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

Percentage Accurate: 95.9% → 97.5%

Time: 5.7s

Alternatives: 9

Speedup: 0.8×

• 20.7% 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: 95.9% 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: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq 10^{+72}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z (- 1.0 y)) 1e+72)
   (* x (+ 1.0 (* z (+ y -1.0))))
   (* (* x z) (+ y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * (1.0 - y)) <= 1e+72) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (x * z) * (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 * (1.0d0 - y)) <= 1d+72) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = (x * z) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * (1.0 - y)) <= 1e+72) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (x * z) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * (1.0 - y)) <= 1e+72:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = (x * z) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * Float64(1.0 - y)) <= 1e+72)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * (1.0 - y)) <= 1e+72)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (x * z) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1e+72], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 9.99999999999999944e71

   1. Initial program 98.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 9.99999999999999944e71 < (*.f64 (-.f64 1 y) z)

   1. Initial program 90.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l* 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq 10^{+72}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

   1. distribute-rgt-out-- 96.9%

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

   2. *-lft-identity 96.9%

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

   3. cancel-sign-sub-inv 96.9%

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

   4. +-commutative 96.9%

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

   5. distribute-lft-neg-in 96.9%

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

   6. associate-*l* 97.8%

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

   7. fma-def 97.8%

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

   8. neg-sub0 97.8%

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

   9. associate--r- 97.8%

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

   10. metadata-eval 97.8%

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

   11. +-commutative 97.8%

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

   12. *-commutative 97.8%

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

3. Simplified 97.8%

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

4. Final simplification 97.8%

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

Alternative 3: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= y -2.6e+15)
     t_1
     (if (<= y -1.55e-58)
       x
       (if (<= y -2.7e-113)
         t_0
         (if (<= y 7e-240) x (if (<= y 1.0) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -2.6e+15) {
		tmp = t_1;
	} else if (y <= -1.55e-58) {
		tmp = x;
	} else if (y <= -2.7e-113) {
		tmp = t_0;
	} else if (y <= 7e-240) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = t_0;
	} 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 * -z
    t_1 = x * (y * z)
    if (y <= (-2.6d+15)) then
        tmp = t_1
    else if (y <= (-1.55d-58)) then
        tmp = x
    else if (y <= (-2.7d-113)) then
        tmp = t_0
    else if (y <= 7d-240) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = t_0
    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 * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (y <= -2.6e+15) {
		tmp = t_1;
	} else if (y <= -1.55e-58) {
		tmp = x;
	} else if (y <= -2.7e-113) {
		tmp = t_0;
	} else if (y <= 7e-240) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if y <= -2.6e+15:
		tmp = t_1
	elif y <= -1.55e-58:
		tmp = x
	elif y <= -2.7e-113:
		tmp = t_0
	elif y <= 7e-240:
		tmp = x
	elif y <= 1.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -2.6e+15)
		tmp = t_1;
	elseif (y <= -1.55e-58)
		tmp = x;
	elseif (y <= -2.7e-113)
		tmp = t_0;
	elseif (y <= 7e-240)
		tmp = x;
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (y <= -2.6e+15)
		tmp = t_1;
	elseif (y <= -1.55e-58)
		tmp = x;
	elseif (y <= -2.7e-113)
		tmp = t_0;
	elseif (y <= 7e-240)
		tmp = x;
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+15], t$95$1, If[LessEqual[y, -1.55e-58], x, If[LessEqual[y, -2.7e-113], t$95$0, If[LessEqual[y, 7e-240], x, If[LessEqual[y, 1.0], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e15 or 1 < y

   1. Initial program 94.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 93.5%

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

      1. mul-1-neg 93.5%

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

      2. distribute-lft-neg-out 93.5%

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

      3. *-commutative 93.5%

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

   4. Simplified 93.5%

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

   5. Taylor expanded in z around inf 74.5%

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

      1. *-commutative 74.5%

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

      2. *-commutative 74.5%

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

      3. associate-*r* 72.3%

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

      4. *-commutative 72.3%

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

   7. Simplified 72.3%

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

   if -2.6e15 < y < -1.55e-58 or -2.69999999999999996e-113 < y < 7.00000000000000032e-240

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.7%

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

   if -1.55e-58 < y < -2.69999999999999996e-113 or 7.00000000000000032e-240 < y < 1

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*l* 66.9%

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

      3. sub-neg 66.9%

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

      4. metadata-eval 66.9%

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

      5. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-rgt-neg-in 65.6%

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

   7. Simplified 65.6%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-114}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= y -3.8e+15)
     (* y (* x z))
     (if (<= y -7.6e-58)
       x
       (if (<= y -6.2e-114)
         t_0
         (if (<= y 2.05e-240) x (if (<= y 1.0) t_0 (* z (* y x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (y <= -3.8e+15) {
		tmp = y * (x * z);
	} else if (y <= -7.6e-58) {
		tmp = x;
	} else if (y <= -6.2e-114) {
		tmp = t_0;
	} else if (y <= 2.05e-240) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = t_0;
	} else {
		tmp = z * (y * 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (y <= (-3.8d+15)) then
        tmp = y * (x * z)
    else if (y <= (-7.6d-58)) then
        tmp = x
    else if (y <= (-6.2d-114)) then
        tmp = t_0
    else if (y <= 2.05d-240) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = t_0
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (y <= -3.8e+15) {
		tmp = y * (x * z);
	} else if (y <= -7.6e-58) {
		tmp = x;
	} else if (y <= -6.2e-114) {
		tmp = t_0;
	} else if (y <= 2.05e-240) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = t_0;
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if y <= -3.8e+15:
		tmp = y * (x * z)
	elif y <= -7.6e-58:
		tmp = x
	elif y <= -6.2e-114:
		tmp = t_0
	elif y <= 2.05e-240:
		tmp = x
	elif y <= 1.0:
		tmp = t_0
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (y <= -3.8e+15)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= -7.6e-58)
		tmp = x;
	elseif (y <= -6.2e-114)
		tmp = t_0;
	elseif (y <= 2.05e-240)
		tmp = x;
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (y <= -3.8e+15)
		tmp = y * (x * z);
	elseif (y <= -7.6e-58)
		tmp = x;
	elseif (y <= -6.2e-114)
		tmp = t_0;
	elseif (y <= 2.05e-240)
		tmp = x;
	elseif (y <= 1.0)
		tmp = t_0;
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[y, -3.8e+15], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-58], x, If[LessEqual[y, -6.2e-114], t$95$0, If[LessEqual[y, 2.05e-240], x, If[LessEqual[y, 1.0], t$95$0, N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.8e15

   1. Initial program 91.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 82.1%

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

   if -3.8e15 < y < -7.5999999999999995e-58 or -6.2e-114 < y < 2.0500000000000001e-240

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.7%

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

   if -7.5999999999999995e-58 < y < -6.2e-114 or 2.0500000000000001e-240 < y < 1

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*l* 66.9%

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

      3. sub-neg 66.9%

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

      4. metadata-eval 66.9%

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

      5. *-commutative 66.9%

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

   4. Simplified 66.9%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. mul-1-neg 65.6%

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

      2. distribute-rgt-neg-in 65.6%

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

   7. Simplified 65.6%

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

   if 1 < y

   1. Initial program 97.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 67.6%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

      3. associate-*l* 73.8%

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

   4. Simplified 73.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-114}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 5: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))))
   (if (<= z -5.2e-21)
     t_0
     (if (<= z 4.5e-137)
       x
       (if (<= z 1.62e-105) (* x (* y z)) (if (<= z 6.2e-72) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -5.2e-21) {
		tmp = t_0;
	} else if (z <= 4.5e-137) {
		tmp = x;
	} else if (z <= 1.62e-105) {
		tmp = x * (y * z);
	} else if (z <= 6.2e-72) {
		tmp = x;
	} 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 = y * (x * z)
    if (z <= (-5.2d-21)) then
        tmp = t_0
    else if (z <= 4.5d-137) then
        tmp = x
    else if (z <= 1.62d-105) then
        tmp = x * (y * z)
    else if (z <= 6.2d-72) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double tmp;
	if (z <= -5.2e-21) {
		tmp = t_0;
	} else if (z <= 4.5e-137) {
		tmp = x;
	} else if (z <= 1.62e-105) {
		tmp = x * (y * z);
	} else if (z <= 6.2e-72) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	tmp = 0
	if z <= -5.2e-21:
		tmp = t_0
	elif z <= 4.5e-137:
		tmp = x
	elif z <= 1.62e-105:
		tmp = x * (y * z)
	elif z <= 6.2e-72:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -5.2e-21)
		tmp = t_0;
	elseif (z <= 4.5e-137)
		tmp = x;
	elseif (z <= 1.62e-105)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 6.2e-72)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	tmp = 0.0;
	if (z <= -5.2e-21)
		tmp = t_0;
	elseif (z <= 4.5e-137)
		tmp = x;
	elseif (z <= 1.62e-105)
		tmp = x * (y * z);
	elseif (z <= 6.2e-72)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-21], t$95$0, If[LessEqual[z, 4.5e-137], x, If[LessEqual[z, 1.62e-105], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-72], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000035e-21 or 6.1999999999999996e-72 < z

   1. Initial program 94.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 64.5%

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

   if -5.20000000000000035e-21 < z < 4.4999999999999997e-137 or 1.62e-105 < z < 6.1999999999999996e-72

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 80.7%

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

   if 4.4999999999999997e-137 < z < 1.62e-105

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

      3. associate-*r* 86.0%

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

      4. *-commutative 86.0%

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

   7. Simplified 86.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.05) (not (<= z 1.0)))
   (* (* x z) (+ y -1.0))
   (+ x (* x (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x + (x * (y * 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 ((z <= (-1.05d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x * z) * (y + (-1.0d0))
    else
        tmp = x + (x * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.05) || !(z <= 1.0)) {
		tmp = (x * z) * (y + -1.0);
	} else {
		tmp = x + (x * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.05) or not (z <= 1.0):
		tmp = (x * z) * (y + -1.0)
	else:
		tmp = x + (x * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.05) || !(z <= 1.0))
		tmp = Float64(Float64(x * z) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.05) || ~((z <= 1.0)))
		tmp = (x * z) * (y + -1.0);
	else
		tmp = x + (x * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.05], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x * z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 93.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

      5. *-commutative 99.6%

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

   4. Simplified 99.6%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-lft-neg-out 98.5%

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

      3. *-commutative 98.5%

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

   4. Simplified 98.5%

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

      1. sub-neg 98.5%

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

      2. distribute-rgt-neg-out 98.5%

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

      3. remove-double-neg 98.5%

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

      4. distribute-lft-in 98.5%

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

      5. *-commutative 98.5%

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

      6. *-un-lft-identity 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+33}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.25e+35)
   (* y (* x z))
   (if (<= y 4.3e+33) (- x (* x z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+35) {
		tmp = y * (x * z);
	} else if (y <= 4.3e+33) {
		tmp = x - (x * z);
	} else {
		tmp = z * (y * 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 (y <= (-1.25d+35)) then
        tmp = y * (x * z)
    else if (y <= 4.3d+33) then
        tmp = x - (x * z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.25e+35) {
		tmp = y * (x * z);
	} else if (y <= 4.3e+33) {
		tmp = x - (x * z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.25e+35:
		tmp = y * (x * z)
	elif y <= 4.3e+33:
		tmp = x - (x * z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.25e+35)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 4.3e+33)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.25e+35)
		tmp = y * (x * z);
	elseif (y <= 4.3e+33)
		tmp = x - (x * z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.25e+35], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+33], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000005e35

   1. Initial program 91.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 82.7%

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

   if -1.25000000000000005e35 < y < 4.30000000000000028e33

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 96.2%

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

      1. *-commutative 96.2%

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

      2. distribute-rgt-out-- 96.2%

         \[\leadsto \color{blue}{1 \cdot x - z \cdot x} \]

      3. *-lft-identity 96.2%

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

   4. Simplified 96.2%

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

   if 4.30000000000000028e33 < y

   1. Initial program 96.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 73.5%

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

      1. associate-*r* 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*l* 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+33}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 8: 63.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.62e-16) (not (<= z 1.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.62e-16) || !(z <= 1.0)) {
		tmp = x * -z;
	} 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 <= (-1.62d-16)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.62e-16) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.62e-16) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.62e-16) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.62e-16) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.62e-16], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.61999999999999995e-16 or 1 < z

   1. Initial program 93.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.5%

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

      3. sub-neg 99.5%

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

      4. metadata-eval 99.5%

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

      5. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in y around 0 49.4%

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

      1. mul-1-neg 49.4%

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

      2. distribute-rgt-neg-in 49.4%

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

   7. Simplified 49.4%

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

   if -1.61999999999999995e-16 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 72.2%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{-16} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 38.4% 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 96.9%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 38.2%

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

3. Final simplification 38.2%

   \[\leadsto x \]

Developer target: 99.6% accurate, 0.3× 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 2023192 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (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))))