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

Percentage Accurate: 96.0% → 98.0%

Time: 7.5s

Alternatives: 11

Speedup: 0.6×

• 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: 96.0% 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, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05e+73) (* z (* x (+ -1.0 y))) (* x (- (+ 1.0 (* z y)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+73) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * ((1.0 + (z * y)) - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.05d+73)) then
        tmp = z * (x * ((-1.0d0) + y))
    else
        tmp = x * ((1.0d0 + (z * y)) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05e+73) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * ((1.0 + (z * y)) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05e+73:
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x * ((1.0 + (z * y)) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05e+73)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	else
		tmp = Float64(x * Float64(Float64(1.0 + Float64(z * y)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05e+73)
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x * ((1.0 + (z * y)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05e+73], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e73

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. associate-*r* 99.7%

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

      2. sub-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. +-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. neg-sub0 99.9%

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

      12. associate--r- 99.9%

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

      13. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -1.0500000000000001e73 < z

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000004 or 1 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. associate-*r* 97.7%

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

      2. sub-neg 97.7%

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

      3. remove-double-neg 97.7%

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

      4. distribute-neg-in 97.7%

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

      5. +-commutative 97.7%

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

      6. sub-neg 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-*r* 97.8%

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

      9. *-commutative 97.8%

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

      10. *-commutative 97.8%

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

      11. neg-sub0 97.8%

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

      12. associate--r- 97.8%

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

      13. metadata-eval 97.8%

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

   5. Simplified 97.8%

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

   if -1.05000000000000004 < z < 1

   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 inf 98.0%

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

      1. neg-mul-1 98.0%

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

   5. Simplified 98.0%

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

      1. cancel-sign-sub 98.0%

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

      2. +-commutative 98.0%

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

   7. Applied egg-rr 98.0%

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

4. Final simplification 97.9%

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

Alternative 3: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+18} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+18) (not (<= y 1.0)))
   (* x (+ 1.0 (* z y)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+18) || !(y <= 1.0)) {
		tmp = x * (1.0 + (z * y));
	} 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 ((y <= (-6.5d+18)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * (1.0d0 + (z * y))
    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 ((y <= -6.5e+18) || !(y <= 1.0)) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+18) or not (y <= 1.0):
		tmp = x * (1.0 + (z * y))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+18) || !(y <= 1.0))
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+18) || ~((y <= 1.0)))
		tmp = x * (1.0 + (z * y));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+18], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e18 or 1 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in y around inf 92.0%

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

      1. neg-mul-1 92.0%

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

   5. Simplified 92.0%

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

      1. cancel-sign-sub 92.0%

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

      2. +-commutative 92.0%

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

   7. Applied egg-rr 92.0%

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

   if -6.5e18 < y < 1

   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 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-rgt-in 99.7%

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

      3. *-un-lft-identity 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. unsub-neg 99.7%

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

   5. Applied egg-rr 99.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+18} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-1 + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.95)
   (* z (* x (+ -1.0 y)))
   (if (<= z 1.0) (* x (+ 1.0 (* z y))) (* (* z x) (+ -1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = z * (x * (-1.0 + y));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = (z * x) * (-1.0 + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.95d0)) then
        tmp = z * (x * ((-1.0d0) + y))
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (z * y))
    else
        tmp = (z * x) * ((-1.0d0) + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.95) {
		tmp = z * (x * (-1.0 + y));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = (z * x) * (-1.0 + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.95:
		tmp = z * (x * (-1.0 + y))
	elif z <= 1.0:
		tmp = x * (1.0 + (z * y))
	else:
		tmp = (z * x) * (-1.0 + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.95)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(Float64(z * x) * Float64(-1.0 + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.95)
		tmp = z * (x * (-1.0 + y));
	elseif (z <= 1.0)
		tmp = x * (1.0 + (z * y));
	else
		tmp = (z * x) * (-1.0 + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.95], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.94999999999999996

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf 87.7%

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

      1. associate-*r* 97.9%

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

      2. sub-neg 97.9%

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

      3. remove-double-neg 97.9%

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

      4. distribute-neg-in 97.9%

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

      5. +-commutative 97.9%

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

      6. sub-neg 97.9%

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

      7. *-commutative 97.9%

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

      8. associate-*r* 98.0%

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

      9. *-commutative 98.0%

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

      10. *-commutative 98.0%

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

      11. neg-sub0 98.0%

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

      12. associate--r- 98.0%

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

      13. metadata-eval 98.0%

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

   5. Simplified 98.0%

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

   if -0.94999999999999996 < z < 1

   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 inf 98.0%

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

      1. neg-mul-1 98.0%

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

   5. Simplified 98.0%

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

      1. cancel-sign-sub 98.0%

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

      2. +-commutative 98.0%

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

   7. Applied egg-rr 98.0%

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

   if 1 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 94.6%

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

      1. associate-*r* 97.6%

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

      2. *-commutative 97.6%

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

      3. sub-neg 97.6%

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

      4. metadata-eval 97.6%

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

   5. Simplified 97.6%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-1 + y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+125} \lor \neg \left(y \leq 5200000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.7e+125) (not (<= y 5200000.0)))
   (* z (* x y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.7e+125) || !(y <= 5200000.0)) {
		tmp = z * (x * 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 <= (-6.7d+125)) .or. (.not. (y <= 5200000.0d0))) then
        tmp = z * (x * 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 <= -6.7e+125) || !(y <= 5200000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.7e+125) or not (y <= 5200000.0):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.7e+125) || !(y <= 5200000.0))
		tmp = Float64(z * Float64(x * 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 <= -6.7e+125) || ~((y <= 5200000.0)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.7e+125], N[Not[LessEqual[y, 5200000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7000000000000003e125 or 5.2e6 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. *-commutative 67.9%

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

      3. associate-*l* 70.6%

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

   5. Simplified 70.6%

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

   if -6.7000000000000003e125 < y < 5.2e6

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 92.3%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{+125} \lor \neg \left(y \leq 5200000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+142)
   (* x (* z y))
   (if (<= y 4200000.0) (- x (* z x)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+142) {
		tmp = x * (z * y);
	} else if (y <= 4200000.0) {
		tmp = x - (z * x);
	} else {
		tmp = z * (x * 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 (y <= (-1.3d+142)) then
        tmp = x * (z * y)
    else if (y <= 4200000.0d0) then
        tmp = x - (z * x)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+142) {
		tmp = x * (z * y);
	} else if (y <= 4200000.0) {
		tmp = x - (z * x);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+142:
		tmp = x * (z * y)
	elif y <= 4200000.0:
		tmp = x - (z * x)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+142)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 4200000.0)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+142)
		tmp = x * (z * y);
	elseif (y <= 4200000.0)
		tmp = x - (z * x);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+142], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4200000.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000011e142

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

      2. *-commutative 82.0%

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

   5. Simplified 82.0%

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

   if -1.30000000000000011e142 < y < 4.2e6

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 90.7%

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

      1. sub-neg 90.7%

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

      2. distribute-rgt-in 90.7%

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

      3. *-un-lft-identity 90.7%

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

      4. distribute-lft-neg-out 90.7%

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

      5. unsub-neg 90.7%

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

   5. Applied egg-rr 90.7%

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

   if 4.2e6 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*l* 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 4200000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 6000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e+142)
   (* x (* z y))
   (if (<= y 6000000.0) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+142) {
		tmp = x * (z * y);
	} else if (y <= 6000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * 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 (y <= (-1.3d+142)) then
        tmp = x * (z * y)
    else if (y <= 6000000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e+142) {
		tmp = x * (z * y);
	} else if (y <= 6000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.3e+142:
		tmp = x * (z * y)
	elif y <= 6000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e+142)
		tmp = Float64(x * Float64(z * y));
	elseif (y <= 6000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e+142)
		tmp = x * (z * y);
	elseif (y <= 6000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.3e+142], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.30000000000000011e142

   1. Initial program 94.4%

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

   3. Taylor expanded in y around inf 82.0%

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

      1. *-commutative 82.0%

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

      2. *-commutative 82.0%

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

   5. Simplified 82.0%

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

   if -1.30000000000000011e142 < y < 6e6

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 90.7%

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

   if 6e6 < y

   1. Initial program 92.2%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

      3. associate-*l* 66.4%

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

   5. Simplified 66.4%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+142}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 6000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 93.3%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. associate-*r* 97.7%

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

      2. sub-neg 97.7%

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

      3. remove-double-neg 97.7%

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

      4. distribute-neg-in 97.7%

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

      5. +-commutative 97.7%

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

      6. sub-neg 97.7%

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

      7. *-commutative 97.7%

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

      8. associate-*r* 97.8%

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

      9. *-commutative 97.8%

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

      10. *-commutative 97.8%

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

      11. neg-sub0 97.8%

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

      12. associate--r- 97.8%

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

      13. metadata-eval 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around 0 54.9%

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

      1. neg-mul-1 54.9%

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

   8. Simplified 54.9%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 78.2%

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

4. Final simplification 66.5%

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

Alternative 9: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.75e+72) (* z (* x (+ -1.0 y))) (* x (+ 1.0 (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.75e+72) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.75d+72)) then
        tmp = z * (x * ((-1.0d0) + y))
    else
        tmp = x * (1.0d0 + (z * ((-1.0d0) + y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.75e+72) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * (1.0 + (z * (-1.0 + y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.75e+72:
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x * (1.0 + (z * (-1.0 + y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.75e+72)
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(-1.0 + y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.75e+72)
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x * (1.0 + (z * (-1.0 + y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.75e+72], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e72

   1. Initial program 85.2%

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

   3. Taylor expanded in z around inf 85.2%

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

      1. associate-*r* 99.7%

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

      2. sub-neg 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. +-commutative 99.7%

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

      6. sub-neg 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. neg-sub0 99.9%

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

      12. associate--r- 99.9%

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

      13. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -2.75e72 < z

   1. Initial program 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(-1 + y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

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

3. Taylor expanded in y around 0 68.5%

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

Alternative 11: 37.9% 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. Add Preprocessing

3. Taylor expanded in z around 0 40.5%

   \[\leadsto \color{blue}{x} \]
4. 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 2024139 
(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))))