg 49.1%

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

      6. unsub-neg 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in a around 0 40.3%

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

   if 2.29999999999999995e-303 < y < 3.39999999999999994e-191

   1. Initial program 78.7%

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

   3. Taylor expanded in t around -inf 61.1%

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

      1. mul-1-neg 61.1%

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

      2. *-commutative 61.1%

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

      3. distribute-rgt-neg-in 61.1%

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

      4. +-commutative 61.1%

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

      5. mul-1-neg 61.1%

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

      6. unsub-neg 61.1%

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

   5. Simplified 61.1%

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

   6. Taylor expanded in a around inf 41.7%

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

      1. mul-1-neg 41.7%

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

      2. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 3.39999999999999994e-191 < y < 4.5000000000000002e-151

   1. Initial program 75.7%

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

   3. Taylor expanded in t around -inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. *-commutative 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

      4. +-commutative 75.4%

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

      5. mul-1-neg 75.4%

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

      6. unsub-neg 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in a around 0 64.3%

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

   7. Taylor expanded in a around 0 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*l* 50.9%

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

   9. Simplified 50.9%

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

   if 4.5000000000000002e-151 < y < 1.95000000000000011e-63

   1. Initial program 71.4%

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

   3. Taylor expanded in t around 0 65.1%

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

      1. *-commutative 65.1%

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

      2. associate-*r* 65.2%

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

      3. associate-*r* 65.2%

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

      4. associate-*r* 65.2%

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

      5. distribute-rgt-in 65.2%

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

      6. +-commutative 65.2%

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

      7. mul-1-neg 65.2%

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

      8. unsub-neg 65.2%

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

      9. *-commutative 65.2%

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

   5. Simplified 65.2%

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

      1. cancel-sign-sub-inv 65.2%

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

      2. *-commutative 65.2%

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

      3. fma-define 65.3%

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

      4. *-commutative 65.3%

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

      5. *-commutative 65.3%

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

   7. Applied egg-rr 65.3%

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

   8. Taylor expanded in a around inf 57.9%

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

      1. associate-*r* 64.8%

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

      2. *-commutative 64.8%

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

   10. Simplified 64.8%

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

   if 1.95000000000000011e-63 < y < 6.99999999999999972e87

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 48.4%

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

      1. +-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

      4. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   6. Taylor expanded in z around 0 36.9%

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

      1. associate-*r* 36.9%

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

      2. neg-mul-1 36.9%

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

   8. Simplified 36.9%

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

   if 6.99999999999999972e87 < y

   1. Initial program 73.9%

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

   3. Taylor expanded in t around 0 52.1%

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

      1. *-commutative 52.1%

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

      2. associate-*r* 51.8%

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

      3. associate-*r* 63.2%

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

      4. associate-*r* 63.2%

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

      5. distribute-rgt-in 74.3%

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

      6. +-commutative 74.3%

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

      7. mul-1-neg 74.3%

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

      8. unsub-neg 74.3%

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

      9. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in x around inf 39.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+73}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;y \leq -25.5:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-105}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-227}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-303}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-191}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+87}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;c \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-166}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-23}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (* y z))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= c -7.2e+64)
     t_2
     (if (<= c -2.2e-166)
       t_1
       (if (<= c -9.8e-273)
         (- (* a (* b i)) (* y (* i j)))
         (if (<= c 1.8e-175)
           t_3
           (if (<= c 1.12e-74)
             (* i (- (* a b) (* y j)))
             (if (<= c 8.8e-23) t_3 (if (<= c 1.45e+118) 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 * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -7.2e+64) {
		tmp = t_2;
	} else if (c <= -2.2e-166) {
		tmp = t_1;
	} else if (c <= -9.8e-273) {
		tmp = (a * (b * i)) - (y * (i * j));
	} else if (c <= 1.8e-175) {
		tmp = t_3;
	} else if (c <= 1.12e-74) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 8.8e-23) {
		tmp = t_3;
	} else if (c <= 1.45e+118) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (j * ((t * c) - (y * i))) + (x * (y * z))
    t_2 = c * ((t * j) - (z * b))
    t_3 = x * ((y * z) - (t * a))
    if (c <= (-7.2d+64)) then
        tmp = t_2
    else if (c <= (-2.2d-166)) then
        tmp = t_1
    else if (c <= (-9.8d-273)) then
        tmp = (a * (b * i)) - (y * (i * j))
    else if (c <= 1.8d-175) then
        tmp = t_3
    else if (c <= 1.12d-74) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 8.8d-23) then
        tmp = t_3
    else if (c <= 1.45d+118) 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 * ((t * c) - (y * i))) + (x * (y * z));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (c <= -7.2e+64) {
		tmp = t_2;
	} else if (c <= -2.2e-166) {
		tmp = t_1;
	} else if (c <= -9.8e-273) {
		tmp = (a * (b * i)) - (y * (i * j));
	} else if (c <= 1.8e-175) {
		tmp = t_3;
	} else if (c <= 1.12e-74) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 8.8e-23) {
		tmp = t_3;
	} else if (c <= 1.45e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * (y * z))
	t_2 = c * ((t * j) - (z * b))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if c <= -7.2e+64:
		tmp = t_2
	elif c <= -2.2e-166:
		tmp = t_1
	elif c <= -9.8e-273:
		tmp = (a * (b * i)) - (y * (i * j))
	elif c <= 1.8e-175:
		tmp = t_3
	elif c <= 1.12e-74:
		tmp = i * ((a * b) - (y * j))
	elif c <= 8.8e-23:
		tmp = t_3
	elif c <= 1.45e+118:
		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(t * c) - Float64(y * i))) + Float64(x * Float64(y * z)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (c <= -7.2e+64)
		tmp = t_2;
	elseif (c <= -2.2e-166)
		tmp = t_1;
	elseif (c <= -9.8e-273)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(y * Float64(i * j)));
	elseif (c <= 1.8e-175)
		tmp = t_3;
	elseif (c <= 1.12e-74)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 8.8e-23)
		tmp = t_3;
	elseif (c <= 1.45e+118)
		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 * ((t * c) - (y * i))) + (x * (y * z));
	t_2 = c * ((t * j) - (z * b));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (c <= -7.2e+64)
		tmp = t_2;
	elseif (c <= -2.2e-166)
		tmp = t_1;
	elseif (c <= -9.8e-273)
		tmp = (a * (b * i)) - (y * (i * j));
	elseif (c <= 1.8e-175)
		tmp = t_3;
	elseif (c <= 1.12e-74)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 8.8e-23)
		tmp = t_3;
	elseif (c <= 1.45e+118)
		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[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.2e+64], t$95$2, If[LessEqual[c, -2.2e-166], t$95$1, If[LessEqual[c, -9.8e-273], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e-175], t$95$3, If[LessEqual[c, 1.12e-74], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.8e-23], t$95$3, If[LessEqual[c, 1.45e+118], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.20000000000000027e64 or 1.45000000000000008e118 < c

   1. Initial program 67.8%

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

   3. Taylor expanded in c around inf 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -7.20000000000000027e64 < c < -2.2000000000000001e-166 or 8.7999999999999998e-23 < c < 1.45000000000000008e118

   1. Initial program 87.4%

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

   3. Taylor expanded in b around 0 72.1%

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

   4. Taylor expanded in a around 0 63.6%

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

   if -2.2000000000000001e-166 < c < -9.79999999999999928e-273

   1. Initial program 79.9%

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

   3. Taylor expanded in t around 0 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-*r* 55.6%

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

      3. associate-*r* 59.7%

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

      4. associate-*r* 59.7%

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

      5. distribute-rgt-in 68.1%

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

      6. +-commutative 68.1%

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

      7. mul-1-neg 68.1%

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

      8. unsub-neg 68.1%

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

      9. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in z around 0 59.4%

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

      1. distribute-lft-out-- 59.4%

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

      2. associate-*r* 63.5%

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

   8. Simplified 63.5%

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

   if -9.79999999999999928e-273 < c < 1.8e-175 or 1.11999999999999999e-74 < c < 8.7999999999999998e-23

   1. Initial program 81.5%

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

   3. Taylor expanded in b around 0 77.9%

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

   4. Taylor expanded in j around 0 66.8%

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

   if 1.8e-175 < c < 1.11999999999999999e-74

   1. Initial program 74.9%

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

   3. Taylor expanded in t around 0 57.3%

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

      1. *-commutative 57.3%

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

      2. associate-*r* 69.8%

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

      3. associate-*r* 63.6%

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

      4. associate-*r* 63.6%

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

      5. distribute-rgt-in 69.8%

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

      6. +-commutative 69.8%

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

      7. mul-1-neg 69.8%

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

      8. unsub-neg 69.8%

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

      9. *-commutative 69.8%

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

   5. Simplified 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. *-commutative 69.8%

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

      3. fma-define 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

   7. Applied egg-rr 69.8%

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

   8. Taylor expanded in z around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-in 75.2%

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

      3. mul-1-neg 75.2%

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

      4. associate-*r* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-lft-in 81.2%

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

      7. +-commutative 81.2%

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

      8. mul-1-neg 81.2%

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

      9. unsub-neg 81.2%

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

   10. Simplified 81.2%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-166}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq -9.8 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 8.8 \cdot 10^{-23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1.26 \cdot 10^{-143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-272}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 10^{+61}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* i (- (* a b) (* y j))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -1.15e+64)
     t_3
     (if (<= c -2.5e-33)
       (* j (- (* t c) (* y i)))
       (if (<= c -1.26e-143)
         t_1
         (if (<= c -7.8e-272)
           t_2
           (if (<= c 2.6e-175)
             t_1
             (if (<= c 2.65e-76)
               t_2
               (if (<= c 1.2e-5) t_1 (if (<= c 1e+61) 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 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+64) {
		tmp = t_3;
	} else if (c <= -2.5e-33) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= -1.26e-143) {
		tmp = t_1;
	} else if (c <= -7.8e-272) {
		tmp = t_2;
	} else if (c <= 2.6e-175) {
		tmp = t_1;
	} else if (c <= 2.65e-76) {
		tmp = t_2;
	} else if (c <= 1.2e-5) {
		tmp = t_1;
	} else if (c <= 1e+61) {
		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 = x * ((y * z) - (t * a))
    t_2 = i * ((a * b) - (y * j))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-1.15d+64)) then
        tmp = t_3
    else if (c <= (-2.5d-33)) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= (-1.26d-143)) then
        tmp = t_1
    else if (c <= (-7.8d-272)) then
        tmp = t_2
    else if (c <= 2.6d-175) then
        tmp = t_1
    else if (c <= 2.65d-76) then
        tmp = t_2
    else if (c <= 1.2d-5) then
        tmp = t_1
    else if (c <= 1d+61) 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 = x * ((y * z) - (t * a));
	double t_2 = i * ((a * b) - (y * j));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.15e+64) {
		tmp = t_3;
	} else if (c <= -2.5e-33) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= -1.26e-143) {
		tmp = t_1;
	} else if (c <= -7.8e-272) {
		tmp = t_2;
	} else if (c <= 2.6e-175) {
		tmp = t_1;
	} else if (c <= 2.65e-76) {
		tmp = t_2;
	} else if (c <= 1.2e-5) {
		tmp = t_1;
	} else if (c <= 1e+61) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((a * b) - (y * j))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.15e+64:
		tmp = t_3
	elif c <= -2.5e-33:
		tmp = j * ((t * c) - (y * i))
	elif c <= -1.26e-143:
		tmp = t_1
	elif c <= -7.8e-272:
		tmp = t_2
	elif c <= 2.6e-175:
		tmp = t_1
	elif c <= 2.65e-76:
		tmp = t_2
	elif c <= 1.2e-5:
		tmp = t_1
	elif c <= 1e+61:
		tmp = t_2
	else:
		tmp = t_3
	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(i * Float64(Float64(a * b) - Float64(y * j)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.15e+64)
		tmp = t_3;
	elseif (c <= -2.5e-33)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= -1.26e-143)
		tmp = t_1;
	elseif (c <= -7.8e-272)
		tmp = t_2;
	elseif (c <= 2.6e-175)
		tmp = t_1;
	elseif (c <= 2.65e-76)
		tmp = t_2;
	elseif (c <= 1.2e-5)
		tmp = t_1;
	elseif (c <= 1e+61)
		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 = x * ((y * z) - (t * a));
	t_2 = i * ((a * b) - (y * j));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.15e+64)
		tmp = t_3;
	elseif (c <= -2.5e-33)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= -1.26e-143)
		tmp = t_1;
	elseif (c <= -7.8e-272)
		tmp = t_2;
	elseif (c <= 2.6e-175)
		tmp = t_1;
	elseif (c <= 2.65e-76)
		tmp = t_2;
	elseif (c <= 1.2e-5)
		tmp = t_1;
	elseif (c <= 1e+61)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+64], t$95$3, If[LessEqual[c, -2.5e-33], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.26e-143], t$95$1, If[LessEqual[c, -7.8e-272], t$95$2, If[LessEqual[c, 2.6e-175], t$95$1, If[LessEqual[c, 2.65e-76], t$95$2, If[LessEqual[c, 1.2e-5], t$95$1, If[LessEqual[c, 1e+61], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.15e64 or 9.99999999999999949e60 < c

   1. Initial program 70.8%

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

   3. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -1.15e64 < c < -2.50000000000000014e-33

   1. Initial program 88.0%

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

   3. Taylor expanded in j around inf 70.2%

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

   if -2.50000000000000014e-33 < c < -1.2600000000000001e-143 or -7.7999999999999994e-272 < c < 2.6e-175 or 2.65e-76 < c < 1.2e-5

   1. Initial program 85.1%

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

   3. Taylor expanded in b around 0 77.0%

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

   4. Taylor expanded in j around 0 60.2%

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

   if -1.2600000000000001e-143 < c < -7.7999999999999994e-272 or 2.6e-175 < c < 2.65e-76 or 1.2e-5 < c < 9.99999999999999949e60

   1. Initial program 78.8%

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

   3. Taylor expanded in t around 0 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-*r* 64.4%

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

      3. associate-*r* 63.0%

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

      4. associate-*r* 63.0%

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

      5. distribute-rgt-in 69.2%

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

      6. +-commutative 69.2%

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

      7. mul-1-neg 69.2%

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

      8. unsub-neg 69.2%

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

      9. *-commutative 69.2%

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

   5. Simplified 69.2%

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

      1. cancel-sign-sub-inv 69.2%

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

      2. *-commutative 69.2%

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

      3. fma-define 69.2%

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

      4. *-commutative 69.2%

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

      5. *-commutative 69.2%

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

   7. Applied egg-rr 69.2%

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

   8. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. distribute-rgt-neg-in 63.6%

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

      3. mul-1-neg 63.6%

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

      4. associate-*r* 65.3%

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

      5. *-commutative 65.3%

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

      6. distribute-lft-in 65.3%

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

      7. +-commutative 65.3%

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

      8. mul-1-neg 65.3%

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

      9. unsub-neg 65.3%

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

   10. Simplified 65.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq -1.26 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -7.8 \cdot 10^{-272}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 10^{+61}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a)))))
        (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.9e+69)
     t_2
     (if (<= c -1.65e-246)
       t_1
       (if (<= c -6.2e-271)
         (* i (* a b))
         (if (<= c 1.75e-127)
           t_1
           (if (<= c 1.35e-77)
             (* i (- (* a b) (* y j)))
             (if (<= c 7.4e+118) 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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.9e+69) {
		tmp = t_2;
	} else if (c <= -1.65e-246) {
		tmp = t_1;
	} else if (c <= -6.2e-271) {
		tmp = i * (a * b);
	} else if (c <= 1.75e-127) {
		tmp = t_1;
	} else if (c <= 1.35e-77) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.4e+118) {
		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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.9d+69)) then
        tmp = t_2
    else if (c <= (-1.65d-246)) then
        tmp = t_1
    else if (c <= (-6.2d-271)) then
        tmp = i * (a * b)
    else if (c <= 1.75d-127) then
        tmp = t_1
    else if (c <= 1.35d-77) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= 7.4d+118) 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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.9e+69) {
		tmp = t_2;
	} else if (c <= -1.65e-246) {
		tmp = t_1;
	} else if (c <= -6.2e-271) {
		tmp = i * (a * b);
	} else if (c <= 1.75e-127) {
		tmp = t_1;
	} else if (c <= 1.35e-77) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= 7.4e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.9e+69:
		tmp = t_2
	elif c <= -1.65e-246:
		tmp = t_1
	elif c <= -6.2e-271:
		tmp = i * (a * b)
	elif c <= 1.75e-127:
		tmp = t_1
	elif c <= 1.35e-77:
		tmp = i * ((a * b) - (y * j))
	elif c <= 7.4e+118:
		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(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.9e+69)
		tmp = t_2;
	elseif (c <= -1.65e-246)
		tmp = t_1;
	elseif (c <= -6.2e-271)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 1.75e-127)
		tmp = t_1;
	elseif (c <= 1.35e-77)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= 7.4e+118)
		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 * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.9e+69)
		tmp = t_2;
	elseif (c <= -1.65e-246)
		tmp = t_1;
	elseif (c <= -6.2e-271)
		tmp = i * (a * b);
	elseif (c <= 1.75e-127)
		tmp = t_1;
	elseif (c <= 1.35e-77)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= 7.4e+118)
		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[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.9e+69], t$95$2, If[LessEqual[c, -1.65e-246], t$95$1, If[LessEqual[c, -6.2e-271], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e-127], t$95$1, If[LessEqual[c, 1.35e-77], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.4e+118], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.8999999999999999e69 or 7.39999999999999973e118 < c

   1. Initial program 67.8%

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

   3. Taylor expanded in c around inf 74.7%

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

      1. *-commutative 74.7%

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

   5. Simplified 74.7%

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

   if -3.8999999999999999e69 < c < -1.65e-246 or -6.1999999999999998e-271 < c < 1.74999999999999995e-127 or 1.35e-77 < c < 7.39999999999999973e118

   1. Initial program 85.2%

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

   3. Taylor expanded in b around 0 72.3%

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

   if -1.65e-246 < c < -6.1999999999999998e-271

   1. Initial program 84.5%

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

   3. Taylor expanded in t around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r* 67.8%

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

      3. associate-*r* 84.5%

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

      4. associate-*r* 84.5%

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

      5. distribute-rgt-in 84.5%

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

      6. +-commutative 84.5%

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

      7. mul-1-neg 84.5%

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

      8. unsub-neg 84.5%

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

      9. *-commutative 84.5%

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

   5. Simplified 84.5%

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

      1. cancel-sign-sub-inv 84.5%

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

      2. *-commutative 84.5%

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

      3. fma-define 84.5%

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

      4. *-commutative 84.5%

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

      5. *-commutative 84.5%

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

   7. Applied egg-rr 84.5%

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

   8. Taylor expanded in a around inf 99.7%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

   10. Simplified 100.0%

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

   if 1.74999999999999995e-127 < c < 1.35e-77

   1. Initial program 59.8%

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

   3. Taylor expanded in t around 0 50.6%

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

      1. *-commutative 50.6%

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

      2. associate-*r* 70.6%

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

      3. associate-*r* 70.3%

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

      4. associate-*r* 70.3%

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

      5. distribute-rgt-in 80.3%

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

      6. +-commutative 80.3%

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

      7. mul-1-neg 80.3%

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

      8. unsub-neg 80.3%

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

      9. *-commutative 80.3%

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

   5. Simplified 80.3%

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

      1. cancel-sign-sub-inv 80.3%

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

      2. *-commutative 80.3%

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

      3. fma-define 80.3%

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

      4. *-commutative 80.3%

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

      5. *-commutative 80.3%

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

   7. Applied egg-rr 80.3%

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

   8. Taylor expanded in z around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-rgt-neg-in 80.7%

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

      3. mul-1-neg 80.7%

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

      4. associate-*r* 90.3%

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

      5. *-commutative 90.3%

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

      6. distribute-lft-in 90.3%

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

      7. +-commutative 90.3%

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

      8. mul-1-neg 90.3%

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

      9. unsub-neg 90.3%

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

   10. Simplified 90.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.9 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-246}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-271}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 7.4 \cdot 10^{+118}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t\_3 + x \cdot \left(y \cdot z\right)\\ t_5 := t\_3 + t\_1\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+218}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+280}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* a i) (* z c)))))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ t_3 (* x (* y z))))
        (t_5 (+ t_3 t_1)))
   (if (<= j -2.5e-29)
     t_5
     (if (<= j 3.25e-84)
       t_2
       (if (<= j 2.8e+36)
         t_4
         (if (<= j 1.16e+100)
           t_2
           (if (<= j 1.75e+218)
             t_5
             (if (<= j 2.6e+280) (* c (- (* t j) (* z b))) t_4))))))))

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 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + (x * (y * z));
	double t_5 = t_3 + t_1;
	double tmp;
	if (j <= -2.5e-29) {
		tmp = t_5;
	} else if (j <= 3.25e-84) {
		tmp = t_2;
	} else if (j <= 2.8e+36) {
		tmp = t_4;
	} else if (j <= 1.16e+100) {
		tmp = t_2;
	} else if (j <= 1.75e+218) {
		tmp = t_5;
	} else if (j <= 2.6e+280) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_4;
	}
	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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((a * i) - (z * c)))
    t_3 = j * ((t * c) - (y * i))
    t_4 = t_3 + (x * (y * z))
    t_5 = t_3 + t_1
    if (j <= (-2.5d-29)) then
        tmp = t_5
    else if (j <= 3.25d-84) then
        tmp = t_2
    else if (j <= 2.8d+36) then
        tmp = t_4
    else if (j <= 1.16d+100) then
        tmp = t_2
    else if (j <= 1.75d+218) then
        tmp = t_5
    else if (j <= 2.6d+280) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_4
    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 = t_1 + (b * ((a * i) - (z * c)));
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + (x * (y * z));
	double t_5 = t_3 + t_1;
	double tmp;
	if (j <= -2.5e-29) {
		tmp = t_5;
	} else if (j <= 3.25e-84) {
		tmp = t_2;
	} else if (j <= 2.8e+36) {
		tmp = t_4;
	} else if (j <= 1.16e+100) {
		tmp = t_2;
	} else if (j <= 1.75e+218) {
		tmp = t_5;
	} else if (j <= 2.6e+280) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((a * i) - (z * c)))
	t_3 = j * ((t * c) - (y * i))
	t_4 = t_3 + (x * (y * z))
	t_5 = t_3 + t_1
	tmp = 0
	if j <= -2.5e-29:
		tmp = t_5
	elif j <= 3.25e-84:
		tmp = t_2
	elif j <= 2.8e+36:
		tmp = t_4
	elif j <= 1.16e+100:
		tmp = t_2
	elif j <= 1.75e+218:
		tmp = t_5
	elif j <= 2.6e+280:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_4
	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(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(t_3 + Float64(x * Float64(y * z)))
	t_5 = Float64(t_3 + t_1)
	tmp = 0.0
	if (j <= -2.5e-29)
		tmp = t_5;
	elseif (j <= 3.25e-84)
		tmp = t_2;
	elseif (j <= 2.8e+36)
		tmp = t_4;
	elseif (j <= 1.16e+100)
		tmp = t_2;
	elseif (j <= 1.75e+218)
		tmp = t_5;
	elseif (j <= 2.6e+280)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_4;
	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 = t_1 + (b * ((a * i) - (z * c)));
	t_3 = j * ((t * c) - (y * i));
	t_4 = t_3 + (x * (y * z));
	t_5 = t_3 + t_1;
	tmp = 0.0;
	if (j <= -2.5e-29)
		tmp = t_5;
	elseif (j <= 3.25e-84)
		tmp = t_2;
	elseif (j <= 2.8e+36)
		tmp = t_4;
	elseif (j <= 1.16e+100)
		tmp = t_2;
	elseif (j <= 1.75e+218)
		tmp = t_5;
	elseif (j <= 2.6e+280)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_4;
	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[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -2.5e-29], t$95$5, If[LessEqual[j, 3.25e-84], t$95$2, If[LessEqual[j, 2.8e+36], t$95$4, If[LessEqual[j, 1.16e+100], t$95$2, If[LessEqual[j, 1.75e+218], t$95$5, If[LessEqual[j, 2.6e+280], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -2.49999999999999993e-29 or 1.1600000000000001e100 < j < 1.7500000000000001e218

   1. Initial program 79.7%

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

   3. Taylor expanded in b around 0 77.6%

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

   if -2.49999999999999993e-29 < j < 3.25000000000000011e-84 or 2.8000000000000001e36 < j < 1.1600000000000001e100

   1. Initial program 76.9%

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

   3. Taylor expanded in j around 0 77.0%

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

      1. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   if 3.25000000000000011e-84 < j < 2.8000000000000001e36 or 2.5999999999999999e280 < j

   1. Initial program 78.7%

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

   3. Taylor expanded in b around 0 75.0%

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

   4. Taylor expanded in a around 0 78.3%

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

   if 1.7500000000000001e218 < j < 2.5999999999999999e280

   1. Initial program 81.1%

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

   3. Taylor expanded in c around inf 75.7%

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

      1. *-commutative 75.7%

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

   5. Simplified 75.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{-29}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 1.16 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.75 \cdot 10^{+218}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+280}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;c \leq -1.26 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-162}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 0.00065:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -3.8e+70)
     t_3
     (if (<= c -1.26e-209)
       (* y (- (* x z) (* i j)))
       (if (<= c -6.1e-273)
         (- (* a (* b i)) (* y (* i j)))
         (if (<= c 3.4e-162)
           t_2
           (if (<= c 6.2e-77)
             t_1
             (if (<= c 0.00065) t_2 (if (<= c 3.9e+53) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.8e+70) {
		tmp = t_3;
	} else if (c <= -1.26e-209) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -6.1e-273) {
		tmp = (a * (b * i)) - (y * (i * j));
	} else if (c <= 3.4e-162) {
		tmp = t_2;
	} else if (c <= 6.2e-77) {
		tmp = t_1;
	} else if (c <= 0.00065) {
		tmp = t_2;
	} else if (c <= 3.9e+53) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = i * ((a * b) - (y * j))
    t_2 = x * ((y * z) - (t * a))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-3.8d+70)) then
        tmp = t_3
    else if (c <= (-1.26d-209)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= (-6.1d-273)) then
        tmp = (a * (b * i)) - (y * (i * j))
    else if (c <= 3.4d-162) then
        tmp = t_2
    else if (c <= 6.2d-77) then
        tmp = t_1
    else if (c <= 0.00065d0) then
        tmp = t_2
    else if (c <= 3.9d+53) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((a * b) - (y * j));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.8e+70) {
		tmp = t_3;
	} else if (c <= -1.26e-209) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -6.1e-273) {
		tmp = (a * (b * i)) - (y * (i * j));
	} else if (c <= 3.4e-162) {
		tmp = t_2;
	} else if (c <= 6.2e-77) {
		tmp = t_1;
	} else if (c <= 0.00065) {
		tmp = t_2;
	} else if (c <= 3.9e+53) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = x * ((y * z) - (t * a))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.8e+70:
		tmp = t_3
	elif c <= -1.26e-209:
		tmp = y * ((x * z) - (i * j))
	elif c <= -6.1e-273:
		tmp = (a * (b * i)) - (y * (i * j))
	elif c <= 3.4e-162:
		tmp = t_2
	elif c <= 6.2e-77:
		tmp = t_1
	elif c <= 0.00065:
		tmp = t_2
	elif c <= 3.9e+53:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.8e+70)
		tmp = t_3;
	elseif (c <= -1.26e-209)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= -6.1e-273)
		tmp = Float64(Float64(a * Float64(b * i)) - Float64(y * Float64(i * j)));
	elseif (c <= 3.4e-162)
		tmp = t_2;
	elseif (c <= 6.2e-77)
		tmp = t_1;
	elseif (c <= 0.00065)
		tmp = t_2;
	elseif (c <= 3.9e+53)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((a * b) - (y * j));
	t_2 = x * ((y * z) - (t * a));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.8e+70)
		tmp = t_3;
	elseif (c <= -1.26e-209)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= -6.1e-273)
		tmp = (a * (b * i)) - (y * (i * j));
	elseif (c <= 3.4e-162)
		tmp = t_2;
	elseif (c <= 6.2e-77)
		tmp = t_1;
	elseif (c <= 0.00065)
		tmp = t_2;
	elseif (c <= 3.9e+53)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e+70], t$95$3, If[LessEqual[c, -1.26e-209], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.1e-273], N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] - N[(y * N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e-162], t$95$2, If[LessEqual[c, 6.2e-77], t$95$1, If[LessEqual[c, 0.00065], t$95$2, If[LessEqual[c, 3.9e+53], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.7999999999999998e70 or 3.89999999999999976e53 < c

   1. Initial program 70.8%

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

   3. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -3.7999999999999998e70 < c < -1.26e-209

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

      4. *-commutative 56.2%

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

   5. Simplified 56.2%

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

   if -1.26e-209 < c < -6.09999999999999975e-273

   1. Initial program 92.7%

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

   3. Taylor expanded in t around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 56.0%

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

      3. associate-*r* 63.7%

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

      4. associate-*r* 63.7%

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

      5. distribute-rgt-in 63.7%

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

      6. +-commutative 63.7%

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

      7. mul-1-neg 63.7%

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

      8. unsub-neg 63.7%

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

      9. *-commutative 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. distribute-lft-out-- 63.1%

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

      2. associate-*r* 70.8%

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

   8. Simplified 70.8%

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

   if -6.09999999999999975e-273 < c < 3.4e-162 or 6.20000000000000016e-77 < c < 6.4999999999999997e-4

   1. Initial program 84.1%

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

   3. Taylor expanded in b around 0 81.0%

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

   4. Taylor expanded in j around 0 65.5%

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

   if 3.4e-162 < c < 6.20000000000000016e-77 or 6.4999999999999997e-4 < c < 3.89999999999999976e53

   1. Initial program 77.2%

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

   3. Taylor expanded in t around 0 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*r* 70.0%

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

      3. associate-*r* 64.5%

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

      4. associate-*r* 64.5%

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

      5. distribute-rgt-in 70.3%

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

      6. +-commutative 70.3%

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

      7. mul-1-neg 70.3%

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

      8. unsub-neg 70.3%

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

      9. *-commutative 70.3%

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

   5. Simplified 70.3%

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

      1. cancel-sign-sub-inv 70.3%

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

      2. *-commutative 70.3%

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

      3. fma-define 70.3%

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

      4. *-commutative 70.3%

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

      5. *-commutative 70.3%

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

   7. Applied egg-rr 70.3%

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

   8. Taylor expanded in z around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-rgt-neg-in 71.4%

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

      3. mul-1-neg 71.4%

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

      4. associate-*r* 74.2%

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

      5. *-commutative 74.2%

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

      6. distribute-lft-in 74.2%

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

      7. +-commutative 74.2%

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

      8. mul-1-neg 74.2%

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

      9. unsub-neg 74.2%

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

   10. Simplified 74.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.26 \cdot 10^{-209}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -6.1 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(b \cdot i\right) - y \cdot \left(i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 0.00065:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+95} \lor \neg \left(t \leq -2.4 \cdot 10^{-78}\right) \land \left(t \leq -2.55 \cdot 10^{-124} \lor \neg \left(t \leq 1.02 \cdot 10^{+43}\right) \land t \leq 1.95 \cdot 10^{+262}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.95e+95)
         (and (not (<= t -2.4e-78))
              (or (<= t -2.55e-124)
                  (and (not (<= t 1.02e+43)) (<= t 1.95e+262)))))
   (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))
   (+ (* y (- (* x z) (* i j))) (* b (- (* a 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 tmp;
	if ((t <= -1.95e+95) || (!(t <= -2.4e-78) && ((t <= -2.55e-124) || (!(t <= 1.02e+43) && (t <= 1.95e+262))))) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * 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) :: tmp
    if ((t <= (-1.95d+95)) .or. (.not. (t <= (-2.4d-78))) .and. (t <= (-2.55d-124)) .or. (.not. (t <= 1.02d+43)) .and. (t <= 1.95d+262)) then
        tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * 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 tmp;
	if ((t <= -1.95e+95) || (!(t <= -2.4e-78) && ((t <= -2.55e-124) || (!(t <= 1.02e+43) && (t <= 1.95e+262))))) {
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.95e+95) or (not (t <= -2.4e-78) and ((t <= -2.55e-124) or (not (t <= 1.02e+43) and (t <= 1.95e+262)))):
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.95e+95) || (!(t <= -2.4e-78) && ((t <= -2.55e-124) || (!(t <= 1.02e+43) && (t <= 1.95e+262)))))
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.95e+95) || (~((t <= -2.4e-78)) && ((t <= -2.55e-124) || (~((t <= 1.02e+43)) && (t <= 1.95e+262)))))
		tmp = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.95e+95], And[N[Not[LessEqual[t, -2.4e-78]], $MachinePrecision], Or[LessEqual[t, -2.55e-124], And[N[Not[LessEqual[t, 1.02e+43]], $MachinePrecision], LessEqual[t, 1.95e+262]]]]], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9499999999999999e95 or -2.4e-78 < t < -2.5500000000000001e-124 or 1.02e43 < t < 1.94999999999999993e262

   1. Initial program 74.8%

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

   3. Taylor expanded in b around 0 78.6%

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

   if -1.9499999999999999e95 < t < -2.4e-78 or -2.5500000000000001e-124 < t < 1.02e43 or 1.94999999999999993e262 < t

   1. Initial program 80.7%

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

   3. Taylor expanded in t around 0 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*r* 70.3%

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

      3. associate-*r* 74.0%

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

      4. associate-*r* 74.0%

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

      5. distribute-rgt-in 77.9%

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

      6. +-commutative 77.9%

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

      7. mul-1-neg 77.9%

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

      8. unsub-neg 77.9%

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

      9. *-commutative 77.9%

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

   5. Simplified 77.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+95} \lor \neg \left(t \leq -2.4 \cdot 10^{-78}\right) \land \left(t \leq -2.55 \cdot 10^{-124} \lor \neg \left(t \leq 1.02 \cdot 10^{+43}\right) \land t \leq 1.95 \cdot 10^{+262}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;i \leq -3.35 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3500:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 0.00125:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= i -3.35e+198)
     (* y (* i (- j)))
     (if (<= i -1.35e+102)
       (* a (* b i))
       (if (<= i -3500.0)
         (* c (* t j))
         (if (<= i -9e-64)
           (* t (* x (- a)))
           (if (<= i -1.1e-282)
             t_1
             (if (<= i 7.2e-116)
               (* j (* t c))
               (if (<= i 0.00125) t_1 (* (* y i) (- 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 = b * (z * -c);
	double tmp;
	if (i <= -3.35e+198) {
		tmp = y * (i * -j);
	} else if (i <= -1.35e+102) {
		tmp = a * (b * i);
	} else if (i <= -3500.0) {
		tmp = c * (t * j);
	} else if (i <= -9e-64) {
		tmp = t * (x * -a);
	} else if (i <= -1.1e-282) {
		tmp = t_1;
	} else if (i <= 7.2e-116) {
		tmp = j * (t * c);
	} else if (i <= 0.00125) {
		tmp = t_1;
	} else {
		tmp = (y * i) * -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 = b * (z * -c)
    if (i <= (-3.35d+198)) then
        tmp = y * (i * -j)
    else if (i <= (-1.35d+102)) then
        tmp = a * (b * i)
    else if (i <= (-3500.0d0)) then
        tmp = c * (t * j)
    else if (i <= (-9d-64)) then
        tmp = t * (x * -a)
    else if (i <= (-1.1d-282)) then
        tmp = t_1
    else if (i <= 7.2d-116) then
        tmp = j * (t * c)
    else if (i <= 0.00125d0) then
        tmp = t_1
    else
        tmp = (y * i) * -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 = b * (z * -c);
	double tmp;
	if (i <= -3.35e+198) {
		tmp = y * (i * -j);
	} else if (i <= -1.35e+102) {
		tmp = a * (b * i);
	} else if (i <= -3500.0) {
		tmp = c * (t * j);
	} else if (i <= -9e-64) {
		tmp = t * (x * -a);
	} else if (i <= -1.1e-282) {
		tmp = t_1;
	} else if (i <= 7.2e-116) {
		tmp = j * (t * c);
	} else if (i <= 0.00125) {
		tmp = t_1;
	} else {
		tmp = (y * i) * -j;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if i <= -3.35e+198:
		tmp = y * (i * -j)
	elif i <= -1.35e+102:
		tmp = a * (b * i)
	elif i <= -3500.0:
		tmp = c * (t * j)
	elif i <= -9e-64:
		tmp = t * (x * -a)
	elif i <= -1.1e-282:
		tmp = t_1
	elif i <= 7.2e-116:
		tmp = j * (t * c)
	elif i <= 0.00125:
		tmp = t_1
	else:
		tmp = (y * i) * -j
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (i <= -3.35e+198)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -1.35e+102)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= -3500.0)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= -9e-64)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= -1.1e-282)
		tmp = t_1;
	elseif (i <= 7.2e-116)
		tmp = Float64(j * Float64(t * c));
	elseif (i <= 0.00125)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * i) * Float64(-j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (z * -c);
	tmp = 0.0;
	if (i <= -3.35e+198)
		tmp = y * (i * -j);
	elseif (i <= -1.35e+102)
		tmp = a * (b * i);
	elseif (i <= -3500.0)
		tmp = c * (t * j);
	elseif (i <= -9e-64)
		tmp = t * (x * -a);
	elseif (i <= -1.1e-282)
		tmp = t_1;
	elseif (i <= 7.2e-116)
		tmp = j * (t * c);
	elseif (i <= 0.00125)
		tmp = t_1;
	else
		tmp = (y * i) * -j;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.35e+198], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.35e+102], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3500.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e-64], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.1e-282], t$95$1, If[LessEqual[i, 7.2e-116], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 0.00125], t$95$1, N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -3.35000000000000025e198

   1. Initial program 62.5%

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

   3. Taylor expanded in y around inf 75.4%

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

      1. +-commutative 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in z around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. distribute-lft-neg-out 63.1%

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

      3. *-commutative 63.1%

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

   8. Simplified 63.1%

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

   if -3.35000000000000025e198 < i < -1.3500000000000001e102

   1. Initial program 66.2%

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

   3. Taylor expanded in t around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 66.5%

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

      3. associate-*r* 66.0%

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

      4. associate-*r* 66.0%

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

      5. distribute-rgt-in 66.1%

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

      6. +-commutative 66.1%

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

      7. mul-1-neg 66.1%

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

      8. unsub-neg 66.1%

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

      9. *-commutative 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in a around inf 47.2%

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

   if -1.3500000000000001e102 < i < -3500

   1. Initial program 63.2%

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

   3. Taylor expanded in t around -inf 33.1%

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

      1. mul-1-neg 33.1%

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

      2. *-commutative 33.1%

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

      3. distribute-rgt-neg-in 33.1%

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

      4. +-commutative 33.1%

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

      5. mul-1-neg 33.1%

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

      6. unsub-neg 33.1%

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

   5. Simplified 33.1%

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

   6. Taylor expanded in a around 0 38.5%

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

   if -3500 < i < -9.00000000000000019e-64

   1. Initial program 94.9%

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

   3. Taylor expanded in t around -inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. +-commutative 72.0%

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

      5. mul-1-neg 72.0%

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

      6. unsub-neg 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in a around inf 62.8%

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

   if -9.00000000000000019e-64 < i < -1.09999999999999991e-282 or 7.19999999999999951e-116 < i < 0.00125000000000000003

   1. Initial program 82.2%

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

   3. Taylor expanded in b around inf 48.4%

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

   4. Taylor expanded in a around 0 36.5%

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

      1. associate-*r* 36.5%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 36.5%

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

   6. Simplified 36.5%

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

   if -1.09999999999999991e-282 < i < 7.19999999999999951e-116

   1. Initial program 80.4%

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

   3. Taylor expanded in t around -inf 50.8%

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

      1. mul-1-neg 50.8%

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

      2. *-commutative 50.8%

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

      3. distribute-rgt-neg-in 50.8%

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

      4. +-commutative 50.8%

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

      5. mul-1-neg 50.8%

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

      6. unsub-neg 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in a around 0 48.5%

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

   7. Taylor expanded in a around 0 38.4%

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

      1. *-commutative 38.4%

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

      2. associate-*l* 40.7%

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

   9. Simplified 40.7%

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

   if 0.00125000000000000003 < i

   1. Initial program 82.5%

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

   3. Taylor expanded in j around inf 61.2%

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

   4. Taylor expanded in c around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-lft-neg-out 47.3%

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

      3. *-commutative 47.3%

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

   6. Simplified 47.3%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.35 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{+102}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -3500:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{-116}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;i \leq 0.00125:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -1.45e+23)
   (* a (- (* x t)))
   (if (<= t -2.9e-270)
     (* (* y i) (- j))
     (if (<= t 2e-239)
       (* a (* b i))
       (if (<= t 3.7e-40)
         (* z (* b (- c)))
         (if (<= t 6.5e+49)
           (* y (* i (- j)))
           (if (<= t 1.45e+183) (* j (* t c)) (* t (* x (- a))))))))))

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 <= -1.45e+23) {
		tmp = a * -(x * t);
	} else if (t <= -2.9e-270) {
		tmp = (y * i) * -j;
	} else if (t <= 2e-239) {
		tmp = a * (b * i);
	} else if (t <= 3.7e-40) {
		tmp = z * (b * -c);
	} else if (t <= 6.5e+49) {
		tmp = y * (i * -j);
	} else if (t <= 1.45e+183) {
		tmp = j * (t * c);
	} else {
		tmp = t * (x * -a);
	}
	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 <= (-1.45d+23)) then
        tmp = a * -(x * t)
    else if (t <= (-2.9d-270)) then
        tmp = (y * i) * -j
    else if (t <= 2d-239) then
        tmp = a * (b * i)
    else if (t <= 3.7d-40) then
        tmp = z * (b * -c)
    else if (t <= 6.5d+49) then
        tmp = y * (i * -j)
    else if (t <= 1.45d+183) then
        tmp = j * (t * c)
    else
        tmp = t * (x * -a)
    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 <= -1.45e+23) {
		tmp = a * -(x * t);
	} else if (t <= -2.9e-270) {
		tmp = (y * i) * -j;
	} else if (t <= 2e-239) {
		tmp = a * (b * i);
	} else if (t <= 3.7e-40) {
		tmp = z * (b * -c);
	} else if (t <= 6.5e+49) {
		tmp = y * (i * -j);
	} else if (t <= 1.45e+183) {
		tmp = j * (t * c);
	} else {
		tmp = t * (x * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -1.45e+23:
		tmp = a * -(x * t)
	elif t <= -2.9e-270:
		tmp = (y * i) * -j
	elif t <= 2e-239:
		tmp = a * (b * i)
	elif t <= 3.7e-40:
		tmp = z * (b * -c)
	elif t <= 6.5e+49:
		tmp = y * (i * -j)
	elif t <= 1.45e+183:
		tmp = j * (t * c)
	else:
		tmp = t * (x * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -1.45e+23)
		tmp = Float64(a * Float64(-Float64(x * t)));
	elseif (t <= -2.9e-270)
		tmp = Float64(Float64(y * i) * Float64(-j));
	elseif (t <= 2e-239)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 3.7e-40)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (t <= 6.5e+49)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 1.45e+183)
		tmp = Float64(j * Float64(t * c));
	else
		tmp = Float64(t * Float64(x * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -1.45e+23)
		tmp = a * -(x * t);
	elseif (t <= -2.9e-270)
		tmp = (y * i) * -j;
	elseif (t <= 2e-239)
		tmp = a * (b * i);
	elseif (t <= 3.7e-40)
		tmp = z * (b * -c);
	elseif (t <= 6.5e+49)
		tmp = y * (i * -j);
	elseif (t <= 1.45e+183)
		tmp = j * (t * c);
	else
		tmp = t * (x * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -1.45e+23], N[(a * (-N[(x * t), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, -2.9e-270], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], If[LessEqual[t, 2e-239], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e-40], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+49], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e+183], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.45000000000000006e23

   1. Initial program 75.3%

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

   3. Taylor expanded in t around -inf 64.2%

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

      1. mul-1-neg 64.2%

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

      2. *-commutative 64.2%

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

      3. distribute-rgt-neg-in 64.2%

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

      4. +-commutative 64.2%

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

      5. mul-1-neg 64.2%

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

      6. unsub-neg 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in a around inf 41.9%

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

      1. mul-1-neg 41.9%

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

      2. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -1.45000000000000006e23 < t < -2.89999999999999983e-270

   1. Initial program 85.4%

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

   3. Taylor expanded in j around inf 42.3%

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

   4. Taylor expanded in c around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. distribute-lft-neg-out 36.1%

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

      3. *-commutative 36.1%

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

   6. Simplified 36.1%

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

   if -2.89999999999999983e-270 < t < 2.0000000000000002e-239

   1. Initial program 87.1%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r* 82.7%

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

      3. associate-*r* 91.5%

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

      4. associate-*r* 91.5%

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

      5. distribute-rgt-in 91.5%

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

      6. +-commutative 91.5%

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

      7. mul-1-neg 91.5%

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

      8. unsub-neg 91.5%

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

      9. *-commutative 91.5%

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

   5. Simplified 91.5%

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

   6. Taylor expanded in a around inf 53.1%

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

   if 2.0000000000000002e-239 < t < 3.69999999999999998e-40

   1. Initial program 85.4%

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

   3. Taylor expanded in t around 0 68.4%

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

      1. *-commutative 68.4%

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

      2. associate-*r* 64.0%

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

      3. associate-*r* 63.8%

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

      4. associate-*r* 63.8%

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

      5. distribute-rgt-in 71.1%

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

      6. +-commutative 71.1%

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

      7. mul-1-neg 71.1%

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

      8. unsub-neg 71.1%

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

      9. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in c around inf 50.2%

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

      1. mul-1-neg 50.2%

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

      2. associate-*r* 52.4%

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

      3. distribute-lft-neg-in 52.4%

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

      4. distribute-rgt-neg-in 52.4%

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

   8. Simplified 52.4%

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

   if 3.69999999999999998e-40 < t < 6.5000000000000005e49

   1. Initial program 75.6%

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

   3. Taylor expanded in y around inf 63.0%

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

      1. +-commutative 63.0%

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

      2. mul-1-neg 63.0%

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

      3. unsub-neg 63.0%

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

      4. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in z around 0 39.4%

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

      1. mul-1-neg 39.4%

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

      2. distribute-lft-neg-out 39.4%

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

      3. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   if 6.5000000000000005e49 < t < 1.45e183

   1. Initial program 71.2%

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

   3. Taylor expanded in t around -inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. *-commutative 55.6%

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

      3. distribute-rgt-neg-in 55.6%

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

      4. +-commutative 55.6%

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

      5. mul-1-neg 55.6%

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

      6. unsub-neg 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in a around 0 55.2%

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

   7. Taylor expanded in a around 0 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-*l* 51.8%

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

   9. Simplified 51.8%

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

   if 1.45e183 < t

   1. Initial program 59.1%

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

   3. Taylor expanded in t around -inf 58.9%

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

      1. mul-1-neg 58.9%

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

      2. *-commutative 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

      4. +-commutative 58.9%

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

      5. mul-1-neg 58.9%

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

      6. unsub-neg 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in a around inf 46.4%

      \[\leadsto \color{blue}{\left(a \cdot x\right)} \cdot \left(-t\right) \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(-x \cdot t\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-270}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-239}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-40}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+183}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.35 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -3.35e+68)
     t_2
     (if (<= c -4e-167)
       (* y (- (* x z) (* i j)))
       (if (<= c 3.5e-77)
         t_1
         (if (<= c 2.9e-8)
           (* x (- (* y z) (* t a)))
           (if (<= c 3.4e+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.35e+68) {
		tmp = t_2;
	} else if (c <= -4e-167) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.5e-77) {
		tmp = t_1;
	} else if (c <= 2.9e-8) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.4e+53) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-3.35d+68)) then
        tmp = t_2
    else if (c <= (-4d-167)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 3.5d-77) then
        tmp = t_1
    else if (c <= 2.9d-8) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3.4d+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.35e+68) {
		tmp = t_2;
	} else if (c <= -4e-167) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 3.5e-77) {
		tmp = t_1;
	} else if (c <= 2.9e-8) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.4e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.35e+68:
		tmp = t_2
	elif c <= -4e-167:
		tmp = y * ((x * z) - (i * j))
	elif c <= 3.5e-77:
		tmp = t_1
	elif c <= 2.9e-8:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3.4e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.35e+68)
		tmp = t_2;
	elseif (c <= -4e-167)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 3.5e-77)
		tmp = t_1;
	elseif (c <= 2.9e-8)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3.4e+53)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.35e+68)
		tmp = t_2;
	elseif (c <= -4e-167)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 3.5e-77)
		tmp = t_1;
	elseif (c <= 2.9e-8)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3.4e+53)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.35e+68], t$95$2, If[LessEqual[c, -4e-167], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e-77], t$95$1, If[LessEqual[c, 2.9e-8], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+53], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.3499999999999999e68 or 3.39999999999999998e53 < c

   1. Initial program 70.8%

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

   3. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -3.3499999999999999e68 < c < -4.00000000000000001e-167

   1. Initial program 86.7%

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

   3. Taylor expanded in y around inf 56.4%

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

      1. +-commutative 56.4%

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

      2. mul-1-neg 56.4%

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

      3. unsub-neg 56.4%

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

      4. *-commutative 56.4%

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

   5. Simplified 56.4%

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

   if -4.00000000000000001e-167 < c < 3.50000000000000013e-77 or 2.9000000000000002e-8 < c < 3.39999999999999998e53

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-*r* 61.6%

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

      3. associate-*r* 62.9%

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

      4. associate-*r* 62.9%

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

      5. distribute-rgt-in 67.3%

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

      6. +-commutative 67.3%

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

      7. mul-1-neg 67.3%

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

      8. unsub-neg 67.3%

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

      9. *-commutative 67.3%

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

   5. Simplified 67.3%

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

      1. cancel-sign-sub-inv 67.3%

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

      2. *-commutative 67.3%

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

      3. fma-define 67.3%

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

      4. *-commutative 67.3%

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

      5. *-commutative 67.3%

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

   7. Applied egg-rr 67.3%

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

   8. Taylor expanded in z around 0 55.8%

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

      1. mul-1-neg 55.8%

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

      2. distribute-rgt-neg-in 55.8%

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

      3. mul-1-neg 55.8%

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

      4. associate-*r* 58.0%

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

      5. *-commutative 58.0%

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

      6. distribute-lft-in 58.0%

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

      7. +-commutative 58.0%

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

      8. mul-1-neg 58.0%

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

      9. unsub-neg 58.0%

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

   10. Simplified 58.0%

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

   if 3.50000000000000013e-77 < c < 2.9000000000000002e-8

   1. Initial program 88.4%

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

   3. Taylor expanded in b around 0 94.3%

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

   4. Taylor expanded in j around 0 77.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.35 \cdot 10^{+68}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-167}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 69.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+224}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq -4.05 \cdot 10^{-106}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i - x \cdot t\right) + c \cdot \left(t \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= b -6.4e+224)
     (+ t_2 t_1)
     (if (<= b -4.05e-106)
       (- (+ (* a (- (* b i) (* x t))) (* c (* t j))) (* b (* z c)))
       (if (<= b 1.15e-10)
         (+ (* j (- (* t c) (* y i))) t_2)
         (+ (* y (- (* x z) (* i j))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -6.4e+224) {
		tmp = t_2 + t_1;
	} else if (b <= -4.05e-106) {
		tmp = ((a * ((b * i) - (x * t))) + (c * (t * j))) - (b * (z * c));
	} else if (b <= 1.15e-10) {
		tmp = (j * ((t * c) - (y * i))) + t_2;
	} else {
		tmp = (y * ((x * z) - (i * j))) + 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) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    if (b <= (-6.4d+224)) then
        tmp = t_2 + t_1
    else if (b <= (-4.05d-106)) then
        tmp = ((a * ((b * i) - (x * t))) + (c * (t * j))) - (b * (z * c))
    else if (b <= 1.15d-10) then
        tmp = (j * ((t * c) - (y * i))) + t_2
    else
        tmp = (y * ((x * z) - (i * j))) + 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 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (b <= -6.4e+224) {
		tmp = t_2 + t_1;
	} else if (b <= -4.05e-106) {
		tmp = ((a * ((b * i) - (x * t))) + (c * (t * j))) - (b * (z * c));
	} else if (b <= 1.15e-10) {
		tmp = (j * ((t * c) - (y * i))) + t_2;
	} else {
		tmp = (y * ((x * z) - (i * j))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if b <= -6.4e+224:
		tmp = t_2 + t_1
	elif b <= -4.05e-106:
		tmp = ((a * ((b * i) - (x * t))) + (c * (t * j))) - (b * (z * c))
	elif b <= 1.15e-10:
		tmp = (j * ((t * c) - (y * i))) + t_2
	else:
		tmp = (y * ((x * z) - (i * j))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (b <= -6.4e+224)
		tmp = Float64(t_2 + t_1);
	elseif (b <= -4.05e-106)
		tmp = Float64(Float64(Float64(a * Float64(Float64(b * i) - Float64(x * t))) + Float64(c * Float64(t * j))) - Float64(b * Float64(z * c)));
	elseif (b <= 1.15e-10)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + t_2);
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (b <= -6.4e+224)
		tmp = t_2 + t_1;
	elseif (b <= -4.05e-106)
		tmp = ((a * ((b * i) - (x * t))) + (c * (t * j))) - (b * (z * c));
	elseif (b <= 1.15e-10)
		tmp = (j * ((t * c) - (y * i))) + t_2;
	else
		tmp = (y * ((x * z) - (i * j))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.4e+224], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, -4.05e-106], N[(N[(N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-10], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.4000000000000003e224

   1. Initial program 79.1%

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

   3. Taylor expanded in j around 0 90.2%

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

      1. *-commutative 90.2%

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

   5. Simplified 90.2%

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

   if -6.4000000000000003e224 < b < -4.0500000000000001e-106

   1. Initial program 68.8%

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

   3. Taylor expanded in i around -inf 70.0%

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

   4. Taylor expanded in y around 0 73.1%

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

      1. associate-+r+ 73.1%

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

      2. mul-1-neg 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. mul-1-neg 73.1%

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

      5. distribute-lft-in 78.6%

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

      6. +-commutative 78.6%

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

      7. mul-1-neg 78.6%

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

      8. unsub-neg 78.6%

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

   6. Simplified 78.6%

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

   if -4.0500000000000001e-106 < b < 1.15000000000000004e-10

   1. Initial program 80.3%

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

   3. Taylor expanded in b around 0 74.5%

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

   if 1.15000000000000004e-10 < b

   1. Initial program 86.2%

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

   3. Taylor expanded in t around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-*r* 74.2%

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

      3. associate-*r* 80.0%

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

      4. associate-*r* 80.0%

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

      5. distribute-rgt-in 84.7%

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

      6. +-commutative 84.7%

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

      7. mul-1-neg 84.7%

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

      8. unsub-neg 84.7%

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

      9. *-commutative 84.7%

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

   5. Simplified 84.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+224}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.05 \cdot 10^{-106}:\\ \;\;\;\;\left(a \cdot \left(b \cdot i - x \cdot t\right) + c \cdot \left(t \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-10}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6.3 \cdot 10^{+69}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -6.3e+69)
     t_2
     (if (<= c 5e-74)
       t_1
       (if (<= c 1.9e-22) (* t (* x (- a))) (if (<= c 7.6e+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.3e+69) {
		tmp = t_2;
	} else if (c <= 5e-74) {
		tmp = t_1;
	} else if (c <= 1.9e-22) {
		tmp = t * (x * -a);
	} else if (c <= 7.6e+53) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-6.3d+69)) then
        tmp = t_2
    else if (c <= 5d-74) then
        tmp = t_1
    else if (c <= 1.9d-22) then
        tmp = t * (x * -a)
    else if (c <= 7.6d+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.3e+69) {
		tmp = t_2;
	} else if (c <= 5e-74) {
		tmp = t_1;
	} else if (c <= 1.9e-22) {
		tmp = t * (x * -a);
	} else if (c <= 7.6e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -6.3e+69:
		tmp = t_2
	elif c <= 5e-74:
		tmp = t_1
	elif c <= 1.9e-22:
		tmp = t * (x * -a)
	elif c <= 7.6e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6.3e+69)
		tmp = t_2;
	elseif (c <= 5e-74)
		tmp = t_1;
	elseif (c <= 1.9e-22)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 7.6e+53)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -6.3e+69)
		tmp = t_2;
	elseif (c <= 5e-74)
		tmp = t_1;
	elseif (c <= 1.9e-22)
		tmp = t * (x * -a);
	elseif (c <= 7.6e+53)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.3e+69], t$95$2, If[LessEqual[c, 5e-74], t$95$1, If[LessEqual[c, 1.9e-22], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.30000000000000007e69 or 7.59999999999999995e53 < c

   1. Initial program 70.8%

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

   3. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   if -6.30000000000000007e69 < c < 4.99999999999999998e-74 or 1.90000000000000012e-22 < c < 7.59999999999999995e53

   1. Initial program 82.9%

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

   3. Taylor expanded in t around 0 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-*r* 63.1%

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

      3. associate-*r* 65.7%

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

      4. associate-*r* 65.7%

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

      5. distribute-rgt-in 69.0%

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

      6. +-commutative 69.0%

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

      7. mul-1-neg 69.0%

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

      8. unsub-neg 69.0%

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

      9. *-commutative 69.0%

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

   5. Simplified 69.0%

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

      1. cancel-sign-sub-inv 69.0%

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

      2. *-commutative 69.0%

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

      3. fma-define 69.0%

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

      4. *-commutative 69.0%

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

      5. *-commutative 69.0%

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

   7. Applied egg-rr 69.0%

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

   8. Taylor expanded in z around 0 51.4%

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

      1. mul-1-neg 51.4%

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

      2. distribute-rgt-neg-in 51.4%

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

      3. mul-1-neg 51.4%

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

      4. associate-*r* 52.8%

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

      5. *-commutative 52.8%

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

      6. distribute-lft-in 53.5%

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

      7. +-commutative 53.5%

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

      8. mul-1-neg 53.5%

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

      9. unsub-neg 53.5%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

   10. Simplified 53.5%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b - j \cdot y\right)} \]

   if 4.99999999999999998e-74 < c < 1.90000000000000012e-22

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 81.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.8%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 81.8%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 81.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 81.8%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 81.8%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 81.8%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 81.8%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around inf 67.4%

      \[\leadsto \color{blue}{\left(a \cdot x\right)} \cdot \left(-t\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.3 \cdot 10^{+69}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-22}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -8.5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -8.5e+60)
     t_2
     (if (<= c 7e-77)
       t_1
       (if (<= c 1.1e-21)
         (* t (- (* c j) (* x a)))
         (if (<= c 3.4e+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e+60) {
		tmp = t_2;
	} else if (c <= 7e-77) {
		tmp = t_1;
	} else if (c <= 1.1e-21) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 3.4e+53) {
		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 = i * ((a * b) - (y * j))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-8.5d+60)) then
        tmp = t_2
    else if (c <= 7d-77) then
        tmp = t_1
    else if (c <= 1.1d-21) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 3.4d+53) 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 = i * ((a * b) - (y * j));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -8.5e+60) {
		tmp = t_2;
	} else if (c <= 7e-77) {
		tmp = t_1;
	} else if (c <= 1.1e-21) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 3.4e+53) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -8.5e+60:
		tmp = t_2
	elif c <= 7e-77:
		tmp = t_1
	elif c <= 1.1e-21:
		tmp = t * ((c * j) - (x * a))
	elif c <= 3.4e+53:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -8.5e+60)
		tmp = t_2;
	elseif (c <= 7e-77)
		tmp = t_1;
	elseif (c <= 1.1e-21)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 3.4e+53)
		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 = i * ((a * b) - (y * j));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -8.5e+60)
		tmp = t_2;
	elseif (c <= 7e-77)
		tmp = t_1;
	elseif (c <= 1.1e-21)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 3.4e+53)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.5e+60], t$95$2, If[LessEqual[c, 7e-77], t$95$1, If[LessEqual[c, 1.1e-21], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.4e+53], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.50000000000000064e60 or 3.39999999999999998e53 < c

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 72.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 72.0%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

   5. Simplified 72.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]

   if -8.50000000000000064e60 < c < 7.00000000000000026e-77 or 1.1e-21 < c < 3.39999999999999998e53

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 63.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 65.7%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 65.7%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 69.0%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 69.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 69.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 69.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 69.0%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 69.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 69.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 69.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 69.0%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 69.0%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 69.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in z around 0 51.4%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. mul-1-neg 51.4%

         \[\leadsto \color{blue}{\left(-i \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      2. distribute-rgt-neg-in 51.4%

         \[\leadsto \color{blue}{i \cdot \left(-j \cdot y\right)} + a \cdot \left(b \cdot i\right) \]

      3. mul-1-neg 51.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} + a \cdot \left(b \cdot i\right) \]

      4. associate-*r* 52.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(a \cdot b\right) \cdot i} \]

      5. *-commutative 52.8%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right)\right) + \color{blue}{i \cdot \left(a \cdot b\right)} \]

      6. distribute-lft-in 53.5%

         \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + a \cdot b\right)} \]

      7. +-commutative 53.5%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      8. mul-1-neg 53.5%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      9. unsub-neg 53.5%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

   10. Simplified 53.5%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b - j \cdot y\right)} \]

   if 7.00000000000000026e-77 < c < 1.1e-21

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 81.8%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 81.8%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 81.8%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 81.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 81.8%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 81.8%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 81.8%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 81.8%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 81.8%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 81.8%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} + c \cdot \left(j \cdot t\right) \]

      2. *-commutative 81.8%

         \[\leadsto \left(-1 \cdot a\right) \cdot \color{blue}{\left(x \cdot t\right)} + c \cdot \left(j \cdot t\right) \]

      3. associate-*r* 81.9%

         \[\leadsto \color{blue}{\left(\left(-1 \cdot a\right) \cdot x\right) \cdot t} + c \cdot \left(j \cdot t\right) \]

      4. associate-*r* 81.9%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \cdot t + c \cdot \left(j \cdot t\right) \]

      5. associate-*r* 81.9%

         \[\leadsto \left(-1 \cdot \left(a \cdot x\right)\right) \cdot t + \color{blue}{\left(c \cdot j\right) \cdot t} \]

      6. distribute-rgt-in 81.8%

         \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + c \cdot j\right)} \]

      7. +-commutative 81.8%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      8. *-commutative 81.8%

         \[\leadsto t \cdot \left(\color{blue}{j \cdot c} + -1 \cdot \left(a \cdot x\right)\right) \]

      9. mul-1-neg 81.8%

         \[\leadsto t \cdot \left(j \cdot c + \color{blue}{\left(-a \cdot x\right)}\right) \]

      10. *-commutative 81.8%

          \[\leadsto t \cdot \left(j \cdot c + \left(-\color{blue}{x \cdot a}\right)\right) \]

      11. unsub-neg 81.8%

          \[\leadsto t \cdot \color{blue}{\left(j \cdot c - x \cdot a\right)} \]

      12. *-commutative 81.8%

          \[\leadsto t \cdot \left(\color{blue}{c \cdot j} - x \cdot a\right) \]

      13. *-commutative 81.8%

          \[\leadsto t \cdot \left(c \cdot j - \color{blue}{a \cdot x}\right) \]

   8. Simplified 81.8%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.5 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+53}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 920:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= a -7.6e+31)
     (* i (* a b))
     (if (<= a -1.65e-140)
       t_1
       (if (<= a -6.2e-299)
         (* c (* t j))
         (if (<= a 920.0) t_1 (* b (* a i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (a <= -7.6e+31) {
		tmp = i * (a * b);
	} else if (a <= -1.65e-140) {
		tmp = t_1;
	} else if (a <= -6.2e-299) {
		tmp = c * (t * j);
	} else if (a <= 920.0) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (a <= (-7.6d+31)) then
        tmp = i * (a * b)
    else if (a <= (-1.65d-140)) then
        tmp = t_1
    else if (a <= (-6.2d-299)) then
        tmp = c * (t * j)
    else if (a <= 920.0d0) then
        tmp = t_1
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (i * -j);
	double tmp;
	if (a <= -7.6e+31) {
		tmp = i * (a * b);
	} else if (a <= -1.65e-140) {
		tmp = t_1;
	} else if (a <= -6.2e-299) {
		tmp = c * (t * j);
	} else if (a <= 920.0) {
		tmp = t_1;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if a <= -7.6e+31:
		tmp = i * (a * b)
	elif a <= -1.65e-140:
		tmp = t_1
	elif a <= -6.2e-299:
		tmp = c * (t * j)
	elif a <= 920.0:
		tmp = t_1
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (a <= -7.6e+31)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= -1.65e-140)
		tmp = t_1;
	elseif (a <= -6.2e-299)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 920.0)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (a <= -7.6e+31)
		tmp = i * (a * b);
	elseif (a <= -1.65e-140)
		tmp = t_1;
	elseif (a <= -6.2e-299)
		tmp = c * (t * j);
	elseif (a <= 920.0)
		tmp = t_1;
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.6e+31], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.65e-140], t$95$1, If[LessEqual[a, -6.2e-299], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 920.0], t$95$1, N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.6000000000000003e31

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 57.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 61.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 61.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 61.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 61.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 61.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 61.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 61.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 61.6%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 61.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 61.5%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 61.5%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 61.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 44.6%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   10. Simplified 44.6%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -7.6000000000000003e31 < a < -1.64999999999999994e-140 or -6.1999999999999999e-299 < a < 920

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 52.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 52.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 52.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 52.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   5. Simplified 52.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   6. Taylor expanded in z around 0 39.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-lft-neg-out 39.1%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      3. *-commutative 39.1%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 39.1%

      \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   if -1.64999999999999994e-140 < a < -6.1999999999999999e-299

   1. Initial program 82.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 39.7%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 39.7%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 39.7%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 39.7%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 39.7%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 39.7%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 39.7%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 39.7%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 39.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 920 < a

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 63.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 63.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 64.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 64.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 64.9%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 64.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 36.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 38.4%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

      3. associate-*r* 44.3%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.6 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-140}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-299}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 920:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* a b))))
   (if (<= a -2.6e-9)
     t_1
     (if (<= a -1.3e-245)
       (* c (* t j))
       (if (<= a 1.15e-110)
         (* x (* y z))
         (if (<= a 2.6e+72) (* t (* c j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (a <= -2.6e-9) {
		tmp = t_1;
	} else if (a <= -1.3e-245) {
		tmp = c * (t * j);
	} else if (a <= 1.15e-110) {
		tmp = x * (y * z);
	} else if (a <= 2.6e+72) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (a * b)
    if (a <= (-2.6d-9)) then
        tmp = t_1
    else if (a <= (-1.3d-245)) then
        tmp = c * (t * j)
    else if (a <= 1.15d-110) then
        tmp = x * (y * z)
    else if (a <= 2.6d+72) then
        tmp = t * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (a * b);
	double tmp;
	if (a <= -2.6e-9) {
		tmp = t_1;
	} else if (a <= -1.3e-245) {
		tmp = c * (t * j);
	} else if (a <= 1.15e-110) {
		tmp = x * (y * z);
	} else if (a <= 2.6e+72) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (a * b)
	tmp = 0
	if a <= -2.6e-9:
		tmp = t_1
	elif a <= -1.3e-245:
		tmp = c * (t * j)
	elif a <= 1.15e-110:
		tmp = x * (y * z)
	elif a <= 2.6e+72:
		tmp = t * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(a * b))
	tmp = 0.0
	if (a <= -2.6e-9)
		tmp = t_1;
	elseif (a <= -1.3e-245)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 1.15e-110)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.6e+72)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (a * b);
	tmp = 0.0;
	if (a <= -2.6e-9)
		tmp = t_1;
	elseif (a <= -1.3e-245)
		tmp = c * (t * j);
	elseif (a <= 1.15e-110)
		tmp = x * (y * z);
	elseif (a <= 2.6e+72)
		tmp = t * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e-9], t$95$1, If[LessEqual[a, -1.3e-245], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-110], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.6e+72], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.6000000000000001e-9 or 2.59999999999999981e72 < a

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 59.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 62.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 62.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 64.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 64.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 64.9%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 64.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 43.8%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   10. Simplified 43.8%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -2.6000000000000001e-9 < a < -1.30000000000000003e-245

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 35.6%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 35.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 35.6%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 35.6%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 35.6%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 35.6%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 30.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -1.30000000000000003e-245 < a < 1.1500000000000001e-110

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 71.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 73.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 35.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 1.1500000000000001e-110 < a < 2.59999999999999981e72

   1. Initial program 87.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 46.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around inf 27.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 27.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 29.7%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

      4. *-commutative 29.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   6. Simplified 29.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{-9}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-245}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+72}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.3e-8)
   (* i (* a b))
   (if (<= a -2.8e-247)
     (* c (* t j))
     (if (<= a 5e-110)
       (* x (* y z))
       (if (<= a 1.35e+70) (* t (* c j)) (* b (* a i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.3e-8) {
		tmp = i * (a * b);
	} else if (a <= -2.8e-247) {
		tmp = c * (t * j);
	} else if (a <= 5e-110) {
		tmp = x * (y * z);
	} else if (a <= 1.35e+70) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-3.3d-8)) then
        tmp = i * (a * b)
    else if (a <= (-2.8d-247)) then
        tmp = c * (t * j)
    else if (a <= 5d-110) then
        tmp = x * (y * z)
    else if (a <= 1.35d+70) then
        tmp = t * (c * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.3e-8) {
		tmp = i * (a * b);
	} else if (a <= -2.8e-247) {
		tmp = c * (t * j);
	} else if (a <= 5e-110) {
		tmp = x * (y * z);
	} else if (a <= 1.35e+70) {
		tmp = t * (c * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -3.3e-8:
		tmp = i * (a * b)
	elif a <= -2.8e-247:
		tmp = c * (t * j)
	elif a <= 5e-110:
		tmp = x * (y * z)
	elif a <= 1.35e+70:
		tmp = t * (c * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.3e-8)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= -2.8e-247)
		tmp = Float64(c * Float64(t * j));
	elseif (a <= 5e-110)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.35e+70)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -3.3e-8)
		tmp = i * (a * b);
	elseif (a <= -2.8e-247)
		tmp = c * (t * j);
	elseif (a <= 5e-110)
		tmp = x * (y * z);
	elseif (a <= 1.35e+70)
		tmp = t * (c * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -3.3e-8], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.8e-247], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-110], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+70], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.29999999999999977e-8

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 58.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 57.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 61.0%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.0%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 62.8%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 62.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 62.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 62.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 62.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 62.8%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 62.8%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 62.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 62.8%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 62.8%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 62.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 39.4%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 42.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 42.9%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   10. Simplified 42.9%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -3.29999999999999977e-8 < a < -2.79999999999999986e-247

   1. Initial program 77.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 35.6%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 35.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 35.6%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 35.6%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 35.6%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 35.6%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 30.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -2.79999999999999986e-247 < a < 5e-110

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 71.3%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 71.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 71.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 73.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 73.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 75.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 75.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 75.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 75.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 75.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 35.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if 5e-110 < a < 1.35e70

   1. Initial program 87.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 46.3%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around inf 27.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 27.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 29.7%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

      4. *-commutative 29.7%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   6. Simplified 29.7%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j\right)} \]

   if 1.35e70 < a

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 60.9%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 60.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 63.0%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 65.2%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 65.2%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 67.4%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 67.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 67.4%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 67.4%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 67.4%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 67.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 67.4%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 67.4%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 67.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 67.4%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 67.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 42.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.9%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 44.9%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

      3. associate-*r* 53.3%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   10. Simplified 53.3%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-8}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-247}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 45.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-50} \lor \neg \left(a \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.5e-50) (not (<= a 1.1e+41)))
   (* b (- (* a i) (* z c)))
   (* c (- (* t j) (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.5e-50) || !(a <= 1.1e+41)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-4.5d-50)) .or. (.not. (a <= 1.1d+41))) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.5e-50) || !(a <= 1.1e+41)) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.5e-50) or not (a <= 1.1e+41):
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.5e-50) || !(a <= 1.1e+41))
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.5e-50) || ~((a <= 1.1e+41)))
		tmp = b * ((a * i) - (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.5e-50], N[Not[LessEqual[a, 1.1e+41]], $MachinePrecision]], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.49999999999999962e-50 or 1.09999999999999995e41 < a

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 57.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]

   if -4.49999999999999962e-50 < a < 1.09999999999999995e41

   1. Initial program 82.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 46.8%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - b \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-50} \lor \neg \left(a \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 3400:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -9e+31)
   (* i (* a b))
   (if (<= a 3400.0) (* (* y i) (- j)) (* b (* a i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9e+31) {
		tmp = i * (a * b);
	} else if (a <= 3400.0) {
		tmp = (y * i) * -j;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-9d+31)) then
        tmp = i * (a * b)
    else if (a <= 3400.0d0) then
        tmp = (y * i) * -j
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -9e+31) {
		tmp = i * (a * b);
	} else if (a <= 3400.0) {
		tmp = (y * i) * -j;
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -9e+31:
		tmp = i * (a * b)
	elif a <= 3400.0:
		tmp = (y * i) * -j
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -9e+31)
		tmp = Float64(i * Float64(a * b));
	elseif (a <= 3400.0)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -9e+31)
		tmp = i * (a * b);
	elseif (a <= 3400.0)
		tmp = (y * i) * -j;
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -9e+31], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3400.0], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.9999999999999992e31

   1. Initial program 75.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 57.3%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 61.6%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 61.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 61.6%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 61.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 61.6%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 61.6%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 61.6%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 61.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 61.6%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 61.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 61.5%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 61.5%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 61.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 40.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 44.6%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 44.6%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   10. Simplified 44.6%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -8.9999999999999992e31 < a < 3400

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 50.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 31.4%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 31.4%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. distribute-lft-neg-out 31.4%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y\right)} \]

      3. *-commutative 31.4%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   6. Simplified 31.4%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if 3400 < a

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 61.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 63.4%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 63.4%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 64.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 64.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 64.9%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 64.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 36.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 38.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 38.4%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

      3. associate-*r* 44.3%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   10. Simplified 44.3%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+31}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;a \leq 3400:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-28} \lor \neg \left(j \leq 7.2 \cdot 10^{+226}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -8e-28) (not (<= j 7.2e+226))) (* c (* t j)) (* a (* 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 ((j <= -8e-28) || !(j <= 7.2e+226)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (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 ((j <= (-8d-28)) .or. (.not. (j <= 7.2d+226))) then
        tmp = c * (t * j)
    else
        tmp = a * (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 ((j <= -8e-28) || !(j <= 7.2e+226)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -8e-28) or not (j <= 7.2e+226):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -8e-28) || !(j <= 7.2e+226))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * 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 ((j <= -8e-28) || ~((j <= 7.2e+226)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -8e-28], N[Not[LessEqual[j, 7.2e+226]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -7.99999999999999977e-28 or 7.19999999999999962e226 < j

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 43.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 43.5%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 43.5%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 43.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 43.5%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 43.5%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 43.5%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 43.5%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 39.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -7.99999999999999977e-28 < j < 7.19999999999999962e226

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 63.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 63.2%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 63.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 65.5%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 65.5%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 68.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 68.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 68.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 68.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 68.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

   6. Taylor expanded in a around inf 29.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8 \cdot 10^{-28} \lor \neg \left(j \leq 7.2 \cdot 10^{+226}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-10} \lor \neg \left(a \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -2.05e-10) (not (<= a 2.3e+71))) (* i (* a b)) (* c (* t 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 ((a <= -2.05e-10) || !(a <= 2.3e+71)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * 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 ((a <= (-2.05d-10)) .or. (.not. (a <= 2.3d+71))) then
        tmp = i * (a * b)
    else
        tmp = c * (t * 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 ((a <= -2.05e-10) || !(a <= 2.3e+71)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -2.05e-10) or not (a <= 2.3e+71):
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -2.05e-10) || !(a <= 2.3e+71))
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -2.05e-10) || ~((a <= 2.3e+71)))
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -2.05e-10], N[Not[LessEqual[a, 2.3e+71]], $MachinePrecision]], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.0499999999999999e-10 or 2.3000000000000002e71 < a

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 59.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 59.9%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 62.9%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 62.9%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 64.9%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 64.9%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 64.9%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 64.9%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 64.9%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)} \]

      2. *-commutative 64.9%

         \[\leadsto \color{blue}{\left(z \cdot x - i \cdot j\right) \cdot y} + \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right) \]

      3. fma-define 64.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(c \cdot z - a \cdot i\right)\right)} \]

      4. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

      5. *-commutative 64.9%

         \[\leadsto \mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - \color{blue}{i \cdot a}\right)\right) \]

   7. Applied egg-rr 64.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z \cdot x - i \cdot j, y, \left(-b\right) \cdot \left(z \cdot c - i \cdot a\right)\right)} \]

   8. Taylor expanded in a around inf 41.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 43.8%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 43.8%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   10. Simplified 43.8%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -2.0499999999999999e-10 < a < 2.3000000000000002e71

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around -inf 34.5%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 34.5%

         \[\leadsto \color{blue}{-t \cdot \left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right)} \]

      2. *-commutative 34.5%

         \[\leadsto -\color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot t} \]

      3. distribute-rgt-neg-in 34.5%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(c \cdot j\right) + a \cdot x\right) \cdot \left(-t\right)} \]

      4. +-commutative 34.5%

         \[\leadsto \color{blue}{\left(a \cdot x + -1 \cdot \left(c \cdot j\right)\right)} \cdot \left(-t\right) \]

      5. mul-1-neg 34.5%

         \[\leadsto \left(a \cdot x + \color{blue}{\left(-c \cdot j\right)}\right) \cdot \left(-t\right) \]

      6. unsub-neg 34.5%

         \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right)} \cdot \left(-t\right) \]

   5. Simplified 34.5%

      \[\leadsto \color{blue}{\left(a \cdot x - c \cdot j\right) \cdot \left(-t\right)} \]

   6. Taylor expanded in a around 0 27.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-10} \lor \neg \left(a \leq 2.3 \cdot 10^{+71}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 41.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.2e+79) (* (* y i) (- j)) (* b (- (* a 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 tmp;
	if (y <= -3.2e+79) {
		tmp = (y * i) * -j;
	} else {
		tmp = b * ((a * 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) :: tmp
    if (y <= (-3.2d+79)) then
        tmp = (y * i) * -j
    else
        tmp = b * ((a * 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 tmp;
	if (y <= -3.2e+79) {
		tmp = (y * i) * -j;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.2e+79:
		tmp = (y * i) * -j
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.2e+79)
		tmp = Float64(Float64(y * i) * Float64(-j));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.2e+79)
		tmp = (y * i) * -j;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.2e+79], N[(N[(y * i), $MachinePrecision] * (-j)), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000003e79

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 69.9%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   4. Taylor expanded in c around 0 64.2%

      \[\leadsto j \cdot \color{blue}{\left(-1 \cdot \left(i \cdot y\right)\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 64.2%

         \[\leadsto j \cdot \color{blue}{\left(-i \cdot y\right)} \]

      2. distribute-lft-neg-out 64.2%

         \[\leadsto j \cdot \color{blue}{\left(\left(-i\right) \cdot y\right)} \]

      3. *-commutative 64.2%

         \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   6. Simplified 64.2%

      \[\leadsto j \cdot \color{blue}{\left(y \cdot \left(-i\right)\right)} \]

   if -3.20000000000000003e79 < y

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 45.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+79}:\\ \;\;\;\;\left(y \cdot i\right) \cdot \left(-j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in t around 0 59.6%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
4. Step-by-step derivation

   1. *-commutative 59.6%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   2. associate-*r* 60.3%

      \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   3. associate-*r* 62.9%

      \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   4. associate-*r* 62.9%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   5. distribute-rgt-in 65.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   6. +-commutative 65.7%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   7. mul-1-neg 65.7%

      \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

   8. unsub-neg 65.7%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

   9. *-commutative 65.7%

      \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

5. Simplified 65.7%

   \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]

6. Taylor expanded in a around inf 24.7%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

7. Final simplification 24.7%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 69.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024044 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))