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

Percentage Accurate: 96.5% → 98.1%

Time: 6.9s

Alternatives: 13

Speedup: 0.8×

• 20.8% 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: 96.5% 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: 98.1% 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 96.6%

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

   1. distribute-rgt-out-- 96.6%

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

   2. *-lft-identity 96.6%

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

   3. cancel-sign-sub-inv 96.6%

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

   4. +-commutative 96.6%

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

   5. distribute-lft-neg-in 96.6%

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

   6. associate-*l* 98.6%

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

   7. fma-def 98.6%

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

   8. neg-sub0 98.6%

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

   9. associate--r- 98.6%

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

   10. metadata-eval 98.6%

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

   11. +-commutative 98.6%

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

   12. *-commutative 98.6%

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

3. Simplified 98.6%

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

4. Final simplification 98.6%

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

Alternative 2: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+270}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))) (t_1 (* x (- z))))
   (if (<= z -1.3e+270)
     t_0
     (if (<= z -3.7e+71)
       t_1
       (if (<= z -1.02e-16)
         t_0
         (if (<= z 3.75e-103)
           x
           (if (<= z 9e-65)
             t_0
             (if (<= z 1.6e-11) x (if (<= z 1.95e+85) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double t_1 = x * -z;
	double tmp;
	if (z <= -1.3e+270) {
		tmp = t_0;
	} else if (z <= -3.7e+71) {
		tmp = t_1;
	} else if (z <= -1.02e-16) {
		tmp = t_0;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 1.6e-11) {
		tmp = x;
	} else if (z <= 1.95e+85) {
		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 = y * (x * z)
    t_1 = x * -z
    if (z <= (-1.3d+270)) then
        tmp = t_0
    else if (z <= (-3.7d+71)) then
        tmp = t_1
    else if (z <= (-1.02d-16)) then
        tmp = t_0
    else if (z <= 3.75d-103) then
        tmp = x
    else if (z <= 9d-65) then
        tmp = t_0
    else if (z <= 1.6d-11) then
        tmp = x
    else if (z <= 1.95d+85) 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 = y * (x * z);
	double t_1 = x * -z;
	double tmp;
	if (z <= -1.3e+270) {
		tmp = t_0;
	} else if (z <= -3.7e+71) {
		tmp = t_1;
	} else if (z <= -1.02e-16) {
		tmp = t_0;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 1.6e-11) {
		tmp = x;
	} else if (z <= 1.95e+85) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	t_1 = x * -z
	tmp = 0
	if z <= -1.3e+270:
		tmp = t_0
	elif z <= -3.7e+71:
		tmp = t_1
	elif z <= -1.02e-16:
		tmp = t_0
	elif z <= 3.75e-103:
		tmp = x
	elif z <= 9e-65:
		tmp = t_0
	elif z <= 1.6e-11:
		tmp = x
	elif z <= 1.95e+85:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -1.3e+270)
		tmp = t_0;
	elseif (z <= -3.7e+71)
		tmp = t_1;
	elseif (z <= -1.02e-16)
		tmp = t_0;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 1.6e-11)
		tmp = x;
	elseif (z <= 1.95e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -1.3e+270)
		tmp = t_0;
	elseif (z <= -3.7e+71)
		tmp = t_1;
	elseif (z <= -1.02e-16)
		tmp = t_0;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 1.6e-11)
		tmp = x;
	elseif (z <= 1.95e+85)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -1.3e+270], t$95$0, If[LessEqual[z, -3.7e+71], t$95$1, If[LessEqual[z, -1.02e-16], t$95$0, If[LessEqual[z, 3.75e-103], x, If[LessEqual[z, 9e-65], t$95$0, If[LessEqual[z, 1.6e-11], x, If[LessEqual[z, 1.95e+85], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000006e270 or -3.7e71 < z < -1.0200000000000001e-16 or 3.75e-103 < z < 8.9999999999999995e-65 or 1.59999999999999997e-11 < z < 1.95000000000000017e85

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf 70.1%

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

   if -1.30000000000000006e270 < z < -3.7e71 or 1.95000000000000017e85 < z

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. neg-mul-1 69.5%

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

   7. Simplified 69.5%

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

   if -1.0200000000000001e-16 < z < 3.75e-103 or 8.9999999999999995e-65 < z < 1.59999999999999997e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+270}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot z\right)\\ t_1 := z \cdot \left(y \cdot x\right)\\ t_2 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* x z))) (t_1 (* z (* y x))) (t_2 (* x (- z))))
   (if (<= z -9e+273)
     t_1
     (if (<= z -7e+75)
       t_2
       (if (<= z -9.2e-26)
         t_0
         (if (<= z 3.75e-103)
           x
           (if (<= z 9e-65)
             t_0
             (if (<= z 2.5e-12) x (if (<= z 3e+86) t_1 t_2)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double t_1 = z * (y * x);
	double t_2 = x * -z;
	double tmp;
	if (z <= -9e+273) {
		tmp = t_1;
	} else if (z <= -7e+75) {
		tmp = t_2;
	} else if (z <= -9.2e-26) {
		tmp = t_0;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 2.5e-12) {
		tmp = x;
	} else if (z <= 3e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = y * (x * z)
    t_1 = z * (y * x)
    t_2 = x * -z
    if (z <= (-9d+273)) then
        tmp = t_1
    else if (z <= (-7d+75)) then
        tmp = t_2
    else if (z <= (-9.2d-26)) then
        tmp = t_0
    else if (z <= 3.75d-103) then
        tmp = x
    else if (z <= 9d-65) then
        tmp = t_0
    else if (z <= 2.5d-12) then
        tmp = x
    else if (z <= 3d+86) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x * z);
	double t_1 = z * (y * x);
	double t_2 = x * -z;
	double tmp;
	if (z <= -9e+273) {
		tmp = t_1;
	} else if (z <= -7e+75) {
		tmp = t_2;
	} else if (z <= -9.2e-26) {
		tmp = t_0;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 2.5e-12) {
		tmp = x;
	} else if (z <= 3e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x * z)
	t_1 = z * (y * x)
	t_2 = x * -z
	tmp = 0
	if z <= -9e+273:
		tmp = t_1
	elif z <= -7e+75:
		tmp = t_2
	elif z <= -9.2e-26:
		tmp = t_0
	elif z <= 3.75e-103:
		tmp = x
	elif z <= 9e-65:
		tmp = t_0
	elif z <= 2.5e-12:
		tmp = x
	elif z <= 3e+86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x * z))
	t_1 = Float64(z * Float64(y * x))
	t_2 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -9e+273)
		tmp = t_1;
	elseif (z <= -7e+75)
		tmp = t_2;
	elseif (z <= -9.2e-26)
		tmp = t_0;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 2.5e-12)
		tmp = x;
	elseif (z <= 3e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x * z);
	t_1 = z * (y * x);
	t_2 = x * -z;
	tmp = 0.0;
	if (z <= -9e+273)
		tmp = t_1;
	elseif (z <= -7e+75)
		tmp = t_2;
	elseif (z <= -9.2e-26)
		tmp = t_0;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 2.5e-12)
		tmp = x;
	elseif (z <= 3e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -9e+273], t$95$1, If[LessEqual[z, -7e+75], t$95$2, If[LessEqual[z, -9.2e-26], t$95$0, If[LessEqual[z, 3.75e-103], x, If[LessEqual[z, 9e-65], t$95$0, If[LessEqual[z, 2.5e-12], x, If[LessEqual[z, 3e+86], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999987e273 or 2.49999999999999985e-12 < z < 2.99999999999999977e86

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*r* 68.9%

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

      3. *-commutative 68.9%

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

   4. Simplified 68.9%

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

   if -8.99999999999999987e273 < z < -6.9999999999999997e75 or 2.99999999999999977e86 < z

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around 0 69.5%

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

      1. neg-mul-1 69.5%

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

   7. Simplified 69.5%

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

   if -6.9999999999999997e75 < z < -9.20000000000000035e-26 or 3.75e-103 < z < 8.9999999999999995e-65

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 72.3%

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

   if -9.20000000000000035e-26 < z < 3.75e-103 or 8.9999999999999995e-65 < z < 2.49999999999999985e-12

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 87.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+273}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 4: 64.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))) (t_1 (* x (- z))))
   (if (<= z -6e+272)
     t_0
     (if (<= z -1.0)
       t_1
       (if (<= z 3.75e-103)
         x
         (if (<= z 9e-65)
           t_0
           (if (<= z 2.9e-11) x (if (<= z 6e+84) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double t_1 = x * -z;
	double tmp;
	if (z <= -6e+272) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 2.9e-11) {
		tmp = x;
	} else if (z <= 6e+84) {
		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 * (y * z)
    t_1 = x * -z
    if (z <= (-6d+272)) then
        tmp = t_0
    else if (z <= (-1.0d0)) then
        tmp = t_1
    else if (z <= 3.75d-103) then
        tmp = x
    else if (z <= 9d-65) then
        tmp = t_0
    else if (z <= 2.9d-11) then
        tmp = x
    else if (z <= 6d+84) 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 * (y * z);
	double t_1 = x * -z;
	double tmp;
	if (z <= -6e+272) {
		tmp = t_0;
	} else if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 3.75e-103) {
		tmp = x;
	} else if (z <= 9e-65) {
		tmp = t_0;
	} else if (z <= 2.9e-11) {
		tmp = x;
	} else if (z <= 6e+84) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	t_1 = x * -z
	tmp = 0
	if z <= -6e+272:
		tmp = t_0
	elif z <= -1.0:
		tmp = t_1
	elif z <= 3.75e-103:
		tmp = x
	elif z <= 9e-65:
		tmp = t_0
	elif z <= 2.9e-11:
		tmp = x
	elif z <= 6e+84:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -6e+272)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = t_1;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 2.9e-11)
		tmp = x;
	elseif (z <= 6e+84)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -6e+272)
		tmp = t_0;
	elseif (z <= -1.0)
		tmp = t_1;
	elseif (z <= 3.75e-103)
		tmp = x;
	elseif (z <= 9e-65)
		tmp = t_0;
	elseif (z <= 2.9e-11)
		tmp = x;
	elseif (z <= 6e+84)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -6e+272], t$95$0, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 3.75e-103], x, If[LessEqual[z, 9e-65], t$95$0, If[LessEqual[z, 2.9e-11], x, If[LessEqual[z, 6e+84], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000004e272 or 3.75e-103 < z < 8.9999999999999995e-65 or 2.9e-11 < z < 5.99999999999999992e84

   1. Initial program 95.7%

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

      1. distribute-rgt-out-- 95.8%

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

      2. *-lft-identity 95.8%

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

      3. cancel-sign-sub-inv 95.8%

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

      4. +-commutative 95.8%

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

      5. distribute-lft-neg-in 95.8%

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

      6. associate-*l* 99.9%

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

      7. fma-def 99.9%

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

      8. neg-sub0 99.9%

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

      9. associate--r- 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

      12. *-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

      2. flip-+ 36.1%

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

      3. associate-*r* 36.0%

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

      4. associate-*r* 36.0%

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

      5. associate-*r* 35.7%

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

   5. Applied egg-rr 35.7%

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

      1. difference-of-squares 36.1%

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

      2. fma-def 36.1%

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

      3. associate-/l* 58.5%

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

      4. fma-def 58.5%

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

      5. metadata-eval 58.5%

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

      6. sub-neg 58.5%

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

      7. *-commutative 58.5%

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

      8. associate-*r* 54.4%

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

      9. distribute-lft1-in 54.4%

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

      10. +-commutative 54.4%

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

      11. *-inverses 95.7%

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

      12. associate-/l* 95.6%

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

   7. Simplified 95.6%

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

   8. Taylor expanded in y around inf 70.2%

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

      1. associate-*r* 66.0%

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

      2. *-commutative 66.0%

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

      3. *-commutative 66.0%

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

   10. Simplified 66.0%

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

   if -6.0000000000000004e272 < z < -1 or 5.99999999999999992e84 < z

   1. Initial program 92.7%

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

   2. Taylor expanded in z around inf 99.2%

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

      1. *-commutative 99.2%

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

      2. sub-neg 99.2%

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

      3. metadata-eval 99.2%

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

      4. distribute-rgt-in 99.2%

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

      5. neg-mul-1 99.2%

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

      6. unsub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in y around 0 66.1%

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

      1. neg-mul-1 66.1%

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

   7. Simplified 66.1%

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

   if -1 < z < 3.75e-103 or 8.9999999999999995e-65 < z < 2.9e-11

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 86.1%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+272}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 3.75 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 5: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -160000000.0) (not (<= y 1.95e-5)))
   (+ x (* z (* y x)))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -160000000.0) || !(y <= 1.95e-5)) {
		tmp = x + (z * (y * x));
	} 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 <= (-160000000.0d0)) .or. (.not. (y <= 1.95d-5))) then
        tmp = x + (z * (y * x))
    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 <= -160000000.0) || !(y <= 1.95e-5)) {
		tmp = x + (z * (y * x));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -160000000.0) or not (y <= 1.95e-5):
		tmp = x + (z * (y * x))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -160000000.0) || !(y <= 1.95e-5))
		tmp = Float64(x + Float64(z * Float64(y * x)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -160000000.0) || ~((y <= 1.95e-5)))
		tmp = x + (z * (y * x));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -160000000.0], N[Not[LessEqual[y, 1.95e-5]], $MachinePrecision]], N[(x + N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e8 or 1.95e-5 < y

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. distribute-rgt-in 92.3%

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

      3. *-un-lft-identity 92.3%

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

      4. distribute-rgt-neg-in 92.3%

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

   3. Applied egg-rr 92.3%

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

   4. Taylor expanded in y around inf 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*r* 89.0%

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

   6. Simplified 89.0%

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

   if -1.6e8 < y < 1.95e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.2%

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

      1. *-commutative 99.2%

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

      2. distribute-rgt-out-- 99.2%

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

      3. *-lft-identity 99.2%

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

   4. Simplified 99.2%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-5}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 6: 97.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-5}\right):\\ \;\;\;\;x + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -160000000.0) (not (<= y 1.95e-5)))
   (+ x (* y (* x z)))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -160000000.0) || !(y <= 1.95e-5)) {
		tmp = x + (y * (x * z));
	} 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 <= (-160000000.0d0)) .or. (.not. (y <= 1.95d-5))) then
        tmp = x + (y * (x * z))
    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 <= -160000000.0) || !(y <= 1.95e-5)) {
		tmp = x + (y * (x * z));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -160000000.0) or not (y <= 1.95e-5):
		tmp = x + (y * (x * z))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -160000000.0) || !(y <= 1.95e-5))
		tmp = Float64(x + Float64(y * Float64(x * z)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -160000000.0) || ~((y <= 1.95e-5)))
		tmp = x + (y * (x * z));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -160000000.0], N[Not[LessEqual[y, 1.95e-5]], $MachinePrecision]], N[(x + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e8 or 1.95e-5 < y

   1. Initial program 92.3%

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

      1. sub-neg 92.3%

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

      2. distribute-rgt-in 92.3%

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

      3. *-un-lft-identity 92.3%

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

      4. distribute-rgt-neg-in 92.3%

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

   3. Applied egg-rr 92.3%

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

   4. Taylor expanded in y around inf 96.6%

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

      1. *-commutative 96.6%

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

   6. Simplified 96.6%

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

   if -1.6e8 < y < 1.95e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.2%

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

      1. *-commutative 99.2%

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

      2. distribute-rgt-out-- 99.2%

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

      3. *-lft-identity 99.2%

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

   4. Simplified 99.2%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160000000 \lor \neg \left(y \leq 1.95 \cdot 10^{-5}\right):\\ \;\;\;\;x + y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 7: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.6e+112) (* z (- (* y x) x)) (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.6e+112) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x * (1.0 + (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 <= (-2.6d+112)) then
        tmp = z * ((y * x) - x)
    else
        tmp = x * (1.0d0 + (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 <= -2.6e+112) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.6e+112:
		tmp = z * ((y * x) - x)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.6e+112)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.6e+112)
		tmp = z * ((y * x) - x);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.6e+112], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000001e112

   1. Initial program 87.2%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

   if -2.6000000000000001e112 < z

   1. Initial program 98.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+112}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 8: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4e+116) (- x (* z (* x (- 1.0 y)))) (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+116) {
		tmp = x - (z * (x * (1.0 - y)));
	} else {
		tmp = x * (1.0 + (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 (x <= 4d+116) then
        tmp = x - (z * (x * (1.0d0 - y)))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 4e+116) {
		tmp = x - (z * (x * (1.0 - y)));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4e+116:
		tmp = x - (z * (x * (1.0 - y)))
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 4e+116)
		tmp = Float64(x - Float64(z * Float64(x * Float64(1.0 - y))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 4e+116)
		tmp = x - (z * (x * (1.0 - y)));
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 4e+116], N[(x - N[(z * N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.00000000000000006e116

   1. Initial program 95.8%

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

      1. distribute-rgt-out-- 95.8%

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

      2. *-lft-identity 95.8%

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

      3. cancel-sign-sub-inv 95.8%

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

      4. +-commutative 95.8%

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

      5. distribute-lft-neg-in 95.8%

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

      6. associate-*l* 98.2%

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

      7. fma-def 98.2%

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

      8. neg-sub0 98.2%

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

      9. associate--r- 98.2%

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

      10. metadata-eval 98.2%

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

      11. +-commutative 98.2%

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

      12. *-commutative 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 98.2%

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

      2. associate-*r* 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 4.00000000000000006e116 < x

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 9: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.2e+116) (- x (* z (* x (- 1.0 y)))) (- x (* x (* z (- 1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.2e+116) {
		tmp = x - (z * (x * (1.0 - y)));
	} else {
		tmp = x - (x * (z * (1.0 - 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 (x <= 2.2d+116) then
        tmp = x - (z * (x * (1.0d0 - y)))
    else
        tmp = x - (x * (z * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.2e+116) {
		tmp = x - (z * (x * (1.0 - y)));
	} else {
		tmp = x - (x * (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.2e+116:
		tmp = x - (z * (x * (1.0 - y)))
	else:
		tmp = x - (x * (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.2e+116)
		tmp = Float64(x - Float64(z * Float64(x * Float64(1.0 - y))));
	else
		tmp = Float64(x - Float64(x * Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.2e+116)
		tmp = x - (z * (x * (1.0 - y)));
	else
		tmp = x - (x * (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.2e+116], N[(x - N[(z * N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.2e116

   1. Initial program 95.8%

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

      1. distribute-rgt-out-- 95.8%

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

      2. *-lft-identity 95.8%

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

      3. cancel-sign-sub-inv 95.8%

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

      4. +-commutative 95.8%

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

      5. distribute-lft-neg-in 95.8%

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

      6. associate-*l* 98.2%

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

      7. fma-def 98.2%

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

      8. neg-sub0 98.2%

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

      9. associate--r- 98.2%

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

      10. metadata-eval 98.2%

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

      11. +-commutative 98.2%

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

      12. *-commutative 98.2%

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

   3. Simplified 98.2%

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

      1. fma-udef 98.2%

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

      2. associate-*r* 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 2.2e116 < x

   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-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   3. Applied egg-rr 100.0%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.2 \cdot 10^{+116}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 10: 83.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+22}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+154)
   (* y (* x z))
   (if (<= y 1.75e+22) (- x (* x z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+154) {
		tmp = y * (x * z);
	} else if (y <= 1.75e+22) {
		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 <= (-5.8d+154)) then
        tmp = y * (x * z)
    else if (y <= 1.75d+22) 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 <= -5.8e+154) {
		tmp = y * (x * z);
	} else if (y <= 1.75e+22) {
		tmp = x - (x * z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+154:
		tmp = y * (x * z)
	elif y <= 1.75e+22:
		tmp = x - (x * z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+154)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 1.75e+22)
		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 <= -5.8e+154)
		tmp = y * (x * z);
	elseif (y <= 1.75e+22)
		tmp = x - (x * z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+154], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+22], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999959e154

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 99.6%

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

   if -5.79999999999999959e154 < y < 1.75e22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.0%

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

      1. *-commutative 93.0%

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

      2. distribute-rgt-out-- 93.0%

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

      3. *-lft-identity 93.0%

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

   4. Simplified 93.0%

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

   if 1.75e22 < y

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*r* 77.9%

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

      3. *-commutative 77.9%

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

   4. Simplified 77.9%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+154}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+22}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 11: 65.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1900\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1900.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1900.0)) {
		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 <= (-1.0d0)) .or. (.not. (z <= 1900.0d0))) 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 <= -1.0) || !(z <= 1900.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1900.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1900.0))
		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 <= -1.0) || ~((z <= 1900.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1900.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1900 < z

   1. Initial program 93.1%

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

   2. Taylor expanded in z around inf 99.4%

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

      1. *-commutative 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. distribute-rgt-in 99.4%

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

      5. neg-mul-1 99.4%

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

      6. unsub-neg 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in y around 0 58.3%

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

      1. neg-mul-1 58.3%

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

   7. Simplified 58.3%

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

   if -1 < z < 1900

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.9%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1900\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 40.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -7.5e+176) (* x z) (if (<= z 1.25e+47) x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+176) {
		tmp = x * z;
	} else if (z <= 1.25e+47) {
		tmp = x;
	} else {
		tmp = 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 (z <= (-7.5d+176)) then
        tmp = x * z
    else if (z <= 1.25d+47) then
        tmp = x
    else
        tmp = x * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -7.5e+176) {
		tmp = x * z;
	} else if (z <= 1.25e+47) {
		tmp = x;
	} else {
		tmp = x * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -7.5e+176:
		tmp = x * z
	elif z <= 1.25e+47:
		tmp = x
	else:
		tmp = x * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -7.5e+176)
		tmp = Float64(x * z);
	elseif (z <= 1.25e+47)
		tmp = x;
	else
		tmp = Float64(x * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -7.5e+176)
		tmp = x * z;
	elseif (z <= 1.25e+47)
		tmp = x;
	else
		tmp = x * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -7.5e+176], N[(x * z), $MachinePrecision], If[LessEqual[z, 1.25e+47], x, N[(x * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.499999999999999e176 or 1.25000000000000005e47 < z

   1. Initial program 91.7%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

      4. distribute-rgt-in 99.9%

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

      5. neg-mul-1 99.9%

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

      6. unsub-neg 99.9%

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

   4. Simplified 99.9%

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

      1. sub-neg 99.9%

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

      2. flip-+ 61.8%

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

      3. pow2 61.8%

         \[\leadsto z \cdot \frac{\color{blue}{{\left(y \cdot x\right)}^{2}} - \left(-x\right) \cdot \left(-x\right)}{y \cdot x - \left(-x\right)} \]

   6. Applied egg-rr 61.8%

      \[\leadsto z \cdot \color{blue}{\frac{{\left(y \cdot x\right)}^{2} - \left(-x\right) \cdot \left(-x\right)}{y \cdot x - \left(-x\right)}} \]
   7. Step-by-step derivation

      1. clear-num 61.7%

         \[\leadsto z \cdot \color{blue}{\frac{1}{\frac{y \cdot x - \left(-x\right)}{{\left(y \cdot x\right)}^{2} - \left(-x\right) \cdot \left(-x\right)}}} \]

      2. un-div-inv 61.6%

         \[\leadsto \color{blue}{\frac{z}{\frac{y \cdot x - \left(-x\right)}{{\left(y \cdot x\right)}^{2} - \left(-x\right) \cdot \left(-x\right)}}} \]

      3. clear-num 61.7%

         \[\leadsto \frac{z}{\color{blue}{\frac{1}{\frac{{\left(y \cdot x\right)}^{2} - \left(-x\right) \cdot \left(-x\right)}{y \cdot x - \left(-x\right)}}}} \]

      4. unpow2 61.7%

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

      5. sqr-neg 61.7%

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

      6. sub-neg 61.7%

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

      7. remove-double-neg 61.7%

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

      8. flip-- 99.8%

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

      9. sub-neg 99.8%

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

      10. fma-def 99.8%

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

      11. add-sqr-sqrt 38.3%

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

      12. sqrt-prod 55.1%

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

      13. sqr-neg 55.1%

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

      14. sqrt-prod 29.8%

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

      15. add-sqr-sqrt 46.3%

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

   8. Applied egg-rr 46.3%

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

   9. Taylor expanded in y around 0 13.8%

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

   if -7.499999999999999e176 < z < 1.25000000000000005e47

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 64.9%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+176}:\\ \;\;\;\;x \cdot z\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot z\\ \end{array} \]

Alternative 13: 39.0% 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 96.6%

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

2. Taylor expanded in z around 0 42.8%

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

3. Final simplification 42.8%

   \[\leadsto x \]

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 2023228 
(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))))