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

Percentage Accurate: 96.1% → 97.8%

Time: 7.1s

Alternatives: 9

Speedup: 0.8×

• 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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;t_0 \leq 10^{+304}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ 1.0 (* z (+ y -1.0))))))
   (if (<= t_0 1e+304) t_0 (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 1e+304) {
		tmp = t_0;
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 + (z * (y + (-1.0d0))))
    if (t_0 <= 1d+304) then
        tmp = t_0
    else
        tmp = (z * x) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 + (z * (y + -1.0)));
	double tmp;
	if (t_0 <= 1e+304) {
		tmp = t_0;
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 + (z * (y + -1.0)))
	tmp = 0
	if t_0 <= 1e+304:
		tmp = t_0
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))))
	tmp = 0.0
	if (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 + (z * (y + -1.0)));
	tmp = 0.0;
	if (t_0 <= 1e+304)
		tmp = t_0;
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 1e+304], t$95$0, N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 9.9999999999999994e303

   1. Initial program 98.6%

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

   if 9.9999999999999994e303 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 80.2%

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

   2. Taylor expanded in z around inf 80.2%

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

      1. associate-*r* 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right) \leq 10^{+304}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 2: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+149} \lor \neg \left(y \leq -7 \cdot 10^{+89}\right) \land \left(y \leq -1.05 \cdot 10^{+43} \lor \neg \left(y \leq 1.2 \cdot 10^{+69}\right)\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.5e+149)
         (and (not (<= y -7e+89)) (or (<= y -1.05e+43) (not (<= y 1.2e+69)))))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+149) || (!(y <= -7e+89) && ((y <= -1.05e+43) || !(y <= 1.2e+69)))) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.5d+149)) .or. (.not. (y <= (-7d+89))) .and. (y <= (-1.05d+43)) .or. (.not. (y <= 1.2d+69))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.5e+149) || (!(y <= -7e+89) && ((y <= -1.05e+43) || !(y <= 1.2e+69)))) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.5e+149) or (not (y <= -7e+89) and ((y <= -1.05e+43) or not (y <= 1.2e+69))):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.5e+149) || (!(y <= -7e+89) && ((y <= -1.05e+43) || !(y <= 1.2e+69))))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.5e+149) || (~((y <= -7e+89)) && ((y <= -1.05e+43) || ~((y <= 1.2e+69)))))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+149], And[N[Not[LessEqual[y, -7e+89]], $MachinePrecision], Or[LessEqual[y, -1.05e+43], N[Not[LessEqual[y, 1.2e+69]], $MachinePrecision]]]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999982e149 or -7.0000000000000001e89 < y < -1.05000000000000001e43 or 1.2000000000000001e69 < y

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -4.49999999999999982e149 < y < -7.0000000000000001e89 or -1.05000000000000001e43 < y < 1.2000000000000001e69

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 93.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+149} \lor \neg \left(y \leq -7 \cdot 10^{+89}\right) \land \left(y \leq -1.05 \cdot 10^{+43} \lor \neg \left(y \leq 1.2 \cdot 10^{+69}\right)\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+43} \lor \neg \left(y \leq 3.5 \cdot 10^{+67}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))))
   (if (<= y -6.2e+149)
     t_0
     (if (<= y -8e+88)
       (* x (- 1.0 z))
       (if (or (<= y -2.15e+43) (not (<= y 3.5e+67))) t_0 (- x (* z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double tmp;
	if (y <= -6.2e+149) {
		tmp = t_0;
	} else if (y <= -8e+88) {
		tmp = x * (1.0 - z);
	} else if ((y <= -2.15e+43) || !(y <= 3.5e+67)) {
		tmp = t_0;
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (z * y)
    if (y <= (-6.2d+149)) then
        tmp = t_0
    else if (y <= (-8d+88)) then
        tmp = x * (1.0d0 - z)
    else if ((y <= (-2.15d+43)) .or. (.not. (y <= 3.5d+67))) then
        tmp = t_0
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double tmp;
	if (y <= -6.2e+149) {
		tmp = t_0;
	} else if (y <= -8e+88) {
		tmp = x * (1.0 - z);
	} else if ((y <= -2.15e+43) || !(y <= 3.5e+67)) {
		tmp = t_0;
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * y)
	tmp = 0
	if y <= -6.2e+149:
		tmp = t_0
	elif y <= -8e+88:
		tmp = x * (1.0 - z)
	elif (y <= -2.15e+43) or not (y <= 3.5e+67):
		tmp = t_0
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (y <= -6.2e+149)
		tmp = t_0;
	elseif (y <= -8e+88)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= -2.15e+43) || !(y <= 3.5e+67))
		tmp = t_0;
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * y);
	tmp = 0.0;
	if (y <= -6.2e+149)
		tmp = t_0;
	elseif (y <= -8e+88)
		tmp = x * (1.0 - z);
	elseif ((y <= -2.15e+43) || ~((y <= 3.5e+67)))
		tmp = t_0;
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+149], t$95$0, If[LessEqual[y, -8e+88], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.15e+43], N[Not[LessEqual[y, 3.5e+67]], $MachinePrecision]], t$95$0, N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999974e149 or -7.99999999999999968e88 < y < -2.15e43 or 3.5e67 < y

   1. Initial program 92.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -6.19999999999999974e149 < y < -7.99999999999999968e88

   1. Initial program 90.5%

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

   2. Taylor expanded in y around 0 80.7%

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

   if -2.15e43 < y < 3.5e67

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 94.0%

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

      1. sub-neg 94.0%

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

      2. distribute-rgt-in 94.0%

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

      3. *-lft-identity 94.0%

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

      4. distribute-lft-neg-in 94.0%

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

      5. *-commutative 94.0%

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

      6. unsub-neg 94.0%

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

      7. *-commutative 94.0%

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

   4. Applied egg-rr 94.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+149}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{+43} \lor \neg \left(y \leq 3.5 \cdot 10^{+67}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-13} \lor \neg \left(z \leq 23500\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.95e-13) (not (<= z 23500.0)))
   (* (* z x) (+ y -1.0))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-13) || !(z <= 23500.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x - (z * 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 <= (-1.95d-13)) .or. (.not. (z <= 23500.0d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.95e-13) || !(z <= 23500.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.95e-13) or not (z <= 23500.0):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.95e-13) || !(z <= 23500.0))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.95e-13) || ~((z <= 23500.0)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.95e-13], N[Not[LessEqual[z, 23500.0]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95000000000000002e-13 or 23500 < z

   1. Initial program 93.5%

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

   2. Taylor expanded in z around inf 92.1%

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

      1. associate-*r* 98.5%

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

      2. sub-neg 98.5%

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

      3. metadata-eval 98.5%

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

   4. Simplified 98.5%

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

   if -1.95000000000000002e-13 < z < 23500

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.5%

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

      1. sub-neg 76.5%

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

      2. distribute-rgt-in 76.5%

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

      3. *-lft-identity 76.5%

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

      4. distribute-lft-neg-in 76.5%

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

      5. *-commutative 76.5%

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

      6. unsub-neg 76.5%

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

      7. *-commutative 76.5%

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

   4. Applied egg-rr 76.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-13} \lor \neg \left(z \leq 23500\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 5: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+20} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e+20) (not (<= z 1.0)))
   (* (* z x) (+ y -1.0))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e+20) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.6d+20)) .or. (.not. (z <= 1.0d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e+20) || !(z <= 1.0)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e+20) or not (z <= 1.0):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e+20) || !(z <= 1.0))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.6e+20) || ~((z <= 1.0)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e+20], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e20 or 1 < z

   1. Initial program 93.2%

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

   2. Taylor expanded in z around inf 92.2%

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

      1. associate-*r* 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

   4. Simplified 98.9%

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

   if -4.6e20 < z < 1

   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. +-commutative 99.9%

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

      3. distribute-rgt-in 99.9%

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

      4. distribute-lft-neg-in 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-*l* 91.4%

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

      7. sub-neg 91.4%

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

      8. distribute-neg-in 91.4%

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

      9. metadata-eval 91.4%

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

      10. +-commutative 91.4%

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

      11. remove-double-neg 91.4%

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

      12. *-lft-identity 91.4%

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

   3. Applied egg-rr 91.4%

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

   4. Taylor expanded in y around inf 98.0%

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

      1. *-commutative 98.0%

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

   6. Simplified 98.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+20} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 6: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{z \cdot x}{\frac{1}{y + -1}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((z * x) / (1.0 / (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 + ((z * x) / (1.0d0 / (y + (-1.0d0))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

   1. sub-neg 96.6%

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

   2. +-commutative 96.6%

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

   3. distribute-rgt-in 96.6%

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

   4. distribute-lft-neg-in 96.6%

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

   5. *-commutative 96.6%

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

   6. associate-*l* 95.5%

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

   7. sub-neg 95.5%

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

   8. distribute-neg-in 95.5%

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

   9. metadata-eval 95.5%

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

   10. +-commutative 95.5%

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

   11. remove-double-neg 95.5%

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

   12. *-lft-identity 95.5%

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

3. Applied egg-rr 95.5%

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

   1. associate-*r* 96.6%

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

   2. *-commutative 96.6%

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

   3. associate-*l* 97.6%

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

   4. flip-+ 85.7%

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

   5. clear-num 85.7%

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

   6. un-div-inv 85.7%

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

   7. *-commutative 85.7%

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

   8. clear-num 85.7%

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

   9. flip-+ 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 7: 64.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9000000.0) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9000000.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9000000.0) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9000000.0) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9000000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9000000.0) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9e6 or 1 < z

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 92.3%

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

      1. *-commutative 92.3%

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

      2. sub-neg 92.3%

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

      3. metadata-eval 92.3%

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

      4. *-commutative 92.3%

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

      5. distribute-rgt-in 92.4%

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

      6. neg-mul-1 92.4%

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

      7. unsub-neg 92.4%

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

      8. *-commutative 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in y around 0 59.5%

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

      1. mul-1-neg 59.5%

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

   7. Simplified 59.5%

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

   if -9e6 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 72.8%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 61.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.2e-13) (* x (* z y)) (if (<= z 1.0) x (* z (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e-13) {
		tmp = x * (z * y);
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * -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 <= (-8.2d-13)) then
        tmp = x * (z * y)
    else if (z <= 1.0d0) then
        tmp = x
    else
        tmp = z * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.2e-13) {
		tmp = x * (z * y);
	} else if (z <= 1.0) {
		tmp = x;
	} else {
		tmp = z * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.2e-13:
		tmp = x * (z * y)
	elif z <= 1.0:
		tmp = x
	else:
		tmp = z * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.2e-13)
		tmp = Float64(x * Float64(z * y));
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = Float64(z * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.2e-13)
		tmp = x * (z * y);
	elseif (z <= 1.0)
		tmp = x;
	else
		tmp = z * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.2e-13], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], x, N[(z * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000004e-13

   1. Initial program 91.6%

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

   2. Taylor expanded in y around inf 51.9%

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

      1. *-commutative 51.9%

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

   4. Simplified 51.9%

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

   if -8.2000000000000004e-13 < 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 74.8%

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

   if 1 < z

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. metadata-eval 93.6%

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

      4. *-commutative 93.6%

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

      5. distribute-rgt-in 93.6%

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

      6. neg-mul-1 93.6%

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

      7. unsub-neg 93.6%

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

      8. *-commutative 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in y around 0 68.5%

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

      1. mul-1-neg 68.5%

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

   7. Simplified 68.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 9: 37.6% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.6%

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

2. Taylor expanded in z around 0 37.8%

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

3. Final simplification 37.8%

   \[\leadsto x \]

Developer target: 99.7% 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 2023297 
(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))))