Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 72.7% → 83.4%

Time: 35.4s

Alternatives: 22

Speedup: 0.5×

• 58.6% 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: 72.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 83.4% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* a i) (* z c))) (* x (- (* t a) (* y z)))))
        (t_2 (- (* t c) (* y i))))
   (if (<= (+ t_1 (* j t_2)) INFINITY)
     (fma j t_2 t_1)
     (fma i (- (* a b) (* y j)) (* z (fma x y (* b (- c))))))))

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x * y + N[(b * (-c)), $MachinePrecision]), $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 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-def 92.2%

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

      3. *-commutative 92.2%

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

      4. *-commutative 92.2%

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

      5. cancel-sign-sub-inv 92.2%

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

      6. cancel-sign-sub 92.2%

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

      7. remove-double-neg 92.2%

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

      8. *-commutative 92.2%

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

      9. *-commutative 92.2%

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

   3. Simplified 92.2%

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

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

   1. Initial program 0.0%

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

      1. +-commutative 0.0%

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

      2. fma-def 8.9%

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

      3. *-commutative 8.9%

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

      4. *-commutative 8.9%

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

      5. cancel-sign-sub-inv 8.9%

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

      6. cancel-sign-sub 8.9%

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

      7. remove-double-neg 8.9%

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

      8. *-commutative 8.9%

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

      9. *-commutative 8.9%

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

   3. Simplified 8.9%

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

   4. Taylor expanded in z around 0 46.4%

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

      1. +-commutative 46.4%

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

      2. associate--l+ 46.4%

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

      3. sub-neg 46.4%

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

      4. sub-neg 46.4%

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

      5. associate-*r* 46.4%

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

      6. associate-*r* 46.4%

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

      7. distribute-lft-out-- 50.0%

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

      8. associate-*r* 50.0%

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

      9. +-commutative 50.0%

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

      10. *-commutative 50.0%

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

      11. associate-*l* 50.0%

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

      12. *-commutative 50.0%

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

      13. distribute-lft-out-- 50.0%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in t around 0 50.4%

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

      1. associate-*r* 45.0%

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

      2. *-commutative 45.0%

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

      3. associate-+l+ 45.0%

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

      4. mul-1-neg 45.0%

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

      5. distribute-rgt-neg-in 45.0%

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

      6. mul-1-neg 45.0%

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

      7. distribute-lft-in 53.9%

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

      8. fma-def 61.1%

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

      9. +-commutative 61.1%

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

      10. mul-1-neg 61.1%

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

      11. unsub-neg 61.1%

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

      12. *-commutative 61.1%

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

      13. fma-neg 61.1%

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

      14. *-commutative 61.1%

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

      15. distribute-rgt-neg-in 61.1%

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

   9. Simplified 61.1%

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

4. Final simplification 85.4%

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

Alternative 2: 81.6% accurate, 0.2× speedup

Math

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

FPCore

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision], Infinity], N[(j * t$95$2 + t$95$1), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $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 92.2%

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

      1. +-commutative 92.2%

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

      2. fma-def 92.2%

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

      3. *-commutative 92.2%

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

      4. *-commutative 92.2%

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

      5. cancel-sign-sub-inv 92.2%

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

      6. cancel-sign-sub 92.2%

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

      7. remove-double-neg 92.2%

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

      8. *-commutative 92.2%

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

      9. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   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. Taylor expanded in c around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. *-commutative 54.1%

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

   4. Simplified 54.1%

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

4. Final simplification 83.9%

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

Alternative 3: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(x * Float64(Float64(t * a) - Float64(y * z)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	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)
	t_1 = ((b * ((a * i) - (z * c))) - (x * ((t * a) - (y * z)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $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 92.2%

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

   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. Taylor expanded in c around inf 54.1%

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

      1. *-commutative 54.1%

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

      2. *-commutative 54.1%

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

   4. Simplified 54.1%

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

4. Final simplification 83.9%

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

Alternative 4: 67.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3e+208)
     t_1
     (if (<= c -1.45e+178)
       (* x (- (* y z) (* t a)))
       (if (<= c -4.2e+134)
         t_1
         (if (<= c 5.5e+15)
           (+ (* y (- (* x z) (* i j))) (* a (- (* b i) (* x t))))
           (if (<= c 1.35e+156)
             (+ (* t (* c j)) (* b (- (* a i) (* z c))))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+208) {
		tmp = t_1;
	} else if (c <= -1.45e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -4.2e+134) {
		tmp = t_1;
	} else if (c <= 5.5e+15) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	} else if (c <= 1.35e+156) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-3d+208)) then
        tmp = t_1
    else if (c <= (-1.45d+178)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= (-4.2d+134)) then
        tmp = t_1
    else if (c <= 5.5d+15) then
        tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
    else if (c <= 1.35d+156) then
        tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3e+208) {
		tmp = t_1;
	} else if (c <= -1.45e+178) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= -4.2e+134) {
		tmp = t_1;
	} else if (c <= 5.5e+15) {
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	} else if (c <= 1.35e+156) {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3e+208:
		tmp = t_1
	elif c <= -1.45e+178:
		tmp = x * ((y * z) - (t * a))
	elif c <= -4.2e+134:
		tmp = t_1
	elif c <= 5.5e+15:
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)))
	elif c <= 1.35e+156:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3e+208)
		tmp = t_1;
	elseif (c <= -1.45e+178)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= -4.2e+134)
		tmp = t_1;
	elseif (c <= 5.5e+15)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(a * Float64(Float64(b * i) - Float64(x * t))));
	elseif (c <= 1.35e+156)
		tmp = Float64(Float64(t * Float64(c * j)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3e+208)
		tmp = t_1;
	elseif (c <= -1.45e+178)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= -4.2e+134)
		tmp = t_1;
	elseif (c <= 5.5e+15)
		tmp = (y * ((x * z) - (i * j))) + (a * ((b * i) - (x * t)));
	elseif (c <= 1.35e+156)
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+208], t$95$1, If[LessEqual[c, -1.45e+178], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4.2e+134], t$95$1, If[LessEqual[c, 5.5e+15], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e+156], N[(N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.99999999999999995e208 or -1.45e178 < c < -4.2000000000000002e134 or 1.35e156 < c

   1. Initial program 64.7%

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

   2. Taylor expanded in c around inf 88.7%

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

      1. *-commutative 88.7%

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

      2. *-commutative 88.7%

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

   4. Simplified 88.7%

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

   if -2.99999999999999995e208 < c < -1.45e178

   1. Initial program 16.5%

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

      1. +-commutative 16.5%

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

      2. fma-def 16.5%

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

      3. *-commutative 16.5%

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

      4. *-commutative 16.5%

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

      5. cancel-sign-sub-inv 16.5%

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

      6. cancel-sign-sub 16.5%

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

      7. remove-double-neg 16.5%

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

      8. *-commutative 16.5%

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

      9. *-commutative 16.5%

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

   3. Simplified 16.5%

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

   4. Taylor expanded in z around 0 57.1%

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

      1. +-commutative 57.1%

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

      2. associate--l+ 57.1%

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

      3. sub-neg 57.1%

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

      4. sub-neg 57.1%

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

      5. associate-*r* 57.1%

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

      6. associate-*r* 57.1%

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

      7. distribute-lft-out-- 57.1%

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

      8. associate-*r* 57.1%

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

      9. +-commutative 57.1%

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

      10. *-commutative 57.1%

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

      11. associate-*l* 57.1%

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

      12. *-commutative 57.1%

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

      13. distribute-lft-out-- 57.1%

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

   6. Simplified 57.1%

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

   7. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. mul-1-neg 86.3%

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

      3. unsub-neg 86.3%

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

      4. *-commutative 86.3%

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

   9. Simplified 86.3%

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

   if -4.2000000000000002e134 < c < 5.5e15

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

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

      2. fma-def 77.0%

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

      3. *-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. cancel-sign-sub-inv 77.0%

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

      6. cancel-sign-sub 77.0%

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

      7. remove-double-neg 77.0%

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

      8. *-commutative 77.0%

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

      9. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around 0 81.3%

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

      1. +-commutative 81.3%

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

      2. associate--l+ 81.3%

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

      3. sub-neg 81.3%

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

      4. sub-neg 81.3%

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

      5. associate-*r* 81.3%

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

      6. associate-*r* 81.3%

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

      7. distribute-lft-out-- 82.0%

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

      8. associate-*r* 82.0%

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

      9. +-commutative 82.0%

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

      10. *-commutative 82.0%

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

      11. associate-*l* 82.0%

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

      12. *-commutative 82.0%

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

      13. distribute-lft-out-- 82.0%

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

   6. Simplified 82.7%

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

   7. Taylor expanded in c around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-+l+ 71.9%

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

      3. *-commutative 71.9%

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

      4. associate-*l* 71.4%

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

      5. mul-1-neg 71.4%

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

      6. associate-*r* 74.0%

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

      7. *-commutative 74.0%

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

      8. distribute-lft-neg-out 74.0%

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

      9. distribute-rgt-in 74.6%

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

      10. neg-mul-1 74.6%

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

      11. *-commutative 74.6%

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

      12. mul-1-neg 74.6%

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

      13. unsub-neg 74.6%

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

   9. Simplified 74.6%

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

   if 5.5e15 < c < 1.35e156

   1. Initial program 89.4%

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

   2. Taylor expanded in y around 0 78.4%

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

      1. *-commutative 78.4%

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

      2. *-commutative 78.4%

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

      3. *-commutative 78.4%

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

      4. *-rgt-identity 78.4%

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

      5. cancel-sign-sub-inv 78.4%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in j around inf 78.0%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+208}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1.45 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{+134}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 5: 30.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -5.5 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+153} \lor \neg \left(c \leq 5.8 \cdot 10^{+227}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* j (* t c))))
   (if (<= c -5.5e+145)
     t_2
     (if (<= c -3.1e+40)
       t_1
       (if (<= c -2.8e+34)
         (* (* x t) (- a))
         (if (<= c -5e-213)
           (* x (* y z))
           (if (<= c 3.2e-85)
             (* b (* a i))
             (if (<= c 5.8e+45)
               (* y (* i (- j)))
               (if (<= c 6.2e+103)
                 t_2
                 (if (or (<= c 1.8e+153) (not (<= c 5.8e+227)))
                   t_1
                   (* 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 t_1 = b * (z * -c);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -5.5e+145) {
		tmp = t_2;
	} else if (c <= -3.1e+40) {
		tmp = t_1;
	} else if (c <= -2.8e+34) {
		tmp = (x * t) * -a;
	} else if (c <= -5e-213) {
		tmp = x * (y * z);
	} else if (c <= 3.2e-85) {
		tmp = b * (a * i);
	} else if (c <= 5.8e+45) {
		tmp = y * (i * -j);
	} else if (c <= 6.2e+103) {
		tmp = t_2;
	} else if ((c <= 1.8e+153) || !(c <= 5.8e+227)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = j * (t * c)
    if (c <= (-5.5d+145)) then
        tmp = t_2
    else if (c <= (-3.1d+40)) then
        tmp = t_1
    else if (c <= (-2.8d+34)) then
        tmp = (x * t) * -a
    else if (c <= (-5d-213)) then
        tmp = x * (y * z)
    else if (c <= 3.2d-85) then
        tmp = b * (a * i)
    else if (c <= 5.8d+45) then
        tmp = y * (i * -j)
    else if (c <= 6.2d+103) then
        tmp = t_2
    else if ((c <= 1.8d+153) .or. (.not. (c <= 5.8d+227))) then
        tmp = t_1
    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 t_1 = b * (z * -c);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -5.5e+145) {
		tmp = t_2;
	} else if (c <= -3.1e+40) {
		tmp = t_1;
	} else if (c <= -2.8e+34) {
		tmp = (x * t) * -a;
	} else if (c <= -5e-213) {
		tmp = x * (y * z);
	} else if (c <= 3.2e-85) {
		tmp = b * (a * i);
	} else if (c <= 5.8e+45) {
		tmp = y * (i * -j);
	} else if (c <= 6.2e+103) {
		tmp = t_2;
	} else if ((c <= 1.8e+153) || !(c <= 5.8e+227)) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -5.5e+145:
		tmp = t_2
	elif c <= -3.1e+40:
		tmp = t_1
	elif c <= -2.8e+34:
		tmp = (x * t) * -a
	elif c <= -5e-213:
		tmp = x * (y * z)
	elif c <= 3.2e-85:
		tmp = b * (a * i)
	elif c <= 5.8e+45:
		tmp = y * (i * -j)
	elif c <= 6.2e+103:
		tmp = t_2
	elif (c <= 1.8e+153) or not (c <= 5.8e+227):
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(z * Float64(-c)))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -5.5e+145)
		tmp = t_2;
	elseif (c <= -3.1e+40)
		tmp = t_1;
	elseif (c <= -2.8e+34)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (c <= -5e-213)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 3.2e-85)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 5.8e+45)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 6.2e+103)
		tmp = t_2;
	elseif ((c <= 1.8e+153) || !(c <= 5.8e+227))
		tmp = t_1;
	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)
	t_1 = b * (z * -c);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -5.5e+145)
		tmp = t_2;
	elseif (c <= -3.1e+40)
		tmp = t_1;
	elseif (c <= -2.8e+34)
		tmp = (x * t) * -a;
	elseif (c <= -5e-213)
		tmp = x * (y * z);
	elseif (c <= 3.2e-85)
		tmp = b * (a * i);
	elseif (c <= 5.8e+45)
		tmp = y * (i * -j);
	elseif (c <= 6.2e+103)
		tmp = t_2;
	elseif ((c <= 1.8e+153) || ~((c <= 5.8e+227)))
		tmp = t_1;
	else
		tmp = c * (t * 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]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.5e+145], t$95$2, If[LessEqual[c, -3.1e+40], t$95$1, If[LessEqual[c, -2.8e+34], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[c, -5e-213], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.2e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+45], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.2e+103], t$95$2, If[Or[LessEqual[c, 1.8e+153], N[Not[LessEqual[c, 5.8e+227]], $MachinePrecision]], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -5.4999999999999995e145 or 5.7999999999999994e45 < c < 6.2000000000000003e103

   1. Initial program 52.0%

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

   2. Taylor expanded in c around inf 65.6%

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

      1. *-commutative 65.6%

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

      2. *-commutative 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in t around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. *-commutative 44.2%

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

      3. *-commutative 44.2%

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

      4. associate-*r* 49.3%

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

   7. Simplified 49.3%

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

   if -5.4999999999999995e145 < c < -3.0999999999999998e40 or 6.2000000000000003e103 < c < 1.8e153 or 5.7999999999999997e227 < c

   1. Initial program 75.0%

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

   2. Taylor expanded in y around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. *-commutative 77.2%

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

      3. *-commutative 77.2%

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

      4. *-rgt-identity 77.2%

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

      5. cancel-sign-sub-inv 77.2%

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

   4. Simplified 74.1%

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

   5. Taylor expanded in j around inf 75.6%

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

   6. Taylor expanded in z around inf 53.1%

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

      1. mul-1-neg 53.1%

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

      2. *-commutative 53.1%

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

   8. Simplified 53.1%

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

   if -3.0999999999999998e40 < c < -2.80000000000000008e34

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. cancel-sign-sub 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in i around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -2.80000000000000008e34 < c < -4.99999999999999977e-213

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. fma-def 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. cancel-sign-sub-inv 77.7%

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

      6. cancel-sign-sub 77.7%

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

      7. remove-double-neg 77.7%

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

      8. *-commutative 77.7%

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

      9. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate--l+ 82.4%

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

      3. sub-neg 82.4%

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

      4. sub-neg 82.4%

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

      5. associate-*r* 82.4%

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

      6. associate-*r* 82.4%

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

      7. distribute-lft-out-- 84.6%

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

      8. associate-*r* 84.6%

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

      9. +-commutative 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-*l* 84.6%

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

      12. *-commutative 84.6%

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

      13. distribute-lft-out-- 84.6%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   10. Taylor expanded in z around inf 47.7%

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

   if -4.99999999999999977e-213 < c < 3.20000000000000027e-85

   1. Initial program 77.7%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

      4. *-rgt-identity 60.8%

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

      5. cancel-sign-sub-inv 60.8%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in j around inf 42.1%

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

   6. Taylor expanded in c around 0 35.9%

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

      1. associate-*r* 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 38.9%

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

   8. Simplified 38.9%

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

   if 3.20000000000000027e-85 < c < 5.7999999999999994e45

   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. Taylor expanded in j around inf 51.3%

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

   3. Taylor expanded in c around 0 35.5%

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

      1. mul-1-neg 35.5%

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

      2. *-commutative 35.5%

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

      3. distribute-rgt-neg-in 35.5%

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

      4. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around 0 35.5%

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

      1. *-commutative 35.5%

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

      2. *-commutative 35.5%

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

      3. neg-mul-1 35.5%

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

      4. distribute-rgt-neg-in 35.5%

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

      5. associate-*r* 31.7%

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

   8. Simplified 31.7%

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

   if 1.8e153 < c < 5.7999999999999997e227

   1. Initial program 59.9%

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

   2. Taylor expanded in j around inf 53.3%

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

   3. Taylor expanded in c around inf 54.6%

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

      1. *-commutative 54.6%

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

   5. Simplified 54.6%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.5 \cdot 10^{+145}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.1 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{+34}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.2 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+153} \lor \neg \left(c \leq 5.8 \cdot 10^{+227}\right):\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 6: 49.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.2 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -4.2e+133)
     t_2
     (if (<= c -8.6e+70)
       t_1
       (if (<= c -4.9e+29)
         t_2
         (if (<= c -5.6e-141)
           (* x (* y z))
           (if (<= c 4e-83)
             (* a (- (* b i) (* x t)))
             (if (<= c 3.5e+98)
               (* j (- (* t c) (* y i)))
               (if (<= c 6.3e+106) 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 <= -4.2e+133) {
		tmp = t_2;
	} else if (c <= -8.6e+70) {
		tmp = t_1;
	} else if (c <= -4.9e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 4e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.5e+98) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 6.3e+106) {
		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 <= (-4.2d+133)) then
        tmp = t_2
    else if (c <= (-8.6d+70)) then
        tmp = t_1
    else if (c <= (-4.9d+29)) then
        tmp = t_2
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 4d-83) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3.5d+98) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= 6.3d+106) 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 <= -4.2e+133) {
		tmp = t_2;
	} else if (c <= -8.6e+70) {
		tmp = t_1;
	} else if (c <= -4.9e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 4e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.5e+98) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 6.3e+106) {
		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 <= -4.2e+133:
		tmp = t_2
	elif c <= -8.6e+70:
		tmp = t_1
	elif c <= -4.9e+29:
		tmp = t_2
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 4e-83:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3.5e+98:
		tmp = j * ((t * c) - (y * i))
	elif c <= 6.3e+106:
		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 <= -4.2e+133)
		tmp = t_2;
	elseif (c <= -8.6e+70)
		tmp = t_1;
	elseif (c <= -4.9e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 4e-83)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3.5e+98)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= 6.3e+106)
		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 <= -4.2e+133)
		tmp = t_2;
	elseif (c <= -8.6e+70)
		tmp = t_1;
	elseif (c <= -4.9e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 4e-83)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3.5e+98)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= 6.3e+106)
		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, -4.2e+133], t$95$2, If[LessEqual[c, -8.6e+70], t$95$1, If[LessEqual[c, -4.9e+29], t$95$2, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4e-83], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+98], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.3e+106], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.2e133 or -8.6000000000000002e70 < c < -4.9000000000000001e29 or 6.29999999999999974e106 < c

   1. Initial program 65.1%

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

   2. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

   4. Simplified 79.2%

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

   if -4.2e133 < c < -8.6000000000000002e70 or 3.5e98 < c < 6.29999999999999974e106

   1. Initial program 60.9%

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

   2. Taylor expanded in i around inf 63.6%

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

      1. cancel-sign-sub-inv 63.6%

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

      2. metadata-eval 63.6%

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

      3. *-lft-identity 63.6%

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

      4. +-commutative 63.6%

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

      5. mul-1-neg 63.6%

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

      6. unsub-neg 63.6%

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

      7. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   if -4.9000000000000001e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. fma-def 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. cancel-sign-sub-inv 74.1%

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

      6. cancel-sign-sub 74.1%

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

      7. remove-double-neg 74.1%

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

      8. *-commutative 74.1%

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

      9. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate--l+ 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. associate-*r* 80.9%

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

      6. associate-*r* 80.9%

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

      7. distribute-lft-out-- 84.1%

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

      8. associate-*r* 84.1%

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

      9. +-commutative 84.1%

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

      10. *-commutative 84.1%

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

      11. associate-*l* 84.1%

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

      12. *-commutative 84.1%

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

      13. distribute-lft-out-- 84.1%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in x around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   10. Taylor expanded in z around inf 52.7%

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

   if -5.60000000000000023e-141 < c < 4.0000000000000001e-83

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. cancel-sign-sub 58.4%

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

      4. +-commutative 58.4%

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

      5. mul-1-neg 58.4%

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

      6. unsub-neg 58.4%

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

      7. *-commutative 58.4%

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

      8. *-commutative 58.4%

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

   4. Simplified 58.4%

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

   if 4.0000000000000001e-83 < c < 3.5e98

   1. Initial program 89.0%

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

   2. Taylor expanded in j around inf 54.7%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{+133}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.9 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 7: 48.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 10^{-81}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

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 -3.4e+131)
     t_2
     (if (<= c -2.25e+74)
       t_1
       (if (<= c -4.4e+29)
         t_2
         (if (<= c -5.6e-141)
           (* x (* y z))
           (if (<= c 1e-81)
             (* a (- (* b i) (* x t)))
             (if (<= c 6.3e+97)
               (* t (- (* c j) (* x a)))
               (if (<= c 6.3e+106) 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 <= -3.4e+131) {
		tmp = t_2;
	} else if (c <= -2.25e+74) {
		tmp = t_1;
	} else if (c <= -4.4e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 1e-81) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 6.3e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.3e+106) {
		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 <= (-3.4d+131)) then
        tmp = t_2
    else if (c <= (-2.25d+74)) then
        tmp = t_1
    else if (c <= (-4.4d+29)) then
        tmp = t_2
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 1d-81) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 6.3d+97) then
        tmp = t * ((c * j) - (x * a))
    else if (c <= 6.3d+106) 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 <= -3.4e+131) {
		tmp = t_2;
	} else if (c <= -2.25e+74) {
		tmp = t_1;
	} else if (c <= -4.4e+29) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 1e-81) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 6.3e+97) {
		tmp = t * ((c * j) - (x * a));
	} else if (c <= 6.3e+106) {
		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 <= -3.4e+131:
		tmp = t_2
	elif c <= -2.25e+74:
		tmp = t_1
	elif c <= -4.4e+29:
		tmp = t_2
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 1e-81:
		tmp = a * ((b * i) - (x * t))
	elif c <= 6.3e+97:
		tmp = t * ((c * j) - (x * a))
	elif c <= 6.3e+106:
		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 <= -3.4e+131)
		tmp = t_2;
	elseif (c <= -2.25e+74)
		tmp = t_1;
	elseif (c <= -4.4e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1e-81)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 6.3e+97)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (c <= 6.3e+106)
		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 <= -3.4e+131)
		tmp = t_2;
	elseif (c <= -2.25e+74)
		tmp = t_1;
	elseif (c <= -4.4e+29)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 1e-81)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 6.3e+97)
		tmp = t * ((c * j) - (x * a));
	elseif (c <= 6.3e+106)
		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, -3.4e+131], t$95$2, If[LessEqual[c, -2.25e+74], t$95$1, If[LessEqual[c, -4.4e+29], t$95$2, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e-81], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.3e+97], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.3e+106], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.39999999999999986e131 or -2.25e74 < c < -4.4000000000000003e29 or 6.29999999999999974e106 < c

   1. Initial program 65.1%

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

   2. Taylor expanded in c around inf 79.2%

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

      1. *-commutative 79.2%

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

      2. *-commutative 79.2%

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

   4. Simplified 79.2%

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

   if -3.39999999999999986e131 < c < -2.25e74 or 6.29999999999999997e97 < c < 6.29999999999999974e106

   1. Initial program 60.9%

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

   2. Taylor expanded in i around inf 63.6%

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

      1. cancel-sign-sub-inv 63.6%

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

      2. metadata-eval 63.6%

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

      3. *-lft-identity 63.6%

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

      4. +-commutative 63.6%

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

      5. mul-1-neg 63.6%

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

      6. unsub-neg 63.6%

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

      7. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   if -4.4000000000000003e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. fma-def 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. cancel-sign-sub-inv 74.1%

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

      6. cancel-sign-sub 74.1%

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

      7. remove-double-neg 74.1%

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

      8. *-commutative 74.1%

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

      9. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate--l+ 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. associate-*r* 80.9%

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

      6. associate-*r* 80.9%

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

      7. distribute-lft-out-- 84.1%

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

      8. associate-*r* 84.1%

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

      9. +-commutative 84.1%

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

      10. *-commutative 84.1%

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

      11. associate-*l* 84.1%

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

      12. *-commutative 84.1%

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

      13. distribute-lft-out-- 84.1%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in x around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   10. Taylor expanded in z around inf 52.7%

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

   if -5.60000000000000023e-141 < c < 9.9999999999999996e-82

   1. Initial program 78.1%

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

   2. Taylor expanded in a around inf 58.4%

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

      1. associate-*r* 58.4%

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

      2. neg-mul-1 58.4%

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

      3. cancel-sign-sub 58.4%

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

      4. +-commutative 58.4%

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

      5. mul-1-neg 58.4%

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

      6. unsub-neg 58.4%

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

      7. *-commutative 58.4%

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

      8. *-commutative 58.4%

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

   4. Simplified 58.4%

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

   if 9.9999999999999996e-82 < c < 6.29999999999999997e97

   1. Initial program 89.0%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. +-commutative 56.6%

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

      2. mul-1-neg 56.6%

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

      3. unsub-neg 56.6%

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

      4. *-commutative 56.6%

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

      5. *-commutative 56.6%

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

   4. Simplified 56.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -2.25 \cdot 10^{+74}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 10^{-81}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+97}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;c \leq 6.3 \cdot 10^{+106}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 8: 30.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;c \leq -1.42 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))))
   (if (<= c -1.42e+155)
     (* j (* t c))
     (if (<= c -1.05e+41)
       t_1
       (if (<= c -2.4e+35)
         (* (* x t) (- a))
         (if (<= c -5e-213)
           (* x (* y z))
           (if (<= c 1.5e-85)
             (* b (* a i))
             (if (<= c 8e+29)
               (* i (* y (- j)))
               (if (<= c 1.5e+228) (* 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 = b * (z * -c);
	double tmp;
	if (c <= -1.42e+155) {
		tmp = j * (t * c);
	} else if (c <= -1.05e+41) {
		tmp = t_1;
	} else if (c <= -2.4e+35) {
		tmp = (x * t) * -a;
	} else if (c <= -5e-213) {
		tmp = x * (y * z);
	} else if (c <= 1.5e-85) {
		tmp = b * (a * i);
	} else if (c <= 8e+29) {
		tmp = i * (y * -j);
	} else if (c <= 1.5e+228) {
		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 = b * (z * -c)
    if (c <= (-1.42d+155)) then
        tmp = j * (t * c)
    else if (c <= (-1.05d+41)) then
        tmp = t_1
    else if (c <= (-2.4d+35)) then
        tmp = (x * t) * -a
    else if (c <= (-5d-213)) then
        tmp = x * (y * z)
    else if (c <= 1.5d-85) then
        tmp = b * (a * i)
    else if (c <= 8d+29) then
        tmp = i * (y * -j)
    else if (c <= 1.5d+228) 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 = b * (z * -c);
	double tmp;
	if (c <= -1.42e+155) {
		tmp = j * (t * c);
	} else if (c <= -1.05e+41) {
		tmp = t_1;
	} else if (c <= -2.4e+35) {
		tmp = (x * t) * -a;
	} else if (c <= -5e-213) {
		tmp = x * (y * z);
	} else if (c <= 1.5e-85) {
		tmp = b * (a * i);
	} else if (c <= 8e+29) {
		tmp = i * (y * -j);
	} else if (c <= 1.5e+228) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	tmp = 0
	if c <= -1.42e+155:
		tmp = j * (t * c)
	elif c <= -1.05e+41:
		tmp = t_1
	elif c <= -2.4e+35:
		tmp = (x * t) * -a
	elif c <= -5e-213:
		tmp = x * (y * z)
	elif c <= 1.5e-85:
		tmp = b * (a * i)
	elif c <= 8e+29:
		tmp = i * (y * -j)
	elif c <= 1.5e+228:
		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(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (c <= -1.42e+155)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -1.05e+41)
		tmp = t_1;
	elseif (c <= -2.4e+35)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (c <= -5e-213)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.5e-85)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 8e+29)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 1.5e+228)
		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 = b * (z * -c);
	tmp = 0.0;
	if (c <= -1.42e+155)
		tmp = j * (t * c);
	elseif (c <= -1.05e+41)
		tmp = t_1;
	elseif (c <= -2.4e+35)
		tmp = (x * t) * -a;
	elseif (c <= -5e-213)
		tmp = x * (y * z);
	elseif (c <= 1.5e-85)
		tmp = b * (a * i);
	elseif (c <= 8e+29)
		tmp = i * (y * -j);
	elseif (c <= 1.5e+228)
		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[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.42e+155], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.05e+41], t$95$1, If[LessEqual[c, -2.4e+35], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[c, -5e-213], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+29], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.5e+228], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if c < -1.41999999999999994e155

   1. Initial program 42.2%

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

   2. Taylor expanded in c around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in t around inf 45.7%

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

      1. *-commutative 45.7%

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

      2. *-commutative 45.7%

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

      3. *-commutative 45.7%

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

      4. associate-*r* 52.2%

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

   7. Simplified 52.2%

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

   if -1.41999999999999994e155 < c < -1.05e41 or 1.5000000000000001e228 < c

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

      4. *-rgt-identity 76.3%

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

      5. cancel-sign-sub-inv 76.3%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in j around inf 76.3%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -1.05e41 < c < -2.40000000000000015e35

   1. Initial program 100.0%

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

   2. Taylor expanded in a around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. cancel-sign-sub 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. *-commutative 100.0%

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

      8. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in i around 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -2.40000000000000015e35 < c < -4.99999999999999977e-213

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. fma-def 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. cancel-sign-sub-inv 77.7%

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

      6. cancel-sign-sub 77.7%

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

      7. remove-double-neg 77.7%

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

      8. *-commutative 77.7%

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

      9. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate--l+ 82.4%

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

      3. sub-neg 82.4%

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

      4. sub-neg 82.4%

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

      5. associate-*r* 82.4%

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

      6. associate-*r* 82.4%

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

      7. distribute-lft-out-- 84.6%

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

      8. associate-*r* 84.6%

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

      9. +-commutative 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-*l* 84.6%

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

      12. *-commutative 84.6%

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

      13. distribute-lft-out-- 84.6%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   10. Taylor expanded in z around inf 47.7%

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

   if -4.99999999999999977e-213 < c < 1.50000000000000011e-85

   1. Initial program 77.7%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

      4. *-rgt-identity 60.8%

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

      5. cancel-sign-sub-inv 60.8%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in j around inf 42.1%

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

   6. Taylor expanded in c around 0 35.9%

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

      1. associate-*r* 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 38.9%

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

   8. Simplified 38.9%

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

   if 1.50000000000000011e-85 < c < 7.99999999999999931e29

   1. Initial program 80.6%

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

   2. Taylor expanded in j around inf 44.4%

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

   3. Taylor expanded in c around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. *-commutative 35.8%

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

      3. distribute-rgt-neg-in 35.8%

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

      4. *-commutative 35.8%

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

   5. Simplified 35.8%

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

   if 7.99999999999999931e29 < c < 1.5000000000000001e228

   1. Initial program 75.4%

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

   2. Taylor expanded in j around inf 48.4%

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

   3. Taylor expanded in c around inf 42.7%

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

      1. *-commutative 42.7%

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

      2. *-commutative 42.7%

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

      3. associate-*r* 45.8%

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

   5. Simplified 45.8%

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

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq -5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 9: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+207} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.6e+116)
     t_1
     (if (<= x 8.5e-263)
       (* c (- (* t j) (* z b)))
       (if (<= x 9.4e+33)
         (* i (- (* a b) (* y j)))
         (if (or (<= x 2.4e+207) (not (<= x 1.6e+251)))
           t_1
           (* z (- (* x y) (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.6e+116) {
		tmp = t_1;
	} else if (x <= 8.5e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 9.4e+33) {
		tmp = i * ((a * b) - (y * j));
	} else if ((x <= 2.4e+207) || !(x <= 1.6e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.6d+116)) then
        tmp = t_1
    else if (x <= 8.5d-263) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 9.4d+33) then
        tmp = i * ((a * b) - (y * j))
    else if ((x <= 2.4d+207) .or. (.not. (x <= 1.6d+251))) then
        tmp = t_1
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.6e+116) {
		tmp = t_1;
	} else if (x <= 8.5e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 9.4e+33) {
		tmp = i * ((a * b) - (y * j));
	} else if ((x <= 2.4e+207) || !(x <= 1.6e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.6e+116:
		tmp = t_1
	elif x <= 8.5e-263:
		tmp = c * ((t * j) - (z * b))
	elif x <= 9.4e+33:
		tmp = i * ((a * b) - (y * j))
	elif (x <= 2.4e+207) or not (x <= 1.6e+251):
		tmp = t_1
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.6e+116)
		tmp = t_1;
	elseif (x <= 8.5e-263)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 9.4e+33)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif ((x <= 2.4e+207) || !(x <= 1.6e+251))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.6e+116)
		tmp = t_1;
	elseif (x <= 8.5e-263)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 9.4e+33)
		tmp = i * ((a * b) - (y * j));
	elseif ((x <= 2.4e+207) || ~((x <= 1.6e+251)))
		tmp = t_1;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+116], t$95$1, If[LessEqual[x, 8.5e-263], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.4e+33], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.4e+207], N[Not[LessEqual[x, 1.6e+251]], $MachinePrecision]], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.6e116 or 9.3999999999999996e33 < x < 2.4000000000000001e207 or 1.5999999999999999e251 < x

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. fma-def 83.2%

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

      3. *-commutative 83.2%

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

      4. *-commutative 83.2%

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

      5. cancel-sign-sub-inv 83.2%

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

      6. cancel-sign-sub 83.2%

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

      7. remove-double-neg 83.2%

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

      8. *-commutative 83.2%

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

      9. *-commutative 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in z around 0 72.3%

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

      1. +-commutative 72.3%

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

      2. associate--l+ 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. associate-*r* 72.3%

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

      6. associate-*r* 72.3%

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

      7. distribute-lft-out-- 72.3%

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

      8. associate-*r* 72.3%

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

      9. +-commutative 72.3%

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

      10. *-commutative 72.3%

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

      11. associate-*l* 72.3%

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

      12. *-commutative 72.3%

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

      13. distribute-lft-out-- 72.3%

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

   6. Simplified 73.6%

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

   7. Taylor expanded in x around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. *-commutative 73.8%

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

   9. Simplified 73.8%

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

   if -1.6e116 < x < 8.49999999999999975e-263

   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. Taylor expanded in c around inf 63.7%

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

      1. *-commutative 63.7%

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

      2. *-commutative 63.7%

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

   4. Simplified 63.7%

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

   if 8.49999999999999975e-263 < x < 9.3999999999999996e33

   1. Initial program 68.1%

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

   2. Taylor expanded in i around inf 58.7%

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

      1. cancel-sign-sub-inv 58.7%

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

      2. metadata-eval 58.7%

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

      3. *-lft-identity 58.7%

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

      4. +-commutative 58.7%

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

      5. mul-1-neg 58.7%

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

      6. unsub-neg 58.7%

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

      7. *-commutative 58.7%

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

   4. Simplified 58.7%

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

   if 2.4000000000000001e207 < x < 1.5999999999999999e251

   1. Initial program 36.2%

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

   2. Taylor expanded in z around inf 74.1%

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

      1. *-commutative 74.1%

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

   4. Simplified 74.1%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 9.4 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+207} \lor \neg \left(x \leq 1.6 \cdot 10^{+251}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 10: 49.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 15000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -3.2e+131)
     t_1
     (if (<= c -8.6e+70)
       (* i (- (* a b) (* y j)))
       (if (<= c -6.8e+29)
         t_1
         (if (<= c -5.6e-141)
           (* x (* y z))
           (if (<= c 15000000000000.0) (* a (- (* b i) (* x t))) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+131) {
		tmp = t_1;
	} else if (c <= -8.6e+70) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -6.8e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 15000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} 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 = c * ((t * j) - (z * b))
    if (c <= (-3.2d+131)) then
        tmp = t_1
    else if (c <= (-8.6d+70)) then
        tmp = i * ((a * b) - (y * j))
    else if (c <= (-6.8d+29)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 15000000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -3.2e+131) {
		tmp = t_1;
	} else if (c <= -8.6e+70) {
		tmp = i * ((a * b) - (y * j));
	} else if (c <= -6.8e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 15000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -3.2e+131:
		tmp = t_1
	elif c <= -8.6e+70:
		tmp = i * ((a * b) - (y * j))
	elif c <= -6.8e+29:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 15000000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -3.2e+131)
		tmp = t_1;
	elseif (c <= -8.6e+70)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (c <= -6.8e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 15000000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -3.2e+131)
		tmp = t_1;
	elseif (c <= -8.6e+70)
		tmp = i * ((a * b) - (y * j));
	elseif (c <= -6.8e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 15000000000000.0)
		tmp = a * ((b * i) - (x * t));
	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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.2e+131], t$95$1, If[LessEqual[c, -8.6e+70], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.8e+29], t$95$1, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 15000000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.2000000000000002e131 or -8.6000000000000002e70 < c < -6.79999999999999963e29 or 1.5e13 < c

   1. Initial program 68.5%

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

   2. Taylor expanded in c around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

   4. Simplified 75.8%

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

   if -3.2000000000000002e131 < c < -8.6000000000000002e70

   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. Taylor expanded in i around inf 56.3%

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

      1. cancel-sign-sub-inv 56.3%

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

      2. metadata-eval 56.3%

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

      3. *-lft-identity 56.3%

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

      4. +-commutative 56.3%

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

      5. mul-1-neg 56.3%

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

      6. unsub-neg 56.3%

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

      7. *-commutative 56.3%

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

   4. Simplified 56.3%

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

   if -6.79999999999999963e29 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

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

      1. +-commutative 70.9%

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

      2. fma-def 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. cancel-sign-sub-inv 74.1%

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

      6. cancel-sign-sub 74.1%

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

      7. remove-double-neg 74.1%

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

      8. *-commutative 74.1%

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

      9. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate--l+ 80.9%

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

      3. sub-neg 80.9%

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

      4. sub-neg 80.9%

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

      5. associate-*r* 80.9%

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

      6. associate-*r* 80.9%

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

      7. distribute-lft-out-- 84.1%

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

      8. associate-*r* 84.1%

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

      9. +-commutative 84.1%

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

      10. *-commutative 84.1%

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

      11. associate-*l* 84.1%

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

      12. *-commutative 84.1%

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

      13. distribute-lft-out-- 84.1%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in x around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   9. Simplified 58.8%

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

   10. Taylor expanded in z around inf 52.7%

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

   if -5.60000000000000023e-141 < c < 1.5e13

   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. Taylor expanded in a around inf 54.8%

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

      1. associate-*r* 54.8%

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

      2. neg-mul-1 54.8%

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

      3. cancel-sign-sub 54.8%

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

      4. +-commutative 54.8%

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

      5. mul-1-neg 54.8%

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

      6. unsub-neg 54.8%

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

      7. *-commutative 54.8%

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

      8. *-commutative 54.8%

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

   4. Simplified 54.8%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+131}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 15000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 11: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+100} \lor \neg \left(y \leq 2.6 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -5e+100) (not (<= y 2.6e+119)))
   (* y (- (* x z) (* i j)))
   (+ (* t (* c 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 <= -5e+100) || !(y <= 2.6e+119)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (t * (c * 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 ((y <= (-5d+100)) .or. (.not. (y <= 2.6d+119))) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = (t * (c * 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 ((y <= -5e+100) || !(y <= 2.6e+119)) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -5e+100) or not (y <= 2.6e+119):
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = (t * (c * j)) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -5e+100) || !(y <= 2.6e+119))
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = Float64(Float64(t * Float64(c * 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 ((y <= -5e+100) || ~((y <= 2.6e+119)))
		tmp = y * ((x * z) - (i * j));
	else
		tmp = (t * (c * 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[y, -5e+100], N[Not[LessEqual[y, 2.6e+119]], $MachinePrecision]], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(c * j), $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 y < -4.9999999999999999e100 or 2.6e119 < y

   1. Initial program 62.9%

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

      1. +-commutative 62.9%

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

      2. fma-def 64.1%

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

      3. *-commutative 64.1%

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

      4. *-commutative 64.1%

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

      5. cancel-sign-sub-inv 64.1%

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

      6. cancel-sign-sub 64.1%

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

      7. remove-double-neg 64.1%

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

      8. *-commutative 64.1%

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

      9. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in z around 0 65.6%

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

      1. +-commutative 65.6%

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

      2. associate--l+ 65.6%

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

      3. sub-neg 65.6%

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

      4. sub-neg 65.6%

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

      5. associate-*r* 65.6%

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

      6. associate-*r* 65.6%

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

      7. distribute-lft-out-- 66.7%

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

      8. associate-*r* 66.7%

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

      9. +-commutative 66.7%

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

      10. *-commutative 66.7%

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

      11. associate-*l* 66.7%

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

      12. *-commutative 66.7%

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

      13. distribute-lft-out-- 66.7%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in y around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

   9. Simplified 71.5%

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

   if -4.9999999999999999e100 < y < 2.6e119

   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. Taylor expanded in y around 0 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. *-commutative 72.2%

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

      4. *-rgt-identity 72.2%

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

      5. cancel-sign-sub-inv 72.2%

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

   4. Simplified 73.8%

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

   5. Taylor expanded in j around inf 64.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+100} \lor \neg \left(y \leq 2.6 \cdot 10^{+119}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 12: 30.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := j \cdot \left(t \cdot c\right)\\ \mathbf{if}\;c \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* j (* t c))))
   (if (<= c -3.1e+155)
     t_2
     (if (<= c -3.2e+51)
       t_1
       (if (<= c -5.4e+32)
         t_2
         (if (<= c -3.5e-213)
           (* x (* y z))
           (if (<= c 4.9e-85)
             (* b (* a i))
             (if (<= c 2.5e+228) (* 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 = b * (z * -c);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -3.1e+155) {
		tmp = t_2;
	} else if (c <= -3.2e+51) {
		tmp = t_1;
	} else if (c <= -5.4e+32) {
		tmp = t_2;
	} else if (c <= -3.5e-213) {
		tmp = x * (y * z);
	} else if (c <= 4.9e-85) {
		tmp = b * (a * i);
	} else if (c <= 2.5e+228) {
		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) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = j * (t * c)
    if (c <= (-3.1d+155)) then
        tmp = t_2
    else if (c <= (-3.2d+51)) then
        tmp = t_1
    else if (c <= (-5.4d+32)) then
        tmp = t_2
    else if (c <= (-3.5d-213)) then
        tmp = x * (y * z)
    else if (c <= 4.9d-85) then
        tmp = b * (a * i)
    else if (c <= 2.5d+228) 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 = b * (z * -c);
	double t_2 = j * (t * c);
	double tmp;
	if (c <= -3.1e+155) {
		tmp = t_2;
	} else if (c <= -3.2e+51) {
		tmp = t_1;
	} else if (c <= -5.4e+32) {
		tmp = t_2;
	} else if (c <= -3.5e-213) {
		tmp = x * (y * z);
	} else if (c <= 4.9e-85) {
		tmp = b * (a * i);
	} else if (c <= 2.5e+228) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = j * (t * c)
	tmp = 0
	if c <= -3.1e+155:
		tmp = t_2
	elif c <= -3.2e+51:
		tmp = t_1
	elif c <= -5.4e+32:
		tmp = t_2
	elif c <= -3.5e-213:
		tmp = x * (y * z)
	elif c <= 4.9e-85:
		tmp = b * (a * i)
	elif c <= 2.5e+228:
		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(b * Float64(z * Float64(-c)))
	t_2 = Float64(j * Float64(t * c))
	tmp = 0.0
	if (c <= -3.1e+155)
		tmp = t_2;
	elseif (c <= -3.2e+51)
		tmp = t_1;
	elseif (c <= -5.4e+32)
		tmp = t_2;
	elseif (c <= -3.5e-213)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 4.9e-85)
		tmp = Float64(b * Float64(a * i));
	elseif (c <= 2.5e+228)
		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 = b * (z * -c);
	t_2 = j * (t * c);
	tmp = 0.0;
	if (c <= -3.1e+155)
		tmp = t_2;
	elseif (c <= -3.2e+51)
		tmp = t_1;
	elseif (c <= -5.4e+32)
		tmp = t_2;
	elseif (c <= -3.5e-213)
		tmp = x * (y * z);
	elseif (c <= 4.9e-85)
		tmp = b * (a * i);
	elseif (c <= 2.5e+228)
		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[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.1e+155], t$95$2, If[LessEqual[c, -3.2e+51], t$95$1, If[LessEqual[c, -5.4e+32], t$95$2, If[LessEqual[c, -3.5e-213], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e+228], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.09999999999999989e155 or -3.2000000000000002e51 < c < -5.40000000000000025e32

   1. Initial program 43.2%

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

   2. Taylor expanded in c around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. *-commutative 73.5%

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

   4. Simplified 73.5%

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

   5. Taylor expanded in t around inf 46.3%

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

      1. *-commutative 46.3%

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

      2. *-commutative 46.3%

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

      3. *-commutative 46.3%

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

      4. associate-*r* 52.1%

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

   7. Simplified 52.1%

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

   if -3.09999999999999989e155 < c < -3.2000000000000002e51 or 2.5e228 < c

   1. Initial program 74.4%

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

   2. Taylor expanded in y around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. *-commutative 77.4%

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

      3. *-commutative 77.4%

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

      4. *-rgt-identity 77.4%

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

      5. cancel-sign-sub-inv 77.4%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in j around inf 75.3%

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

   6. Taylor expanded in z around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. *-commutative 54.9%

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

   8. Simplified 54.9%

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

   if -5.40000000000000025e32 < c < -3.50000000000000017e-213

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

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

      2. fma-def 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. cancel-sign-sub-inv 77.7%

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

      6. cancel-sign-sub 77.7%

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

      7. remove-double-neg 77.7%

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

      8. *-commutative 77.7%

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

      9. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in z around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate--l+ 82.4%

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

      3. sub-neg 82.4%

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

      4. sub-neg 82.4%

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

      5. associate-*r* 82.4%

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

      6. associate-*r* 82.4%

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

      7. distribute-lft-out-- 84.6%

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

      8. associate-*r* 84.6%

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

      9. +-commutative 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-*l* 84.6%

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

      12. *-commutative 84.6%

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

      13. distribute-lft-out-- 84.6%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. *-commutative 60.8%

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

   9. Simplified 60.8%

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

   10. Taylor expanded in z around inf 47.7%

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

   if -3.50000000000000017e-213 < c < 4.90000000000000015e-85

   1. Initial program 77.7%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. *-commutative 60.8%

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

      4. *-rgt-identity 60.8%

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

      5. cancel-sign-sub-inv 60.8%

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

   4. Simplified 62.5%

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

   5. Taylor expanded in j around inf 42.1%

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

   6. Taylor expanded in c around 0 35.9%

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

      1. associate-*r* 34.5%

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

      2. *-commutative 34.5%

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

      3. associate-*l* 38.9%

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

   8. Simplified 38.9%

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

   if 4.90000000000000015e-85 < c < 2.5e228

   1. Initial program 77.0%

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

   2. Taylor expanded in j around inf 47.2%

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

   3. Taylor expanded in c around inf 34.0%

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

      1. *-commutative 34.0%

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

      2. *-commutative 34.0%

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

      3. associate-*r* 36.2%

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

   5. Simplified 36.2%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.2 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 13: 30.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_2 := \left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{if}\;c \leq -1.52 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 29000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* z (- c)))) (t_2 (* (* x t) (- a))))
   (if (<= c -1.52e+156)
     (* j (* t c))
     (if (<= c -4e+40)
       t_1
       (if (<= c -4.8e+37)
         t_2
         (if (<= c -3.3e-174)
           (* x (* y z))
           (if (<= c 29000000000000.0)
             t_2
             (if (<= c 1.55e+228) (* 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 = b * (z * -c);
	double t_2 = (x * t) * -a;
	double tmp;
	if (c <= -1.52e+156) {
		tmp = j * (t * c);
	} else if (c <= -4e+40) {
		tmp = t_1;
	} else if (c <= -4.8e+37) {
		tmp = t_2;
	} else if (c <= -3.3e-174) {
		tmp = x * (y * z);
	} else if (c <= 29000000000000.0) {
		tmp = t_2;
	} else if (c <= 1.55e+228) {
		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) :: t_2
    real(8) :: tmp
    t_1 = b * (z * -c)
    t_2 = (x * t) * -a
    if (c <= (-1.52d+156)) then
        tmp = j * (t * c)
    else if (c <= (-4d+40)) then
        tmp = t_1
    else if (c <= (-4.8d+37)) then
        tmp = t_2
    else if (c <= (-3.3d-174)) then
        tmp = x * (y * z)
    else if (c <= 29000000000000.0d0) then
        tmp = t_2
    else if (c <= 1.55d+228) 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 = b * (z * -c);
	double t_2 = (x * t) * -a;
	double tmp;
	if (c <= -1.52e+156) {
		tmp = j * (t * c);
	} else if (c <= -4e+40) {
		tmp = t_1;
	} else if (c <= -4.8e+37) {
		tmp = t_2;
	} else if (c <= -3.3e-174) {
		tmp = x * (y * z);
	} else if (c <= 29000000000000.0) {
		tmp = t_2;
	} else if (c <= 1.55e+228) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (z * -c)
	t_2 = (x * t) * -a
	tmp = 0
	if c <= -1.52e+156:
		tmp = j * (t * c)
	elif c <= -4e+40:
		tmp = t_1
	elif c <= -4.8e+37:
		tmp = t_2
	elif c <= -3.3e-174:
		tmp = x * (y * z)
	elif c <= 29000000000000.0:
		tmp = t_2
	elif c <= 1.55e+228:
		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(b * Float64(z * Float64(-c)))
	t_2 = Float64(Float64(x * t) * Float64(-a))
	tmp = 0.0
	if (c <= -1.52e+156)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -4e+40)
		tmp = t_1;
	elseif (c <= -4.8e+37)
		tmp = t_2;
	elseif (c <= -3.3e-174)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 29000000000000.0)
		tmp = t_2;
	elseif (c <= 1.55e+228)
		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 = b * (z * -c);
	t_2 = (x * t) * -a;
	tmp = 0.0;
	if (c <= -1.52e+156)
		tmp = j * (t * c);
	elseif (c <= -4e+40)
		tmp = t_1;
	elseif (c <= -4.8e+37)
		tmp = t_2;
	elseif (c <= -3.3e-174)
		tmp = x * (y * z);
	elseif (c <= 29000000000000.0)
		tmp = t_2;
	elseif (c <= 1.55e+228)
		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[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision]}, If[LessEqual[c, -1.52e+156], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e+40], t$95$1, If[LessEqual[c, -4.8e+37], t$95$2, If[LessEqual[c, -3.3e-174], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 29000000000000.0], t$95$2, If[LessEqual[c, 1.55e+228], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.52e156

   1. Initial program 42.2%

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

   2. Taylor expanded in c around inf 73.3%

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

      1. *-commutative 73.3%

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

      2. *-commutative 73.3%

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

   4. Simplified 73.3%

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

   5. Taylor expanded in t around inf 45.7%

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

      1. *-commutative 45.7%

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

      2. *-commutative 45.7%

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

      3. *-commutative 45.7%

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

      4. associate-*r* 52.2%

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

   7. Simplified 52.2%

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

   if -1.52e156 < c < -4.00000000000000012e40 or 1.5499999999999999e228 < c

   1. Initial program 71.3%

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

   2. Taylor expanded in y around 0 76.3%

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

      1. *-commutative 76.3%

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

      2. *-commutative 76.3%

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

      3. *-commutative 76.3%

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

      4. *-rgt-identity 76.3%

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

      5. cancel-sign-sub-inv 76.3%

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

   4. Simplified 74.2%

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

   5. Taylor expanded in j around inf 76.3%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. mul-1-neg 54.7%

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

      2. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -4.00000000000000012e40 < c < -4.8e37 or -3.3000000000000001e-174 < c < 2.9e13

   1. Initial program 79.2%

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

   2. Taylor expanded in a around inf 55.4%

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

      1. associate-*r* 55.4%

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

      2. neg-mul-1 55.4%

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

      3. cancel-sign-sub 55.4%

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

      4. +-commutative 55.4%

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

      5. mul-1-neg 55.4%

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

      6. unsub-neg 55.4%

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

      7. *-commutative 55.4%

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

      8. *-commutative 55.4%

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

   4. Simplified 55.4%

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

   5. Taylor expanded in i around 0 34.8%

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

      1. neg-mul-1 34.8%

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

      2. distribute-rgt-neg-in 34.8%

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

   7. Simplified 34.8%

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

   if -4.8e37 < c < -3.3000000000000001e-174

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

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

      2. fma-def 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

      5. cancel-sign-sub-inv 75.5%

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

      6. cancel-sign-sub 75.5%

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

      7. remove-double-neg 75.5%

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

      8. *-commutative 75.5%

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

      9. *-commutative 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in z around 0 81.2%

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

      1. +-commutative 81.2%

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

      2. associate--l+ 81.2%

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

      3. sub-neg 81.2%

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

      4. sub-neg 81.2%

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

      5. associate-*r* 81.2%

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

      6. associate-*r* 81.2%

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

      7. distribute-lft-out-- 83.9%

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

      8. associate-*r* 83.9%

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

      9. +-commutative 83.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 83.9%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 86.7%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 60.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 60.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 60.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 60.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 60.1%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 60.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   10. Taylor expanded in z around inf 52.3%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if 2.9e13 < c < 1.5499999999999999e228

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 48.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. Taylor expanded in c around inf 41.1%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 44.1%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   5. Simplified 44.1%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.52 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -4.8 \cdot 10^{+37}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq -3.3 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 29000000000000:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+228}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 14: 40.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;c \leq -7 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= c -7e+134)
     (* j (* t c))
     (if (<= c -9.5e+37)
       t_1
       (if (<= c -5.6e-141)
         (* x (* y z))
         (if (<= c 3.3e+128)
           t_1
           (if (<= c 5.5e+227) (* t (* c j)) (* b (* z (- c))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -7e+134) {
		tmp = j * (t * c);
	} else if (c <= -9.5e+37) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 3.3e+128) {
		tmp = t_1;
	} else if (c <= 5.5e+227) {
		tmp = t * (c * j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (c <= (-7d+134)) then
        tmp = j * (t * c)
    else if (c <= (-9.5d+37)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 3.3d+128) then
        tmp = t_1
    else if (c <= 5.5d+227) then
        tmp = t * (c * j)
    else
        tmp = b * (z * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -7e+134) {
		tmp = j * (t * c);
	} else if (c <= -9.5e+37) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 3.3e+128) {
		tmp = t_1;
	} else if (c <= 5.5e+227) {
		tmp = t * (c * j);
	} else {
		tmp = b * (z * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if c <= -7e+134:
		tmp = j * (t * c)
	elif c <= -9.5e+37:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 3.3e+128:
		tmp = t_1
	elif c <= 5.5e+227:
		tmp = t * (c * j)
	else:
		tmp = b * (z * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (c <= -7e+134)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -9.5e+37)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 3.3e+128)
		tmp = t_1;
	elseif (c <= 5.5e+227)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(b * Float64(z * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (c <= -7e+134)
		tmp = j * (t * c);
	elseif (c <= -9.5e+37)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 3.3e+128)
		tmp = t_1;
	elseif (c <= 5.5e+227)
		tmp = t * (c * j);
	else
		tmp = b * (z * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7e+134], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -9.5e+37], t$95$1, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e+128], t$95$1, If[LessEqual[c, 5.5e+227], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.00000000000000006e134

   1. Initial program 47.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 77.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 77.2%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 77.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      3. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot c \]

      4. associate-*r* 50.7%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   if -7.00000000000000006e134 < c < -9.4999999999999995e37 or -5.60000000000000023e-141 < c < 3.3000000000000001e128

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 51.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 51.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 51.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 51.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 51.6%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 51.6%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 51.6%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

      7. *-commutative 51.6%

         \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

      8. *-commutative 51.6%

         \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

   4. Simplified 51.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]

   if -9.4999999999999995e37 < c < -5.60000000000000023e-141

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 74.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. remove-double-neg 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      9. *-commutative 74.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 74.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 81.5%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right) \]

      2. associate--l+ 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      3. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right)}\right) \]

      4. sub-neg 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      5. associate-*r* 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. associate-*r* 81.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      7. distribute-lft-out-- 84.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) \]

      8. associate-*r* 84.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) \]

      9. +-commutative 84.6%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 84.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 84.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 84.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 84.6%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 87.8%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 57.1%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 57.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 57.1%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 57.1%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 57.1%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 57.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   10. Taylor expanded in z around inf 51.1%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if 3.3000000000000001e128 < c < 5.5000000000000001e227

   1. Initial program 68.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 45.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. Taylor expanded in c around inf 46.0%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 46.0%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 47.7%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if 5.5000000000000001e227 < c

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 88.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative 88.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b} \]

      2. *-commutative 88.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \left(\color{blue}{z \cdot c} - a \cdot i\right) \cdot b \]

      3. *-commutative 88.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{b \cdot \left(z \cdot c - a \cdot i\right)} \]

      4. *-rgt-identity 88.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

      5. cancel-sign-sub-inv 88.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) + \left(-b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

   4. Simplified 84.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in j around inf 84.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} + b \cdot \left(a \cdot i - z \cdot c\right) \]

   6. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 69.3%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. *-commutative 69.3%

         \[\leadsto -b \cdot \color{blue}{\left(z \cdot c\right)} \]

   8. Simplified 69.3%

      \[\leadsto \color{blue}{-b \cdot \left(z \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7 \cdot 10^{+134}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+227}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \end{array} \]

Alternative 15: 41.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= c -9.5e+156)
     (* j (* t c))
     (if (<= c -1.3e+30)
       t_1
       (if (<= c -5.6e-141)
         (* x (* y z))
         (if (<= c 1.75e+126) (* a (- (* b i) (* x t))) 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 tmp;
	if (c <= -9.5e+156) {
		tmp = j * (t * c);
	} else if (c <= -1.3e+30) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 1.75e+126) {
		tmp = a * ((b * i) - (x * t));
	} 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 = b * ((a * i) - (z * c))
    if (c <= (-9.5d+156)) then
        tmp = j * (t * c)
    else if (c <= (-1.3d+30)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 1.75d+126) then
        tmp = a * ((b * i) - (x * t))
    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 = b * ((a * i) - (z * c));
	double tmp;
	if (c <= -9.5e+156) {
		tmp = j * (t * c);
	} else if (c <= -1.3e+30) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 1.75e+126) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if c <= -9.5e+156:
		tmp = j * (t * c)
	elif c <= -1.3e+30:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 1.75e+126:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = 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)))
	tmp = 0.0
	if (c <= -9.5e+156)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -1.3e+30)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1.75e+126)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = 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));
	tmp = 0.0;
	if (c <= -9.5e+156)
		tmp = j * (t * c);
	elseif (c <= -1.3e+30)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 1.75e+126)
		tmp = a * ((b * i) - (x * t));
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e+156], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e+30], t$95$1, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.75e+126], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.5000000000000002e156

   1. Initial program 42.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 73.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 73.3%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 73.3%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 73.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around inf 45.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.7%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. *-commutative 45.7%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      3. *-commutative 45.7%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot c \]

      4. associate-*r* 52.2%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   7. Simplified 52.2%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   if -9.5000000000000002e156 < c < -1.29999999999999994e30 or 1.7500000000000001e126 < c

   1. Initial program 71.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 55.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 55.9%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   4. Simplified 55.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -1.29999999999999994e30 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. remove-double-neg 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      9. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 80.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right) \]

      2. associate--l+ 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      3. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right)}\right) \]

      4. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      5. associate-*r* 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. associate-*r* 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      7. distribute-lft-out-- 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) \]

      8. associate-*r* 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) \]

      9. +-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 87.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 58.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 58.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 58.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   10. Taylor expanded in z around inf 52.7%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -5.60000000000000023e-141 < c < 1.7500000000000001e126

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 52.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 52.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 52.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 52.9%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 52.9%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

      7. *-commutative 52.9%

         \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

      8. *-commutative 52.9%

         \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

   4. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+30}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 16: 49.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 16000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -2.05e+30)
     t_1
     (if (<= c -5.6e-141)
       (* x (* y z))
       (if (<= c 16000000000000.0) (* a (- (* b i) (* x t))) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.05e+30) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 16000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} 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 = c * ((t * j) - (z * b))
    if (c <= (-2.05d+30)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 16000000000000.0d0) then
        tmp = a * ((b * i) - (x * t))
    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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -2.05e+30) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 16000000000000.0) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -2.05e+30:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 16000000000000.0:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -2.05e+30)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 16000000000000.0)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -2.05e+30)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 16000000000000.0)
		tmp = a * ((b * i) - (x * t));
	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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.05e+30], t$95$1, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 16000000000000.0], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.05000000000000003e30 or 1.6e13 < c

   1. Initial program 67.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 70.3%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 70.3%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 70.3%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 70.3%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -2.05000000000000003e30 < c < -5.60000000000000023e-141

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.9%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 74.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. remove-double-neg 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      9. *-commutative 74.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 74.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 80.9%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right) \]

      2. associate--l+ 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      3. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right)}\right) \]

      4. sub-neg 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      5. associate-*r* 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. associate-*r* 80.9%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      7. distribute-lft-out-- 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) \]

      8. associate-*r* 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) \]

      9. +-commutative 84.1%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 84.1%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 87.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 58.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 58.8%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 58.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 58.8%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 58.8%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   10. Taylor expanded in z around inf 52.7%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -5.60000000000000023e-141 < c < 1.6e13

   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. Taylor expanded in a around inf 54.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 54.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 54.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 54.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 54.8%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 54.8%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 54.8%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

      7. *-commutative 54.8%

         \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

      8. *-commutative 54.8%

         \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

   4. Simplified 54.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 16000000000000:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 17: 52.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.25 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.25e+116)
     t_1
     (if (<= x 2e-263)
       (* c (- (* t j) (* z b)))
       (if (<= x 4.5e+34) (* i (- (* a b) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.25e+116) {
		tmp = t_1;
	} else if (x <= 2e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.5e+34) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2.25d+116)) then
        tmp = t_1
    else if (x <= 2d-263) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 4.5d+34) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.25e+116) {
		tmp = t_1;
	} else if (x <= 2e-263) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 4.5e+34) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.25e+116:
		tmp = t_1
	elif x <= 2e-263:
		tmp = c * ((t * j) - (z * b))
	elif x <= 4.5e+34:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.25e+116)
		tmp = t_1;
	elseif (x <= 2e-263)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 4.5e+34)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * 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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.25e+116)
		tmp = t_1;
	elseif (x <= 2e-263)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 4.5e+34)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.25e+116], t$95$1, If[LessEqual[x, 2e-263], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+34], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.25000000000000008e116 or 4.5e34 < x

   1. Initial program 76.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.3%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 78.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. remove-double-neg 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      9. *-commutative 78.5%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 78.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right) \]

      2. associate--l+ 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      3. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right)}\right) \]

      4. sub-neg 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      5. associate-*r* 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. associate-*r* 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      7. distribute-lft-out-- 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) \]

      8. associate-*r* 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) \]

      9. +-commutative 71.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 71.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 71.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 71.2%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 72.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 69.3%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 69.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 69.3%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 69.3%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 69.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   if -2.25000000000000008e116 < x < 2e-263

   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. Taylor expanded in c around inf 63.7%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 63.7%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 63.7%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 63.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 2e-263 < x < 4.5e34

   1. Initial program 68.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in i around inf 58.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(a \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. cancel-sign-sub-inv 58.7%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + \left(--1\right) \cdot \left(a \cdot b\right)\right)} \]

      2. metadata-eval 58.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{1} \cdot \left(a \cdot b\right)\right) \]

      3. *-lft-identity 58.7%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) + \color{blue}{a \cdot b}\right) \]

      4. +-commutative 58.7%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 58.7%

         \[\leadsto i \cdot \left(a \cdot b + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 58.7%

         \[\leadsto i \cdot \color{blue}{\left(a \cdot b - j \cdot y\right)} \]

      7. *-commutative 58.7%

         \[\leadsto i \cdot \left(a \cdot b - \color{blue}{y \cdot j}\right) \]

   4. Simplified 58.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b - y \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{+116}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-263}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+34}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 18: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.05e+136)
   (* j (* t c))
   (if (<= c -3.6e-213)
     (* x (* y z))
     (if (<= c 4.6e-85) (* b (* a i)) (* t (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.05e+136) {
		tmp = j * (t * c);
	} else if (c <= -3.6e-213) {
		tmp = x * (y * z);
	} else if (c <= 4.6e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.05d+136)) then
        tmp = j * (t * c)
    else if (c <= (-3.6d-213)) then
        tmp = x * (y * z)
    else if (c <= 4.6d-85) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.05e+136) {
		tmp = j * (t * c);
	} else if (c <= -3.6e-213) {
		tmp = x * (y * z);
	} else if (c <= 4.6e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.05e+136:
		tmp = j * (t * c)
	elif c <= -3.6e-213:
		tmp = x * (y * z)
	elif c <= 4.6e-85:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.05e+136)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= -3.6e-213)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 4.6e-85)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.05e+136)
		tmp = j * (t * c);
	elseif (c <= -3.6e-213)
		tmp = x * (y * z);
	elseif (c <= 4.6e-85)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.05e+136], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-213], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.05e136

   1. Initial program 46.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 76.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 76.5%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 76.5%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 76.5%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around inf 46.5%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.5%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. *-commutative 46.5%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      3. *-commutative 46.5%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot c \]

      4. associate-*r* 52.1%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   7. Simplified 52.1%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   if -1.05e136 < c < -3.6000000000000001e-213

   1. Initial program 71.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. cancel-sign-sub-inv 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      6. cancel-sign-sub 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(-\left(-b\right)\right) \cdot \left(c \cdot z - i \cdot a\right)}\right) \]

      7. remove-double-neg 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{b} \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      8. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - i \cdot a\right)\right) \]

      9. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - \color{blue}{a \cdot i}\right)\right) \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 79.3%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)}\right) \]
   5. Step-by-step derivation

      1. +-commutative 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(z \cdot \left(x \cdot y - b \cdot c\right) + -1 \cdot \left(a \cdot \left(t \cdot x\right)\right)\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right) \]

      2. associate--l+ 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right) + \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      3. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + \left(--1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right)}\right) \]

      4. sub-neg 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)}\right) \]

      5. associate-*r* 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} - -1 \cdot \left(a \cdot \left(b \cdot i\right)\right)\right)\right) \]

      6. associate-*r* 79.3%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \left(\left(-1 \cdot a\right) \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot a\right) \cdot \left(b \cdot i\right)}\right)\right) \]

      7. distribute-lft-out-- 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x - b \cdot i\right)}\right) \]

      8. associate-*r* 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, z \cdot \left(x \cdot y - b \cdot c\right) + \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right)}\right) \]

      9. +-commutative 80.8%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x - b \cdot i\right)\right) + z \cdot \left(x \cdot y - b \cdot c\right)}\right) \]

      10. *-commutative 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\left(a \cdot \left(t \cdot x - b \cdot i\right)\right) \cdot -1} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      11. associate-*l* 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{a \cdot \left(\left(t \cdot x - b \cdot i\right) \cdot -1\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      12. *-commutative 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x - b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

      13. distribute-lft-out-- 80.8%

          \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} + z \cdot \left(x \cdot y - b \cdot c\right)\right) \]

   6. Simplified 82.4%

      \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{\mathsf{fma}\left(a, i \cdot b - x \cdot t, z \cdot \left(x \cdot y - c \cdot b\right)\right)}\right) \]

   7. Taylor expanded in x around inf 51.9%

      \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} \]

      2. mul-1-neg 51.9%

         \[\leadsto x \cdot \left(y \cdot z + \color{blue}{\left(-a \cdot t\right)}\right) \]

      3. unsub-neg 51.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - a \cdot t\right)} \]

      4. *-commutative 51.9%

         \[\leadsto x \cdot \left(\color{blue}{z \cdot y} - a \cdot t\right) \]

   9. Simplified 51.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y - a \cdot t\right)} \]

   10. Taylor expanded in z around inf 38.7%

       \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]

   if -3.6000000000000001e-213 < c < 4.6000000000000001e-85

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 60.8%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative 60.8%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b} \]

      2. *-commutative 60.8%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \left(\color{blue}{z \cdot c} - a \cdot i\right) \cdot b \]

      3. *-commutative 60.8%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{b \cdot \left(z \cdot c - a \cdot i\right)} \]

      4. *-rgt-identity 60.8%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

      5. cancel-sign-sub-inv 60.8%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) + \left(-b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

   4. Simplified 62.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in j around inf 42.1%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} + b \cdot \left(a \cdot i - z \cdot c\right) \]

   6. Taylor expanded in c around 0 35.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 34.5%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 34.5%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 38.9%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   8. Simplified 38.9%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   if 4.6000000000000001e-85 < c

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 48.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. Taylor expanded in c around inf 35.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 39.5%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   5. Simplified 39.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+136}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-213}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 19: 29.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.55e+132)
   (* j (* t c))
   (if (<= c 4.9e-85) (* b (* a i)) (* t (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.55e+132) {
		tmp = j * (t * c);
	} else if (c <= 4.9e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.55d+132)) then
        tmp = j * (t * c)
    else if (c <= 4.9d-85) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.55e+132) {
		tmp = j * (t * c);
	} else if (c <= 4.9e-85) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.55e+132:
		tmp = j * (t * c)
	elif c <= 4.9e-85:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.55e+132)
		tmp = Float64(j * Float64(t * c));
	elseif (c <= 4.9e-85)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.55e+132)
		tmp = j * (t * c);
	elseif (c <= 4.9e-85)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.55e+132], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e-85], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.5499999999999999e132

   1. Initial program 47.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in c around inf 77.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 77.2%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 77.2%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   4. Simplified 77.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   5. Taylor expanded in t around inf 45.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   6. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

      2. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      3. *-commutative 45.2%

         \[\leadsto \color{blue}{\left(j \cdot t\right)} \cdot c \]

      4. associate-*r* 50.7%

         \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   7. Simplified 50.7%

      \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

   if -1.5499999999999999e132 < c < 4.90000000000000015e-85

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 51.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative 51.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b} \]

      2. *-commutative 51.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \left(\color{blue}{z \cdot c} - a \cdot i\right) \cdot b \]

      3. *-commutative 51.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{b \cdot \left(z \cdot c - a \cdot i\right)} \]

      4. *-rgt-identity 51.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

      5. cancel-sign-sub-inv 51.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) + \left(-b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

   4. Simplified 55.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in j around inf 39.2%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} + b \cdot \left(a \cdot i - z \cdot c\right) \]

   6. Taylor expanded in c around 0 26.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 26.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 26.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 27.5%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   8. Simplified 27.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   if 4.90000000000000015e-85 < c

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 48.6%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. Taylor expanded in c around inf 35.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

      2. *-commutative 35.9%

         \[\leadsto \color{blue}{\left(t \cdot j\right)} \cdot c \]

      3. associate-*r* 39.5%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   5. Simplified 39.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+132}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 20: 19.4% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -5.8e+31) (* a (* x t)) (* 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 (y <= -5.8e+31) {
		tmp = a * (x * t);
	} 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 (y <= (-5.8d+31)) then
        tmp = a * (x * t)
    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 (y <= -5.8e+31) {
		tmp = a * (x * t);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -5.8e+31:
		tmp = a * (x * t)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -5.8e+31)
		tmp = Float64(a * Float64(x * t));
	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 (y <= -5.8e+31)
		tmp = a * (x * t);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -5.8e+31], N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000001e31

   1. Initial program 56.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 22.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 22.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 22.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 22.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 22.6%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 22.6%

         \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 22.6%

         \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

      7. *-commutative 22.6%

         \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

      8. *-commutative 22.6%

         \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

   4. Simplified 22.6%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]

   5. Taylor expanded in i around 0 14.5%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 14.5%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-rgt-neg-in 14.5%

         \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]

   7. Simplified 14.5%

      \[\leadsto a \cdot \color{blue}{\left(t \cdot \left(-x\right)\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 7.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(a \cdot \left(t \cdot \left(-x\right)\right)\right)\right)} \]

      2. expm1-udef 7.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(a \cdot \left(t \cdot \left(-x\right)\right)\right)} - 1} \]

      3. *-commutative 7.2%

         \[\leadsto e^{\mathsf{log1p}\left(a \cdot \color{blue}{\left(\left(-x\right) \cdot t\right)}\right)} - 1 \]

      4. associate-*r* 8.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(a \cdot \left(-x\right)\right) \cdot t}\right)} - 1 \]

      5. add-sqr-sqrt 8.2%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \cdot t\right)} - 1 \]

      6. sqrt-unprod 12.6%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \cdot t\right)} - 1 \]

      7. sqr-neg 12.6%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot \sqrt{\color{blue}{x \cdot x}}\right) \cdot t\right)} - 1 \]

      8. sqrt-unprod 4.0%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \cdot t\right)} - 1 \]

      9. add-sqr-sqrt 9.4%

         \[\leadsto e^{\mathsf{log1p}\left(\left(a \cdot \color{blue}{x}\right) \cdot t\right)} - 1 \]

   9. Applied egg-rr 9.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(a \cdot x\right) \cdot t\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 9.3%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(a \cdot x\right) \cdot t\right)\right)} \]

       2. expm1-log1p 16.1%

          \[\leadsto \color{blue}{\left(a \cdot x\right) \cdot t} \]

       3. associate-*l* 16.1%

          \[\leadsto \color{blue}{a \cdot \left(x \cdot t\right)} \]

       4. *-commutative 16.1%

          \[\leadsto a \cdot \color{blue}{\left(t \cdot x\right)} \]

   11. Simplified 16.1%

       \[\leadsto \color{blue}{a \cdot \left(t \cdot x\right)} \]

   if -5.8000000000000001e31 < y

   1. Initial program 77.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 69.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative 69.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b} \]

      2. *-commutative 69.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \left(\color{blue}{z \cdot c} - a \cdot i\right) \cdot b \]

      3. *-commutative 69.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{b \cdot \left(z \cdot c - a \cdot i\right)} \]

      4. *-rgt-identity 69.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

      5. cancel-sign-sub-inv 69.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) + \left(-b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

   4. Simplified 68.0%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in j around inf 56.9%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} + b \cdot \left(a \cdot i - z \cdot c\right) \]

   6. Taylor expanded in c around 0 23.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 22.4%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 22.4%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 24.3%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   8. Simplified 24.3%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 21: 25.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 86000000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a 86000000000.0) (* c (* t 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 <= 86000000000.0) {
		tmp = c * (t * 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 <= 86000000000.0d0) then
        tmp = c * (t * 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 <= 86000000000.0) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= 86000000000.0:
		tmp = c * (t * 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 <= 86000000000.0)
		tmp = Float64(c * Float64(t * 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 <= 86000000000.0)
		tmp = c * (t * 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, 86000000000.0], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 8.6e10

   1. Initial program 75.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 42.0%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. Taylor expanded in c around inf 30.4%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 30.4%

         \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]

   5. Simplified 30.4%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 8.6e10 < a

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in y around 0 61.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   3. Step-by-step derivation

      1. *-commutative 61.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(c \cdot z - a \cdot i\right) \cdot b} \]

      2. *-commutative 61.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \left(\color{blue}{z \cdot c} - a \cdot i\right) \cdot b \]

      3. *-commutative 61.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{b \cdot \left(z \cdot c - a \cdot i\right)} \]

      4. *-rgt-identity 61.0%

         \[\leadsto \left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) - \color{blue}{\left(b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

      5. cancel-sign-sub-inv 61.0%

         \[\leadsto \color{blue}{\left(-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + c \cdot \left(j \cdot t\right)\right) + \left(-b \cdot \left(z \cdot c - a \cdot i\right)\right) \cdot 1} \]

   4. Simplified 64.9%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)} \]

   5. Taylor expanded in j around inf 50.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} + b \cdot \left(a \cdot i - z \cdot c\right) \]

   6. Taylor expanded in c around 0 35.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 37.5%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 37.5%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 36.2%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   8. Simplified 36.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 86000000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 22: 21.7% 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 72.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in a around inf 37.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
3. Step-by-step derivation

   1. associate-*r* 37.8%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

   2. neg-mul-1 37.8%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

   3. cancel-sign-sub 37.8%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + b \cdot i\right)} \]

   4. +-commutative 37.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 37.8%

      \[\leadsto a \cdot \left(b \cdot i + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 37.8%

      \[\leadsto a \cdot \color{blue}{\left(b \cdot i - t \cdot x\right)} \]

   7. *-commutative 37.8%

      \[\leadsto a \cdot \left(\color{blue}{i \cdot b} - t \cdot x\right) \]

   8. *-commutative 37.8%

      \[\leadsto a \cdot \left(i \cdot b - \color{blue}{x \cdot t}\right) \]

4. Simplified 37.8%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - x \cdot t\right)} \]

5. Taylor expanded in i around inf 20.3%

   \[\leadsto a \cdot \color{blue}{\left(b \cdot i\right)} \]

6. Final simplification 20.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 68.2% 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 2023279 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))