Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.3% → 98.0%

Time: 9.5s

Alternatives: 11

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 5e+16) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+16) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 5d+16) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e+16) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 5e+16:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e+16)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 5e+16)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e+16], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5e16

   1. Initial program 98.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   if 5e16 < z

   1. Initial program 88.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-*l* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot \left(y + -1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -1.0)
     t_0
     (if (<= z 3.5e-14) x (if (<= z 3.4e+131) (* x (* z y)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 3.5e-14) {
		tmp = x;
	} else if (z <= 3.4e+131) {
		tmp = x * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 3.5d-14) then
        tmp = x
    else if (z <= 3.4d+131) then
        tmp = x * (z * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 3.5e-14) {
		tmp = x;
	} else if (z <= 3.4e+131) {
		tmp = x * (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 3.5e-14:
		tmp = x
	elif z <= 3.4e+131:
		tmp = x * (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 3.5e-14)
		tmp = x;
	elseif (z <= 3.4e+131)
		tmp = Float64(x * Float64(z * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 3.5e-14)
		tmp = x;
	elseif (z <= 3.4e+131)
		tmp = x * (z * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 3.5e-14], x, If[LessEqual[z, 3.4e+131], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 3.39999999999999986e131 < z

   1. Initial program 91.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 91.5%

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

      2. distribute-rgt-neg-out 91.5%

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

      3. +-commutative 91.5%

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

      4. distribute-rgt-neg-out 91.5%

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

      5. *-commutative 91.5%

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

      6. distribute-rgt-neg-in 91.5%

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

      7. fma-define 91.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

      8. neg-sub0 91.5%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{0 - \left(1 - y\right)}, 1\right) \]

      9. associate--r- 91.5%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{\left(0 - 1\right) + y}, 1\right) \]

      10. metadata-eval 91.5%

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

      11. +-commutative 91.5%

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

   3. Simplified 91.5%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 91.5%

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

      2. distribute-rgt-in 91.5%

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

      3. *-un-lft-identity 91.5%

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

   6. Applied egg-rr 91.5%

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

   7. Taylor expanded in z around 0 91.5%

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

      1. sub-neg 91.5%

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

      2. metadata-eval 91.5%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in y around 0 64.6%

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

       1. mul-1-neg 64.6%

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

       2. sub-neg 64.6%

          \[\leadsto \color{blue}{x - x \cdot z} \]

   12. Simplified 64.6%

       \[\leadsto \color{blue}{x - x \cdot z} \]

   13. Taylor expanded in z around inf 63.7%

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

       1. mul-1-neg 63.7%

          \[\leadsto \color{blue}{-x \cdot z} \]

       2. distribute-rgt-neg-out 63.7%

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

   15. Simplified 63.7%

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

   if -1 < z < 3.5000000000000002e-14

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 73.3%

      \[\leadsto \color{blue}{x} \]

   if 3.5000000000000002e-14 < z < 3.39999999999999986e131

   1. Initial program 96.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.4%

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

      1. *-commutative 67.4%

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

   5. Simplified 67.4%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+131}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.95 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.95) (not (<= y 1.0))) (* x (+ 1.0 (* z y))) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.95) || !(y <= 1.0)) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.95d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * (1.0d0 + (z * y))
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.95) || !(y <= 1.0)) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.95) or not (y <= 1.0):
		tmp = x * (1.0 + (z * y))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.95) || !(y <= 1.0))
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.95) || ~((y <= 1.0)))
		tmp = x * (1.0 + (z * y));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.95], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.94999999999999996 or 1 < y

   1. Initial program 91.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-lft-neg-out 91.8%

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

      3. *-commutative 91.8%

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

   5. Simplified 91.8%

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

      1. sub-neg 91.8%

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

      2. distribute-rgt-neg-out 91.8%

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

      3. remove-double-neg 91.8%

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

      4. +-commutative 91.8%

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

   7. Applied egg-rr 91.8%

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

   if -0.94999999999999996 < y < 1

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

      3. +-commutative 100.0%

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

      4. distribute-rgt-neg-out 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-rgt-neg-in 100.0%

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

      7. fma-define 100.0%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{0 - \left(1 - y\right)}, 1\right) \]

      9. associate--r- 100.0%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{\left(0 - 1\right) + y}, 1\right) \]

      10. metadata-eval 100.0%

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

      11. +-commutative 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around 0 99.1%

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

       1. mul-1-neg 99.1%

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

       2. sub-neg 99.1%

          \[\leadsto \color{blue}{x - x \cdot z} \]

   12. Simplified 99.1%

       \[\leadsto \color{blue}{x - x \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.95 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 92.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*l* 98.7%

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

      3. *-commutative 98.7%

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

      4. sub-neg 98.7%

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

      5. metadata-eval 98.7%

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

   5. Simplified 98.7%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-lft-neg-out 98.7%

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

      3. *-commutative 98.7%

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

   5. Simplified 98.7%

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

      1. sub-neg 98.7%

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

      2. distribute-rgt-neg-out 98.7%

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

      3. remove-double-neg 98.7%

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

      4. +-commutative 98.7%

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

   7. Applied egg-rr 98.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+69} \lor \neg \left(y \leq 17000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.06e+69) (not (<= y 17000000000.0)))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.06e+69) || !(y <= 17000000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.06d+69)) .or. (.not. (y <= 17000000000.0d0))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.06e+69) || !(y <= 17000000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.06e+69) or not (y <= 17000000000.0):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.06e+69) || !(y <= 17000000000.0))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.06e+69) || ~((y <= 17000000000.0)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.06e+69], N[Not[LessEqual[y, 17000000000.0]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06000000000000004e69 or 1.7e10 < y

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 70.1%

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

      1. *-commutative 70.1%

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

   5. Simplified 70.1%

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

   if -1.06000000000000004e69 < y < 1.7e10

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.1%

      \[\leadsto \color{blue}{x \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+69} \lor \neg \left(y \leq 17000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 22000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+64)
   (* x (* z y))
   (if (<= y 22000000000.0) (* x (- 1.0 z)) (* (* x z) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+64) {
		tmp = x * (z * y);
	} else if (y <= 22000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6d+64)) then
        tmp = x * (z * y)
    else if (y <= 22000000000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (x * z) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+64) {
		tmp = x * (z * y);
	} else if (y <= 22000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+64:
		tmp = x * (z * y)
	elif y <= 22000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = (x * z) * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+64)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 22000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(x * z) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+64)
		tmp = x * (z * y);
	elseif (y <= 22000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = (x * z) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+64], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 22000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000004e64

   1. Initial program 94.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -6.0000000000000004e64 < y < 2.2e10

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.1%

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

   if 2.2e10 < y

   1. Initial program 90.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 83.6%

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

      1. +-commutative 83.6%

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

      2. associate-/l* 92.1%

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

      3. distribute-lft-out 95.4%

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

   5. Simplified 95.4%

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

   6. Taylor expanded in y around inf 75.6%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 22000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 27000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.3e+63)
   (* x (* z y))
   (if (<= y 27000000000.0) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+63) {
		tmp = x * (z * y);
	} else if (y <= 27000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.3d+63)) then
        tmp = x * (z * y)
    else if (y <= 27000000000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+63) {
		tmp = x * (z * y);
	} else if (y <= 27000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.3e+63:
		tmp = x * (z * y)
	elif y <= 27000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.3e+63)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 27000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.3e+63)
		tmp = x * (z * y);
	elseif (y <= 27000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.3e+63], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 27000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2999999999999999e63

   1. Initial program 94.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -5.2999999999999999e63 < y < 2.7e10

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.1%

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

   if 2.7e10 < y

   1. Initial program 90.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.3%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 27000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 25000000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.1e+65)
   (* x (* z y))
   (if (<= y 25000000000.0) (- x (* x z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+65) {
		tmp = x * (z * y);
	} else if (y <= 25000000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.1d+65)) then
        tmp = x * (z * y)
    else if (y <= 25000000000.0d0) then
        tmp = x - (x * z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.1e+65) {
		tmp = x * (z * y);
	} else if (y <= 25000000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.1e+65:
		tmp = x * (z * y)
	elif y <= 25000000000.0:
		tmp = x - (x * z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.1e+65)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 25000000000.0)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.1e+65)
		tmp = x * (z * y);
	elseif (y <= 25000000000.0)
		tmp = x - (x * z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.1e+65], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 25000000000.0], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999991e65

   1. Initial program 94.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -2.09999999999999991e65 < y < 2.5e10

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 99.3%

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

      2. distribute-rgt-neg-out 99.3%

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

      3. +-commutative 99.3%

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

      4. distribute-rgt-neg-out 99.3%

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

      5. *-commutative 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

      7. fma-define 99.3%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

      8. neg-sub0 99.3%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{0 - \left(1 - y\right)}, 1\right) \]

      9. associate--r- 99.3%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{\left(0 - 1\right) + y}, 1\right) \]

      10. metadata-eval 99.3%

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

      11. +-commutative 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. *-un-lft-identity 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in z around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. metadata-eval 99.3%

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

      3. associate-*r* 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around 0 96.1%

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

       1. mul-1-neg 96.1%

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

       2. sub-neg 96.1%

          \[\leadsto \color{blue}{x - x \cdot z} \]

   12. Simplified 96.1%

       \[\leadsto \color{blue}{x - x \cdot z} \]

   if 2.5e10 < y

   1. Initial program 90.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 69.3%

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

      1. associate-*r* 77.2%

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

      2. *-commutative 77.2%

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

   5. Simplified 77.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 25000000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 92.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 92.5%

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

      2. distribute-rgt-neg-out 92.5%

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

      3. +-commutative 92.5%

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

      4. distribute-rgt-neg-out 92.5%

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

      5. *-commutative 92.5%

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

      6. distribute-rgt-neg-in 92.5%

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

      7. fma-define 92.5%

         \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

      8. neg-sub0 92.5%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{0 - \left(1 - y\right)}, 1\right) \]

      9. associate--r- 92.5%

         \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{\left(0 - 1\right) + y}, 1\right) \]

      10. metadata-eval 92.5%

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

      11. +-commutative 92.5%

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

   3. Simplified 92.5%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 92.5%

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

      2. distribute-rgt-in 92.5%

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

      3. *-un-lft-identity 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in z around 0 92.5%

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

      1. sub-neg 92.5%

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

      2. metadata-eval 92.5%

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

      3. associate-*r* 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in y around 0 58.0%

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

       1. mul-1-neg 58.0%

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

       2. sub-neg 58.0%

          \[\leadsto \color{blue}{x - x \cdot z} \]

   12. Simplified 58.0%

       \[\leadsto \color{blue}{x - x \cdot z} \]

   13. Taylor expanded in z around inf 56.8%

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

       1. mul-1-neg 56.8%

          \[\leadsto \color{blue}{-x \cdot z} \]

       2. distribute-rgt-neg-out 56.8%

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

   15. Simplified 56.8%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 71.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(x \cdot z\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	return x - ((x * z) * (1.0 - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((x * z) * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((x * z) * (1.0 - y));
}

Python

def code(x, y, z):
	return x - ((x * z) * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(x * z) * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((x * z) * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(x * z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Step-by-step derivation

   1. sub-neg 96.2%

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

   2. distribute-rgt-neg-out 96.2%

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

   3. +-commutative 96.2%

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

   4. distribute-rgt-neg-out 96.2%

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

   5. *-commutative 96.2%

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

   6. distribute-rgt-neg-in 96.2%

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

   7. fma-define 96.2%

      \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   8. neg-sub0 96.2%

      \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{0 - \left(1 - y\right)}, 1\right) \]

   9. associate--r- 96.2%

      \[\leadsto x \cdot \mathsf{fma}\left(z, \color{blue}{\left(0 - 1\right) + y}, 1\right) \]

   10. metadata-eval 96.2%

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

   11. +-commutative 96.2%

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

3. Simplified 96.2%

   \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 96.2%

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

   2. distribute-rgt-in 96.3%

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

   3. *-un-lft-identity 96.3%

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

6. Applied egg-rr 96.3%

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

7. Taylor expanded in z around 0 96.3%

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

   1. sub-neg 96.3%

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

   2. metadata-eval 96.3%

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

   3. associate-*r* 97.3%

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

9. Simplified 97.3%

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

10. Final simplification 97.3%

    \[\leadsto x - \left(x \cdot z\right) \cdot \left(1 - y\right) \]
11. Add Preprocessing

Alternative 11: 38.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.2%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 38.1%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 38.1%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))