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

Percentage Accurate: 95.9% → 98.0%

Time: 7.3s

Alternatives: 12

Speedup: 1.0×

• 21.2% 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: 98.0% 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 97.7%

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

   1. distribute-rgt-out-- 97.7%

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

   2. *-lft-identity 97.7%

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

   3. cancel-sign-sub-inv 97.7%

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

   4. +-commutative 97.7%

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

   5. distribute-lft-neg-in 97.7%

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

   6. associate-*l* 98.2%

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

   7. fma-def 98.3%

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

   8. neg-sub0 98.3%

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

   9. associate--r- 98.3%

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

   10. metadata-eval 98.3%

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

   11. +-commutative 98.3%

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

   12. *-commutative 98.3%

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

3. Simplified 98.3%

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

4. Final simplification 98.3%

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

Alternative 2: 63.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+158}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+44} \lor \neg \left(z \leq 2.7 \cdot 10^{+72}\right) \land z \leq 4.8 \cdot 10^{+119}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* y z))))
   (if (<= z -3.9e+158)
     t_0
     (if (<= z -3.6e-32)
       t_1
       (if (<= z 5.2e-87)
         x
         (if (or (<= z 1.3e+44) (and (not (<= z 2.7e+72)) (<= z 4.8e+119)))
           t_1
           t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -3.9e+158) {
		tmp = t_0;
	} else if (z <= -3.6e-32) {
		tmp = t_1;
	} else if (z <= 5.2e-87) {
		tmp = x;
	} else if ((z <= 1.3e+44) || (!(z <= 2.7e+72) && (z <= 4.8e+119))) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = x * (y * z)
    if (z <= (-3.9d+158)) then
        tmp = t_0
    else if (z <= (-3.6d-32)) then
        tmp = t_1
    else if (z <= 5.2d-87) then
        tmp = x
    else if ((z <= 1.3d+44) .or. (.not. (z <= 2.7d+72)) .and. (z <= 4.8d+119)) then
        tmp = t_1
    else
        tmp = t_0
    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 (z <= -3.9e+158) {
		tmp = t_0;
	} else if (z <= -3.6e-32) {
		tmp = t_1;
	} else if (z <= 5.2e-87) {
		tmp = x;
	} else if ((z <= 1.3e+44) || (!(z <= 2.7e+72) && (z <= 4.8e+119))) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (y * z)
	tmp = 0
	if z <= -3.9e+158:
		tmp = t_0
	elif z <= -3.6e-32:
		tmp = t_1
	elif z <= 5.2e-87:
		tmp = x
	elif (z <= 1.3e+44) or (not (z <= 2.7e+72) and (z <= 4.8e+119)):
		tmp = t_1
	else:
		tmp = t_0
	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 (z <= -3.9e+158)
		tmp = t_0;
	elseif (z <= -3.6e-32)
		tmp = t_1;
	elseif (z <= 5.2e-87)
		tmp = x;
	elseif ((z <= 1.3e+44) || (!(z <= 2.7e+72) && (z <= 4.8e+119)))
		tmp = t_1;
	else
		tmp = t_0;
	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 (z <= -3.9e+158)
		tmp = t_0;
	elseif (z <= -3.6e-32)
		tmp = t_1;
	elseif (z <= 5.2e-87)
		tmp = x;
	elseif ((z <= 1.3e+44) || (~((z <= 2.7e+72)) && (z <= 4.8e+119)))
		tmp = t_1;
	else
		tmp = t_0;
	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[z, -3.9e+158], t$95$0, If[LessEqual[z, -3.6e-32], t$95$1, If[LessEqual[z, 5.2e-87], x, If[Or[LessEqual[z, 1.3e+44], And[N[Not[LessEqual[z, 2.7e+72]], $MachinePrecision], LessEqual[z, 4.8e+119]]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9e158 or 1.3e44 < z < 2.7000000000000001e72 or 4.8e119 < z

   1. Initial program 95.1%

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

   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 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

   7. Simplified 68.8%

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

   if -3.9e158 < z < -3.59999999999999993e-32 or 5.20000000000000005e-87 < z < 1.3e44 or 2.7000000000000001e72 < z < 4.8e119

   1. Initial program 96.7%

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

   2. Taylor expanded in y around inf 62.1%

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

      1. *-commutative 62.1%

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

   4. Simplified 62.1%

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

   if -3.59999999999999993e-32 < z < 5.20000000000000005e-87

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+44} \lor \neg \left(z \leq 2.7 \cdot 10^{+72}\right) \land z \leq 4.8 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]

Alternative 3: 64.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+71} \lor \neg \left(z \leq 4 \cdot 10^{+119}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* y (* x z))))
   (if (<= z -8.5e+161)
     t_0
     (if (<= z -3e-32)
       t_1
       (if (<= z 7e-87)
         x
         (if (<= z 2.75e+51)
           t_1
           (if (or (<= z 4.5e+71) (not (<= z 4e+119))) t_0 (* x (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = y * (x * z);
	double tmp;
	if (z <= -8.5e+161) {
		tmp = t_0;
	} else if (z <= -3e-32) {
		tmp = t_1;
	} else if (z <= 7e-87) {
		tmp = x;
	} else if (z <= 2.75e+51) {
		tmp = t_1;
	} else if ((z <= 4.5e+71) || !(z <= 4e+119)) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = y * (x * z)
    if (z <= (-8.5d+161)) then
        tmp = t_0
    else if (z <= (-3d-32)) then
        tmp = t_1
    else if (z <= 7d-87) then
        tmp = x
    else if (z <= 2.75d+51) then
        tmp = t_1
    else if ((z <= 4.5d+71) .or. (.not. (z <= 4d+119))) then
        tmp = t_0
    else
        tmp = x * (y * z)
    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 = y * (x * z);
	double tmp;
	if (z <= -8.5e+161) {
		tmp = t_0;
	} else if (z <= -3e-32) {
		tmp = t_1;
	} else if (z <= 7e-87) {
		tmp = x;
	} else if (z <= 2.75e+51) {
		tmp = t_1;
	} else if ((z <= 4.5e+71) || !(z <= 4e+119)) {
		tmp = t_0;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = y * (x * z)
	tmp = 0
	if z <= -8.5e+161:
		tmp = t_0
	elif z <= -3e-32:
		tmp = t_1
	elif z <= 7e-87:
		tmp = x
	elif z <= 2.75e+51:
		tmp = t_1
	elif (z <= 4.5e+71) or not (z <= 4e+119):
		tmp = t_0
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (z <= -8.5e+161)
		tmp = t_0;
	elseif (z <= -3e-32)
		tmp = t_1;
	elseif (z <= 7e-87)
		tmp = x;
	elseif (z <= 2.75e+51)
		tmp = t_1;
	elseif ((z <= 4.5e+71) || !(z <= 4e+119))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = y * (x * z);
	tmp = 0.0;
	if (z <= -8.5e+161)
		tmp = t_0;
	elseif (z <= -3e-32)
		tmp = t_1;
	elseif (z <= 7e-87)
		tmp = x;
	elseif (z <= 2.75e+51)
		tmp = t_1;
	elseif ((z <= 4.5e+71) || ~((z <= 4e+119)))
		tmp = t_0;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+161], t$95$0, If[LessEqual[z, -3e-32], t$95$1, If[LessEqual[z, 7e-87], x, If[LessEqual[z, 2.75e+51], t$95$1, If[Or[LessEqual[z, 4.5e+71], N[Not[LessEqual[z, 4e+119]], $MachinePrecision]], t$95$0, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.50000000000000007e161 or 2.75e51 < z < 4.50000000000000043e71 or 3.99999999999999978e119 < z

   1. Initial program 95.1%

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

   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 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

   7. Simplified 68.8%

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

   if -8.50000000000000007e161 < z < -3e-32 or 7.00000000000000023e-87 < z < 2.75e51

   1. Initial program 95.9%

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

   2. Taylor expanded in y around inf 62.1%

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

   if -3e-32 < z < 7.00000000000000023e-87

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.1%

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

   if 4.50000000000000043e71 < z < 3.99999999999999978e119

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-32}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+71} \lor \neg \left(z \leq 4 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+73} \lor \neg \left(z \leq 6.4 \cdot 10^{+119}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))))
   (if (<= z -4.8e+160)
     t_0
     (if (<= z -1.38e-31)
       (* z (* y x))
       (if (<= z 6.8e-87)
         x
         (if (<= z 6.1e+47)
           (* y (* x z))
           (if (or (<= z 1.8e+73) (not (<= z 6.4e+119)))
             t_0
             (* x (* y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double tmp;
	if (z <= -4.8e+160) {
		tmp = t_0;
	} else if (z <= -1.38e-31) {
		tmp = z * (y * x);
	} else if (z <= 6.8e-87) {
		tmp = x;
	} else if (z <= 6.1e+47) {
		tmp = y * (x * z);
	} else if ((z <= 1.8e+73) || !(z <= 6.4e+119)) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = x * -z
    if (z <= (-4.8d+160)) then
        tmp = t_0
    else if (z <= (-1.38d-31)) then
        tmp = z * (y * x)
    else if (z <= 6.8d-87) then
        tmp = x
    else if (z <= 6.1d+47) then
        tmp = y * (x * z)
    else if ((z <= 1.8d+73) .or. (.not. (z <= 6.4d+119))) then
        tmp = t_0
    else
        tmp = x * (y * z)
    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 (z <= -4.8e+160) {
		tmp = t_0;
	} else if (z <= -1.38e-31) {
		tmp = z * (y * x);
	} else if (z <= 6.8e-87) {
		tmp = x;
	} else if (z <= 6.1e+47) {
		tmp = y * (x * z);
	} else if ((z <= 1.8e+73) || !(z <= 6.4e+119)) {
		tmp = t_0;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	tmp = 0
	if z <= -4.8e+160:
		tmp = t_0
	elif z <= -1.38e-31:
		tmp = z * (y * x)
	elif z <= 6.8e-87:
		tmp = x
	elif z <= 6.1e+47:
		tmp = y * (x * z)
	elif (z <= 1.8e+73) or not (z <= 6.4e+119):
		tmp = t_0
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -4.8e+160)
		tmp = t_0;
	elseif (z <= -1.38e-31)
		tmp = Float64(z * Float64(y * x));
	elseif (z <= 6.8e-87)
		tmp = x;
	elseif (z <= 6.1e+47)
		tmp = Float64(y * Float64(x * z));
	elseif ((z <= 1.8e+73) || !(z <= 6.4e+119))
		tmp = t_0;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	tmp = 0.0;
	if (z <= -4.8e+160)
		tmp = t_0;
	elseif (z <= -1.38e-31)
		tmp = z * (y * x);
	elseif (z <= 6.8e-87)
		tmp = x;
	elseif (z <= 6.1e+47)
		tmp = y * (x * z);
	elseif ((z <= 1.8e+73) || ~((z <= 6.4e+119)))
		tmp = t_0;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -4.8e+160], t$95$0, If[LessEqual[z, -1.38e-31], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-87], x, If[LessEqual[z, 6.1e+47], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.8e+73], N[Not[LessEqual[z, 6.4e+119]], $MachinePrecision]], t$95$0, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.8000000000000003e160 or 6.10000000000000019e47 < z < 1.7999999999999999e73 or 6.39999999999999979e119 < z

   1. Initial program 95.1%

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

   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 100.0%

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

      5. neg-mul-1 100.0%

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

      6. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.8%

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

      1. neg-mul-1 68.8%

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

   7. Simplified 68.8%

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

   if -4.8000000000000003e160 < z < -1.38000000000000004e-31

   1. Initial program 93.6%

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

   2. Taylor expanded in y around inf 59.5%

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

      1. associate-*r* 53.4%

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

      2. *-commutative 53.4%

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

      3. associate-*l* 59.6%

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

   4. Simplified 59.6%

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

   if -1.38000000000000004e-31 < z < 6.7999999999999997e-87

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 81.1%

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

   if 6.7999999999999997e-87 < z < 6.10000000000000019e47

   1. Initial program 99.5%

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

   2. Taylor expanded in y around inf 66.0%

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

   if 1.7999999999999999e73 < z < 6.39999999999999979e119

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.3%

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

      1. *-commutative 78.3%

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

   4. Simplified 78.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+160}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.38 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+73} \lor \neg \left(z \leq 6.4 \cdot 10^{+119}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-33} \lor \neg \left(z \leq 8 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.55e-33) (not (<= z 8e-88)))
   (* x (* z (+ y -1.0)))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.55e-33) || !(z <= 8e-88)) {
		tmp = x * (z * (y + -1.0));
	} 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 ((z <= (-2.55d-33)) .or. (.not. (z <= 8d-88))) then
        tmp = x * (z * (y + (-1.0d0)))
    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 ((z <= -2.55e-33) || !(z <= 8e-88)) {
		tmp = x * (z * (y + -1.0));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.55e-33) or not (z <= 8e-88):
		tmp = x * (z * (y + -1.0))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.55e-33) || !(z <= 8e-88))
		tmp = Float64(x * Float64(z * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.55e-33) || ~((z <= 8e-88)))
		tmp = x * (z * (y + -1.0));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.55e-33], N[Not[LessEqual[z, 8e-88]], $MachinePrecision]], N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.55000000000000004e-33 or 7.99999999999999947e-88 < z

   1. Initial program 95.8%

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

   2. Taylor expanded in z around inf 90.4%

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

   if -2.55000000000000004e-33 < z < 7.99999999999999947e-88

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 81.1%

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

      1. *-commutative 81.1%

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

      2. distribute-rgt-out-- 81.1%

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

      3. *-lft-identity 81.1%

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

   4. Simplified 81.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-33} \lor \neg \left(z \leq 8 \cdot 10^{-88}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 6: 87.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-31} \lor \neg \left(z \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.05e-31) (not (<= z 7.8e-16)))
   (* z (- (* y x) x))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.05e-31) || !(z <= 7.8e-16)) {
		tmp = z * ((y * x) - 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 ((z <= (-3.05d-31)) .or. (.not. (z <= 7.8d-16))) then
        tmp = z * ((y * x) - 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 ((z <= -3.05e-31) || !(z <= 7.8e-16)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.05e-31) or not (z <= 7.8e-16):
		tmp = z * ((y * x) - x)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.05e-31) || !(z <= 7.8e-16))
		tmp = Float64(z * Float64(Float64(y * x) - x));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.05e-31) || ~((z <= 7.8e-16)))
		tmp = z * ((y * x) - x);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.05e-31], N[Not[LessEqual[z, 7.8e-16]], $MachinePrecision]], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0499999999999999e-31 or 7.79999999999999954e-16 < z

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 97.8%

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

      1. *-commutative 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. distribute-rgt-in 97.8%

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

      5. neg-mul-1 97.8%

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

      6. unsub-neg 97.8%

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

   4. Simplified 97.8%

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

   if -3.0499999999999999e-31 < z < 7.79999999999999954e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.2%

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

      1. *-commutative 78.2%

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

      2. distribute-rgt-out-- 78.2%

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

      3. *-lft-identity 78.2%

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

   4. Simplified 78.2%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{-31} \lor \neg \left(z \leq 7.8 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 7: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \lor \neg \left(z \leq 2.9 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.02) (not (<= z 2.9e-10)))
   (* z (- (* y x) x))
   (+ x (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02) || !(z <= 2.9e-10)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x + (y * (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 <= (-1.02d0)) .or. (.not. (z <= 2.9d-10))) then
        tmp = z * ((y * x) - x)
    else
        tmp = x + (y * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.02) || !(z <= 2.9e-10)) {
		tmp = z * ((y * x) - x);
	} else {
		tmp = x + (y * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.02) or not (z <= 2.9e-10):
		tmp = z * ((y * x) - x)
	else:
		tmp = x + (y * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.02) || !(z <= 2.9e-10))
		tmp = Float64(z * Float64(Float64(y * x) - x));
	else
		tmp = Float64(x + Float64(y * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.02) || ~((z <= 2.9e-10)))
		tmp = z * ((y * x) - x);
	else
		tmp = x + (y * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.02], N[Not[LessEqual[z, 2.9e-10]], $MachinePrecision]], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.02 or 2.89999999999999981e-10 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in z around inf 99.8%

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

      1. *-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      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 -1.02 < z < 2.89999999999999981e-10

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around inf 96.0%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \lor \neg \left(z \leq 2.9 \cdot 10^{-10}\right):\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.55e+186)
   (* z (* y x))
   (if (<= y 1.55e+21) (- x (* x z)) (* y (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+186) {
		tmp = z * (y * x);
	} else if (y <= 1.55e+21) {
		tmp = x - (x * z);
	} else {
		tmp = y * (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 <= (-3.55d+186)) then
        tmp = z * (y * x)
    else if (y <= 1.55d+21) then
        tmp = x - (x * z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.55e+186) {
		tmp = z * (y * x);
	} else if (y <= 1.55e+21) {
		tmp = x - (x * z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.55e+186:
		tmp = z * (y * x)
	elif y <= 1.55e+21:
		tmp = x - (x * z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.55e+186)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 1.55e+21)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.55e+186)
		tmp = z * (y * x);
	elseif (y <= 1.55e+21)
		tmp = x - (x * z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.55e+186], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+21], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.54999999999999978e186

   1. Initial program 88.4%

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

   2. Taylor expanded in y around inf 72.5%

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

      1. associate-*r* 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-*l* 84.0%

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

   4. Simplified 84.0%

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

   if -3.54999999999999978e186 < y < 1.55e21

   1. Initial program 98.9%

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

   2. Taylor expanded in y around 0 87.2%

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

      1. *-commutative 87.2%

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

      2. distribute-rgt-out-- 87.2%

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

      3. *-lft-identity 87.2%

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

   4. Simplified 87.2%

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

   if 1.55e21 < y

   1. Initial program 96.6%

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

   2. Taylor expanded in y around inf 83.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+21}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 9: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z * (y + (-1.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

2. Final simplification 97.7%

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

Alternative 10: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

   1. sub-neg 97.7%

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

   2. distribute-rgt-in 97.7%

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

   3. *-un-lft-identity 97.7%

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

   4. distribute-rgt-neg-in 97.7%

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

3. Applied egg-rr 97.7%

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

4. Taylor expanded in y around 0 92.0%

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

   1. +-commutative 92.0%

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

   2. associate-*r* 92.0%

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

   3. associate-*r* 93.4%

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

   4. distribute-rgt-out 97.7%

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

   5. distribute-rgt-in 97.7%

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

6. Simplified 97.7%

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

7. Final simplification 97.7%

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

Alternative 11: 65.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

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

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(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 <= -1.0) || ~((z <= 1.0)))
		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, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 95.3%

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

   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 56.1%

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

      1. neg-mul-1 56.1%

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

   7. Simplified 56.1%

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

   if -1 < 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 75.4%

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

4. Final simplification 66.2%

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

Alternative 12: 38.5% 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 97.7%

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

2. Taylor expanded in z around 0 40.8%

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

3. Final simplification 40.8%

   \[\leadsto x \]

Developer target: 99.8% 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 2023214 
(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))))