Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3

Percentage Accurate: 88.3% → 99.8%

Time: 5.9s

Alternatives: 11

Speedup: 0.8×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+43}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1e+43)
   (+ y (* x (- (/ 1.0 z) (/ y z))))
   (if (<= z 5e-48)
     (/ (+ x (* y (- z x))) z)
     (+ (/ x z) (* y (- 1.0 (/ x z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+43) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} else if (z <= 5e-48) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1d+43)) then
        tmp = y + (x * ((1.0d0 / z) - (y / z)))
    else if (z <= 5d-48) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e+43) {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	} else if (z <= 5e-48) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1e+43:
		tmp = y + (x * ((1.0 / z) - (y / z)))
	elif z <= 5e-48:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = (x / z) + (y * (1.0 - (x / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1e+43)
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	elseif (z <= 5e-48)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1e+43)
		tmp = y + (x * ((1.0 / z) - (y / z)));
	elseif (z <= 5e-48)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = (x / z) + (y * (1.0 - (x / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1e+43], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-48], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.00000000000000001e43

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 100.0%

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

   if -1.00000000000000001e43 < z < 4.9999999999999999e-48

   1. Initial program 100.0%

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

   if 4.9999999999999999e-48 < z

   1. Initial program 76.6%

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

   2. Taylor expanded in y around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+43}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-48}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-30} \lor \neg \left(z \leq 5 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.26e-30) (not (<= z 5e-48)))
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.26e-30) || !(z <= 5e-48)) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.26d-30)) .or. (.not. (z <= 5d-48))) then
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.26e-30) || !(z <= 5e-48)) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.26e-30) or not (z <= 5e-48):
		tmp = (x / z) + (y * (1.0 - (x / z)))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.26e-30) || !(z <= 5e-48))
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.26e-30) || ~((z <= 5e-48)))
		tmp = (x / z) + (y * (1.0 - (x / z)));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.26e-30], N[Not[LessEqual[z, 5e-48]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.26e-30 or 4.9999999999999999e-48 < z

   1. Initial program 77.2%

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

   2. Taylor expanded in y around 0 99.9%

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

   if -1.26e-30 < z < 4.9999999999999999e-48

   1. Initial program 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-30} \lor \neg \left(z \leq 5 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ t_1 := x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 69000000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))) (t_1 (* x (- (/ y z)))))
   (if (<= y -1.22e+233)
     t_0
     (if (<= y -4.8e+32)
       t_1
       (if (<= y 69000000000000.0)
         t_0
         (if (<= y 2.06e+139) t_1 (- y (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = x * -(y / z);
	double tmp;
	if (y <= -1.22e+233) {
		tmp = t_0;
	} else if (y <= -4.8e+32) {
		tmp = t_1;
	} else if (y <= 69000000000000.0) {
		tmp = t_0;
	} else if (y <= 2.06e+139) {
		tmp = t_1;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y + (x / z)
    t_1 = x * -(y / z)
    if (y <= (-1.22d+233)) then
        tmp = t_0
    else if (y <= (-4.8d+32)) then
        tmp = t_1
    else if (y <= 69000000000000.0d0) then
        tmp = t_0
    else if (y <= 2.06d+139) then
        tmp = t_1
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = x * -(y / z);
	double tmp;
	if (y <= -1.22e+233) {
		tmp = t_0;
	} else if (y <= -4.8e+32) {
		tmp = t_1;
	} else if (y <= 69000000000000.0) {
		tmp = t_0;
	} else if (y <= 2.06e+139) {
		tmp = t_1;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	t_1 = x * -(y / z)
	tmp = 0
	if y <= -1.22e+233:
		tmp = t_0
	elif y <= -4.8e+32:
		tmp = t_1
	elif y <= 69000000000000.0:
		tmp = t_0
	elif y <= 2.06e+139:
		tmp = t_1
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	t_1 = Float64(x * Float64(-Float64(y / z)))
	tmp = 0.0
	if (y <= -1.22e+233)
		tmp = t_0;
	elseif (y <= -4.8e+32)
		tmp = t_1;
	elseif (y <= 69000000000000.0)
		tmp = t_0;
	elseif (y <= 2.06e+139)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	t_1 = x * -(y / z);
	tmp = 0.0;
	if (y <= -1.22e+233)
		tmp = t_0;
	elseif (y <= -4.8e+32)
		tmp = t_1;
	elseif (y <= 69000000000000.0)
		tmp = t_0;
	elseif (y <= 2.06e+139)
		tmp = t_1;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-N[(y / z), $MachinePrecision])), $MachinePrecision]}, If[LessEqual[y, -1.22e+233], t$95$0, If[LessEqual[y, -4.8e+32], t$95$1, If[LessEqual[y, 69000000000000.0], t$95$0, If[LessEqual[y, 2.06e+139], t$95$1, N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22e233 or -4.79999999999999983e32 < y < 6.9e13

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0 97.5%

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

   3. Taylor expanded in y around 0 96.7%

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

   if -1.22e233 < y < -4.79999999999999983e32 or 6.9e13 < y < 2.06e139

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf 79.2%

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

   3. Taylor expanded in z around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-lft-neg-out 63.0%

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

      3. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. associate-*r/ 67.1%

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

      3. distribute-rgt-neg-in 67.1%

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

   8. Simplified 67.1%

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

   if 2.06e139 < y

   1. Initial program 61.5%

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

   2. Taylor expanded in x around 0 85.6%

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

   3. Taylor expanded in y around 0 62.6%

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

      1. div-inv 62.6%

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

      2. add-sqr-sqrt 29.6%

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

      3. sqrt-unprod 65.6%

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

      4. sqr-neg 65.6%

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

      5. sqrt-unprod 38.9%

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

      6. add-sqr-sqrt 71.8%

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

      7. cancel-sign-sub-inv 71.8%

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

      8. div-inv 71.8%

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

   5. Applied egg-rr 71.8%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+233}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 69000000000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.06 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \left(-\frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 4: 76.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ t_1 := y \cdot \frac{-x}{z}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{+234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2600000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))) (t_1 (* y (/ (- x) z))))
   (if (<= y -4.1e+234)
     t_0
     (if (<= y -6e+32)
       t_1
       (if (<= y 2600000000000.0)
         t_0
         (if (<= y 1.46e+139) t_1 (- y (/ x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = y * (-x / z);
	double tmp;
	if (y <= -4.1e+234) {
		tmp = t_0;
	} else if (y <= -6e+32) {
		tmp = t_1;
	} else if (y <= 2600000000000.0) {
		tmp = t_0;
	} else if (y <= 1.46e+139) {
		tmp = t_1;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y + (x / z)
    t_1 = y * (-x / z)
    if (y <= (-4.1d+234)) then
        tmp = t_0
    else if (y <= (-6d+32)) then
        tmp = t_1
    else if (y <= 2600000000000.0d0) then
        tmp = t_0
    else if (y <= 1.46d+139) then
        tmp = t_1
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double t_1 = y * (-x / z);
	double tmp;
	if (y <= -4.1e+234) {
		tmp = t_0;
	} else if (y <= -6e+32) {
		tmp = t_1;
	} else if (y <= 2600000000000.0) {
		tmp = t_0;
	} else if (y <= 1.46e+139) {
		tmp = t_1;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	t_1 = y * (-x / z)
	tmp = 0
	if y <= -4.1e+234:
		tmp = t_0
	elif y <= -6e+32:
		tmp = t_1
	elif y <= 2600000000000.0:
		tmp = t_0
	elif y <= 1.46e+139:
		tmp = t_1
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	t_1 = Float64(y * Float64(Float64(-x) / z))
	tmp = 0.0
	if (y <= -4.1e+234)
		tmp = t_0;
	elseif (y <= -6e+32)
		tmp = t_1;
	elseif (y <= 2600000000000.0)
		tmp = t_0;
	elseif (y <= 1.46e+139)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	t_1 = y * (-x / z);
	tmp = 0.0;
	if (y <= -4.1e+234)
		tmp = t_0;
	elseif (y <= -6e+32)
		tmp = t_1;
	elseif (y <= 2600000000000.0)
		tmp = t_0;
	elseif (y <= 1.46e+139)
		tmp = t_1;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e+234], t$95$0, If[LessEqual[y, -6e+32], t$95$1, If[LessEqual[y, 2600000000000.0], t$95$0, If[LessEqual[y, 1.46e+139], t$95$1, N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999974e234 or -6e32 < y < 2.6e12

   1. Initial program 96.6%

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

   2. Taylor expanded in x around 0 97.5%

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

   3. Taylor expanded in y around 0 96.7%

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

   if -4.09999999999999974e234 < y < -6e32 or 2.6e12 < y < 1.46000000000000011e139

   1. Initial program 79.2%

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

   2. Taylor expanded in y around inf 79.2%

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

   3. Taylor expanded in z around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. distribute-lft-neg-out 63.0%

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

      3. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. associate-*l/ 75.2%

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

      3. *-commutative 75.2%

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

      4. distribute-lft-neg-in 75.2%

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

   8. Simplified 75.2%

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

   if 1.46000000000000011e139 < y

   1. Initial program 61.5%

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

   2. Taylor expanded in x around 0 85.6%

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

   3. Taylor expanded in y around 0 62.6%

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

      1. div-inv 62.6%

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

      2. add-sqr-sqrt 29.6%

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

      3. sqrt-unprod 65.6%

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

      4. sqr-neg 65.6%

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

      5. sqrt-unprod 38.9%

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

      6. add-sqr-sqrt 71.8%

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

      7. cancel-sign-sub-inv 71.8%

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

      8. div-inv 71.8%

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

   5. Applied egg-rr 71.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+234}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+32}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 2600000000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+139}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 5: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+84} \lor \neg \left(y \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.9e+84) (not (<= y 6.4e+18)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+84) || !(y <= 6.4e+18)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.9d+84)) .or. (.not. (y <= 6.4d+18))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.9e+84) || !(y <= 6.4e+18)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.9e+84) or not (y <= 6.4e+18):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.9e+84) || !(y <= 6.4e+18))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.9e+84) || ~((y <= 6.4e+18)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.9e+84], N[Not[LessEqual[y, 6.4e+18]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.9e84 or 6.4e18 < y

   1. Initial program 66.8%

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

   2. Taylor expanded in x around 0 85.8%

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

   3. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

   5. Simplified 99.9%

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

   if -1.9e84 < y < 6.4e18

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+84} \lor \neg \left(y \leq 6.4 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+20} \lor \neg \left(y \leq 0.41\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e+20) (not (<= y 0.41))) (* y (- 1.0 (/ x z))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+20) || !(y <= 0.41)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8d+20)) .or. (.not. (y <= 0.41d0))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e+20) || !(y <= 0.41)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e+20) or not (y <= 0.41):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e+20) || !(y <= 0.41))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e+20) || ~((y <= 0.41)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e+20], N[Not[LessEqual[y, 0.41]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8e20 or 0.409999999999999976 < y

   1. Initial program 72.9%

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

   2. Taylor expanded in x around 0 87.5%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

   5. Simplified 99.8%

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

   if -8e20 < y < 0.409999999999999976

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.8%

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

   3. Taylor expanded in y around 0 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+20} \lor \neg \left(y \leq 0.41\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 7: 59.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e-10) y (if (<= y 8.5e-7) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e-10) {
		tmp = y;
	} else if (y <= 8.5e-7) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-2.5d-10)) then
        tmp = y
    else if (y <= 8.5d-7) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e-10) {
		tmp = y;
	} else if (y <= 8.5e-7) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.5e-10:
		tmp = y
	elif y <= 8.5e-7:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e-10)
		tmp = y;
	elseif (y <= 8.5e-7)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.5e-10)
		tmp = y;
	elseif (y <= 8.5e-7)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.5e-10], y, If[LessEqual[y, 8.5e-7], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000016e-10 or 8.50000000000000014e-7 < y

   1. Initial program 74.3%

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

   2. Taylor expanded in x around 0 44.8%

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

   if -2.50000000000000016e-10 < y < 8.50000000000000014e-7

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 74.0%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e-13) (* z (/ y z)) (if (<= y 2.15e-7) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e-13) {
		tmp = z * (y / z);
	} else if (y <= 2.15e-7) {
		tmp = x / z;
	} else {
		tmp = 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 <= (-3.5d-13)) then
        tmp = z * (y / z)
    else if (y <= 2.15d-7) then
        tmp = x / z
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e-13) {
		tmp = z * (y / z);
	} else if (y <= 2.15e-7) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.5e-13:
		tmp = z * (y / z)
	elif y <= 2.15e-7:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e-13)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 2.15e-7)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.5e-13)
		tmp = z * (y / z);
	elseif (y <= 2.15e-7)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.5e-13], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.15e-7], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e-13

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 74.2%

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

   3. Taylor expanded in z around inf 31.3%

      \[\leadsto \frac{\color{blue}{y \cdot z}}{z} \]
   4. Step-by-step derivation

      1. associate-/l* 46.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{z}}} \]

      2. associate-/r/ 48.7%

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

   5. Applied egg-rr 48.7%

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

   if -3.5000000000000002e-13 < y < 2.1500000000000001e-7

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 74.0%

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

   if 2.1500000000000001e-7 < y

   1. Initial program 73.9%

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

   2. Taylor expanded in x around 0 42.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 9: 80.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.41:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 0.41) (+ y (/ x z)) (- y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.41) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 0.41d0) then
        tmp = y + (x / z)
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.41) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 0.41:
		tmp = y + (x / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 0.41)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 0.41)
		tmp = y + (x / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 0.41], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.409999999999999976

   1. Initial program 92.3%

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

   2. Taylor expanded in x around 0 96.0%

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

   3. Taylor expanded in y around 0 86.8%

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

   if 0.409999999999999976 < y

   1. Initial program 73.9%

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

   2. Taylor expanded in x around 0 88.9%

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

   3. Taylor expanded in y around 0 42.1%

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

      1. div-inv 42.1%

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

      2. add-sqr-sqrt 21.5%

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

      3. sqrt-unprod 51.1%

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

      4. sqr-neg 51.1%

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

      5. sqrt-unprod 29.8%

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

      6. add-sqr-sqrt 55.2%

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

      7. cancel-sign-sub-inv 55.2%

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

      8. div-inv 55.2%

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

   5. Applied egg-rr 55.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.41:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 10: 77.1% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y + (x / 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 = y + (x / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

2. Taylor expanded in x around 0 94.3%

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

3. Taylor expanded in y around 0 76.2%

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

4. Final simplification 76.2%

   \[\leadsto y + \frac{x}{z} \]

Alternative 11: 41.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 87.9%

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

2. Taylor expanded in x around 0 36.3%

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

3. Final simplification 36.3%

   \[\leadsto y \]

Developer target: 93.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y + (x / z)) - (y / (z / 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 = (y + (x / z)) - (y / (z / x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))