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

Percentage Accurate: 96.2% → 96.2%

Time: 10.4s

Alternatives: 7

Speedup: 1.0×

• 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: 96.2% 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: 96.2% 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 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* x (* y z)))))
   (if (<= y -2.55e+17) t_0 (if (<= y 1.25e-13) (- x (* x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x * (y * z));
	double tmp;
	if (y <= -2.55e+17) {
		tmp = t_0;
	} else if (y <= 1.25e-13) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (x * (y * z))
    if (y <= (-2.55d+17)) then
        tmp = t_0
    else if (y <= 1.25d-13) then
        tmp = x - (x * z)
    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 + (x * (y * z));
	double tmp;
	if (y <= -2.55e+17) {
		tmp = t_0;
	} else if (y <= 1.25e-13) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x * (y * z))
	tmp = 0
	if y <= -2.55e+17:
		tmp = t_0
	elif y <= 1.25e-13:
		tmp = x - (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x * Float64(y * z)))
	tmp = 0.0
	if (y <= -2.55e+17)
		tmp = t_0;
	elseif (y <= 1.25e-13)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x * (y * z));
	tmp = 0.0;
	if (y <= -2.55e+17)
		tmp = t_0;
	elseif (y <= 1.25e-13)
		tmp = x - (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+17], t$95$0, If[LessEqual[y, 1.25e-13], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e17 or 1.24999999999999997e-13 < y

   1. Initial program 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot z\right)}\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \left(z \cdot \color{blue}{y}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right)\right)\right) \]

   7. Simplified 96.5%

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

      1. associate-/r/ N/A

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

      2. /-rgt-identity N/A

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

      3. *-commutative N/A

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

      4. +-commutative N/A

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

      5. distribute-lft1-in N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(z \cdot \left(x \cdot y\right)\right), \color{blue}{x}\right) \]

      9. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\left(z \cdot x\right) \cdot y\right), x\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\left(\left(x \cdot z\right) \cdot y\right), x\right) \]

      11. associate-*r* N/A

          \[\leadsto \mathsf{+.f64}\left(\left(x \cdot \left(z \cdot y\right)\right), x\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(z \cdot y\right)\right), x\right) \]

      13. *-lowering-*.f64 96.5%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, y\right)\right), x\right) \]

   9. Applied egg-rr 96.5%

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

   if -2.55e17 < y < 1.24999999999999997e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 99.7%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 99.7%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. distribute-rgt-neg-out N/A

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

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z \cdot x\right)\right) + x \cdot 1 \]

      6. mul-1-neg N/A

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

      7. *-rgt-identity N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-1 \cdot \left(z \cdot x\right)\right), \color{blue}{x}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot x\right)\right), x\right) \]

      10. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{neg.f64}\left(\left(z \cdot x\right)\right), x\right) \]

      11. *-lowering-*.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, x\right)\right), x\right) \]

   7. Applied egg-rr 99.7%

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

      1. +-commutative N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot x\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \color{blue}{z}\right)\right) \]

      5. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 99.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+127}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+37}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -3.6e+127) t_0 (if (<= y 1.5e+37) (- x (* x z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -3.6e+127) {
		tmp = t_0;
	} else if (y <= 1.5e+37) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * y)
    if (y <= (-3.6d+127)) then
        tmp = t_0
    else if (y <= 1.5d+37) then
        tmp = x - (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -3.6e+127) {
		tmp = t_0;
	} else if (y <= 1.5e+37) {
		tmp = x - (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	tmp = 0
	if y <= -3.6e+127:
		tmp = t_0
	elif y <= 1.5e+37:
		tmp = x - (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -3.6e+127)
		tmp = t_0;
	elseif (y <= 1.5e+37)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * y);
	tmp = 0.0;
	if (y <= -3.6e+127)
		tmp = t_0;
	elseif (y <= 1.5e+37)
		tmp = x - (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e+127], t$95$0, If[LessEqual[y, 1.5e+37], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.59999999999999979e127 or 1.50000000000000011e37 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y \cdot x\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{y}\right)\right) \]

      6. *-lowering-*.f64 81.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   5. Simplified 81.0%

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

   if -3.59999999999999979e127 < y < 1.50000000000000011e37

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 95.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 95.3%

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. distribute-rgt-neg-out N/A

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

      5. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(z \cdot x\right)\right) + x \cdot 1 \]

      6. mul-1-neg N/A

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

      7. *-rgt-identity N/A

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

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\left(-1 \cdot \left(z \cdot x\right)\right), \color{blue}{x}\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{+.f64}\left(\left(\mathsf{neg}\left(z \cdot x\right)\right), x\right) \]

      10. neg-lowering-neg.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{neg.f64}\left(\left(z \cdot x\right)\right), x\right) \]

      11. *-lowering-*.f64 95.3%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{neg.f64}\left(\mathsf{*.f64}\left(z, x\right)\right), x\right) \]

   7. Applied egg-rr 95.3%

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

      1. +-commutative N/A

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

      2. unsub-neg N/A

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

      3. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(z \cdot x\right)}\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(x \cdot \color{blue}{z}\right)\right) \]

      5. *-lowering-*.f64 95.3%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{*.f64}\left(x, \color{blue}{z}\right)\right) \]

   9. Applied egg-rr 95.3%

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

Alternative 4: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -9.8e+125) t_0 (if (<= y 1.16e+36) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -9.8e+125) {
		tmp = t_0;
	} else if (y <= 1.16e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * y)
    if (y <= (-9.8d+125)) then
        tmp = t_0
    else if (y <= 1.16d+36) then
        tmp = x * (1.0d0 - z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -9.8e+125) {
		tmp = t_0;
	} else if (y <= 1.16e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	tmp = 0
	if y <= -9.8e+125:
		tmp = t_0
	elif y <= 1.16e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -9.8e+125)
		tmp = t_0;
	elseif (y <= 1.16e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * y);
	tmp = 0.0;
	if (y <= -9.8e+125)
		tmp = t_0;
	elseif (y <= 1.16e+36)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.8e+125], t$95$0, If[LessEqual[y, 1.16e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.80000000000000032e125 or 1.15999999999999998e36 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(y \cdot x\right)}\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(x \cdot \color{blue}{y}\right)\right) \]

      6. *-lowering-*.f64 81.0%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{*.f64}\left(x, \color{blue}{y}\right)\right) \]

   5. Simplified 81.0%

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

   if -9.80000000000000032e125 < y < 1.15999999999999998e36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 95.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 95.3%

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

Alternative 5: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= y -9.2e+125) t_0 (if (<= y 3.5e+36) (* x (- 1.0 z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (y <= -9.2e+125) {
		tmp = t_0;
	} else if (y <= 3.5e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y * z)
    if (y <= (-9.2d+125)) then
        tmp = t_0
    else if (y <= 3.5d+36) then
        tmp = x * (1.0d0 - z)
    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 * (y * z);
	double tmp;
	if (y <= -9.2e+125) {
		tmp = t_0;
	} else if (y <= 3.5e+36) {
		tmp = x * (1.0 - z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if y <= -9.2e+125:
		tmp = t_0
	elif y <= 3.5e+36:
		tmp = x * (1.0 - z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -9.2e+125)
		tmp = t_0;
	elseif (y <= 3.5e+36)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (y <= -9.2e+125)
		tmp = t_0;
	elseif (y <= 3.5e+36)
		tmp = x * (1.0 - z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.2e+125], t$95$0, If[LessEqual[y, 3.5e+36], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.20000000000000051e125 or 3.4999999999999998e36 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      2. *-lowering-*.f64 79.8%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 79.8%

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

   if -9.20000000000000051e125 < y < 3.4999999999999998e36

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 - z\right)}\right) \]

      2. --lowering--.f64 95.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{\_.f64}\left(1, \color{blue}{z}\right)\right) \]

   5. Simplified 95.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y z))))
   (if (<= z -3.1e-19) t_0 (if (<= z 7.2e-134) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (z <= -3.1e-19) {
		tmp = t_0;
	} else if (z <= 7.2e-134) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y * z)
    if (z <= (-3.1d-19)) then
        tmp = t_0
    else if (z <= 7.2d-134) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y * z);
	double tmp;
	if (z <= -3.1e-19) {
		tmp = t_0;
	} else if (z <= 7.2e-134) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y * z)
	tmp = 0
	if z <= -3.1e-19:
		tmp = t_0
	elif z <= 7.2e-134:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -3.1e-19)
		tmp = t_0;
	elseif (z <= 7.2e-134)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y * z);
	tmp = 0.0;
	if (z <= -3.1e-19)
		tmp = t_0;
	elseif (z <= 7.2e-134)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e-19], t$95$0, If[LessEqual[z, 7.2e-134], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999999e-19 or 7.1999999999999998e-134 < z

   1. Initial program 97.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(z \cdot \color{blue}{y}\right)\right) \]

      2. *-lowering-*.f64 45.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{y}\right)\right) \]

   5. Simplified 45.6%

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

   if -3.0999999999999999e-19 < z < 7.1999999999999998e-134

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 88.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-134}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.8% 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 98.4%

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

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 40.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024192 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

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