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

Percentage Accurate: 87.7% → 99.9%

Time: 7.8s

Alternatives: 10

Speedup: 1.0×

• 20.1% 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: 87.7% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.3%

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

3. Taylor expanded in x around -inf 95.2%

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

   1. mul-1-neg 95.2%

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

   2. unsub-neg 95.2%

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

   3. associate-/l* 96.3%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

   \[\leadsto y - \frac{x}{z} \cdot \left(y + -1\right) \]
7. Add Preprocessing

Alternative 2: 78.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+235} \lor \neg \left(y \leq 7.8 \cdot 10^{+275}\right):\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.2e+102)
   (+ y (/ x z))
   (if (or (<= y 5.6e+235) (not (<= y 7.8e+275))) (/ (- y) (/ z x)) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e+102) {
		tmp = y + (x / z);
	} else if ((y <= 5.6e+235) || !(y <= 7.8e+275)) {
		tmp = -y / (z / x);
	} 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 <= 1.2d+102) then
        tmp = y + (x / z)
    else if ((y <= 5.6d+235) .or. (.not. (y <= 7.8d+275))) then
        tmp = -y / (z / x)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.2e+102) {
		tmp = y + (x / z);
	} else if ((y <= 5.6e+235) || !(y <= 7.8e+275)) {
		tmp = -y / (z / x);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.2e+102:
		tmp = y + (x / z)
	elif (y <= 5.6e+235) or not (y <= 7.8e+275):
		tmp = -y / (z / x)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.2e+102)
		tmp = Float64(y + Float64(x / z));
	elseif ((y <= 5.6e+235) || !(y <= 7.8e+275))
		tmp = Float64(Float64(-y) / Float64(z / x));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.2e+102)
		tmp = y + (x / z);
	elseif ((y <= 5.6e+235) || ~((y <= 7.8e+275)))
		tmp = -y / (z / x);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.2e+102], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 5.6e+235], N[Not[LessEqual[y, 7.8e+275]], $MachinePrecision]], N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < 1.19999999999999997e102

   1. Initial program 86.2%

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

   3. Taylor expanded in x around -inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. associate-/l* 96.9%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. distribute-frac-neg 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in y around 0 84.4%

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

       1. +-commutative 84.4%

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

   11. Simplified 84.4%

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

   if 1.19999999999999997e102 < y < 5.60000000000000052e235 or 7.8e275 < y

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf 86.8%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 92.1%

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

   5. Simplified 92.1%

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

   6. Taylor expanded in z around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r/ 63.4%

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

      3. distribute-rgt-neg-in 63.4%

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

   8. Simplified 63.4%

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

      1. distribute-rgt-neg-out 63.4%

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

      2. clear-num 63.4%

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

      3. div-inv 63.4%

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

      4. associate-/r/ 71.2%

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

      5. add-sqr-sqrt 40.5%

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

      6. sqrt-unprod 40.0%

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

      7. sqr-neg 40.0%

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

      8. sqrt-unprod 0.3%

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

      9. add-sqr-sqrt 0.8%

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

      10. *-commutative 0.8%

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

      11. clear-num 0.8%

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

      12. un-div-inv 0.8%

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

      13. add-sqr-sqrt 0.3%

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

      14. sqrt-unprod 39.9%

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

      15. sqr-neg 39.9%

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

      16. sqrt-unprod 40.4%

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

      17. add-sqr-sqrt 71.1%

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

   10. Applied egg-rr 71.1%

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

   if 5.60000000000000052e235 < y < 7.8e275

   1. Initial program 58.6%

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

   3. Taylor expanded in x around 0 78.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{+102}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+235} \lor \neg \left(y \leq 7.8 \cdot 10^{+275}\right):\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+274}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.5e+99)
   (+ y (/ x z))
   (if (<= y 3.75e+233)
     (* y (/ x (- z)))
     (if (<= y 1.55e+274) y (/ (- y) (/ z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.5e+99) {
		tmp = y + (x / z);
	} else if (y <= 3.75e+233) {
		tmp = y * (x / -z);
	} else if (y <= 1.55e+274) {
		tmp = y;
	} else {
		tmp = -y / (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+99) then
        tmp = y + (x / z)
    else if (y <= 3.75d+233) then
        tmp = y * (x / -z)
    else if (y <= 1.55d+274) then
        tmp = y
    else
        tmp = -y / (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+99) {
		tmp = y + (x / z);
	} else if (y <= 3.75e+233) {
		tmp = y * (x / -z);
	} else if (y <= 1.55e+274) {
		tmp = y;
	} else {
		tmp = -y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.5e+99:
		tmp = y + (x / z)
	elif y <= 3.75e+233:
		tmp = y * (x / -z)
	elif y <= 1.55e+274:
		tmp = y
	else:
		tmp = -y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.5e+99)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 3.75e+233)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (y <= 1.55e+274)
		tmp = y;
	else
		tmp = Float64(Float64(-y) / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.5e+99)
		tmp = y + (x / z);
	elseif (y <= 3.75e+233)
		tmp = y * (x / -z);
	elseif (y <= 1.55e+274)
		tmp = y;
	else
		tmp = -y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.5e+99], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.75e+233], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+274], y, N[((-y) / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < 6.5000000000000004e99

   1. Initial program 86.2%

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

   3. Taylor expanded in x around -inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. associate-/l* 96.9%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. distribute-frac-neg 84.4%

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

   8. Simplified 84.4%

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

   9. Taylor expanded in y around 0 84.4%

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

       1. +-commutative 84.4%

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

   11. Simplified 84.4%

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

   if 6.5000000000000004e99 < y < 3.7499999999999998e233

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 85.1%

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

      1. associate-/l* 99.9%

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

      2. associate-/r/ 91.1%

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

   5. Simplified 91.1%

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

   6. Taylor expanded in z around 0 63.6%

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

      1. mul-1-neg 63.6%

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

      2. associate-*r/ 58.9%

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

      3. distribute-rgt-neg-in 58.9%

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

   8. Simplified 58.9%

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

   9. Taylor expanded in x around 0 63.6%

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

       1. associate-*r/ 63.6%

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

       2. neg-mul-1 63.6%

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

       3. distribute-rgt-neg-out 63.6%

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

       4. associate-/l* 58.8%

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

   11. Simplified 58.8%

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

   12. Taylor expanded in x around 0 63.6%

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

       1. associate-*r/ 63.6%

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

       2. associate-*l/ 63.6%

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

       3. metadata-eval 63.6%

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

       4. associate-/r* 63.6%

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

       5. neg-mul-1 63.6%

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

       6. associate-*l/ 63.6%

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

       7. *-lft-identity 63.6%

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

       8. *-commutative 63.6%

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

       9. associate-*r/ 67.6%

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

   14. Simplified 67.6%

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

   if 3.7499999999999998e233 < y < 1.55e274

   1. Initial program 58.6%

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

   3. Taylor expanded in x around 0 78.7%

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

   if 1.55e274 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate-/r/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. distribute-rgt-neg-in 100.0%

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

   8. Simplified 100.0%

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

      1. distribute-rgt-neg-out 100.0%

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

      2. clear-num 100.0%

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

      3. div-inv 100.0%

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

      4. associate-/r/ 100.0%

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

      5. add-sqr-sqrt 75.0%

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

      6. sqrt-unprod 75.0%

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

      7. sqr-neg 75.0%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 0.0%

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

      10. *-commutative 0.0%

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

      11. clear-num 0.0%

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

      12. un-div-inv 0.0%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 75.0%

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

      15. sqr-neg 75.0%

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

      16. sqrt-unprod 75.0%

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

      17. add-sqr-sqrt 100.0%

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

   10. Applied egg-rr 100.0%

       \[\leadsto \color{blue}{-\frac{y}{\frac{z}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+99}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+274}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{-84} \lor \neg \left(z \leq 2.22 \cdot 10^{+18}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -7.1e-84) (not (<= z 2.22e+18)))
   (+ y (/ x z))
   (* (/ x z) (- 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -7.1e-84) || !(z <= 2.22e+18)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / 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 <= (-7.1d-84)) .or. (.not. (z <= 2.22d+18))) then
        tmp = y + (x / z)
    else
        tmp = (x / 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 <= -7.1e-84) || !(z <= 2.22e+18)) {
		tmp = y + (x / z);
	} else {
		tmp = (x / z) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -7.1e-84) or not (z <= 2.22e+18):
		tmp = y + (x / z)
	else:
		tmp = (x / z) * (1.0 - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -7.1e-84) || !(z <= 2.22e+18))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -7.1e-84) || ~((z <= 2.22e+18)))
		tmp = y + (x / z);
	else
		tmp = (x / z) * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -7.1e-84], N[Not[LessEqual[z, 2.22e+18]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.0999999999999997e-84 or 2.22e18 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in x around -inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

      3. associate-/l* 99.9%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-frac-neg 86.0%

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

   8. Simplified 86.0%

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

   9. Taylor expanded in y around 0 86.0%

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

       1. +-commutative 86.0%

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

   11. Simplified 86.0%

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

   if -7.0999999999999997e-84 < z < 2.22e18

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 87.5%

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

      1. associate-/l* 81.7%

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

      2. associate-/r/ 87.5%

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

      3. mul-1-neg 87.5%

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

      4. unsub-neg 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.1 \cdot 10^{-84} \lor \neg \left(z \leq 2.22 \cdot 10^{+18}\right):\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -27000000 \lor \neg \left(y \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -27000000.0) (not (<= y 4.2e-6)))
   (* (- z x) (/ y z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -27000000.0) || !(y <= 4.2e-6)) {
		tmp = (z - x) * (y / 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 <= (-27000000.0d0)) .or. (.not. (y <= 4.2d-6))) then
        tmp = (z - x) * (y / 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 <= -27000000.0) || !(y <= 4.2e-6)) {
		tmp = (z - x) * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -27000000.0) or not (y <= 4.2e-6):
		tmp = (z - x) * (y / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -27000000.0) || !(y <= 4.2e-6))
		tmp = Float64(Float64(z - x) * Float64(y / 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 <= -27000000.0) || ~((y <= 4.2e-6)))
		tmp = (z - x) * (y / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -27000000.0], N[Not[LessEqual[y, 4.2e-6]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e7 or 4.1999999999999996e-6 < y

   1. Initial program 72.5%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 99.1%

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

      2. associate-/r/ 92.1%

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

   5. Simplified 92.1%

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

   if -2.7e7 < y < 4.1999999999999996e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-frac-neg 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in y around 0 99.3%

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

       1. +-commutative 99.3%

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

   11. Simplified 99.3%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27000000 \lor \neg \left(y \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -27000000 \lor \neg \left(y \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -27000000.0) (not (<= y 4.2e-6)))
   (/ y (/ z (- z x)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -27000000.0) || !(y <= 4.2e-6)) {
		tmp = y / (z / (z - x));
	} 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 <= (-27000000.0d0)) .or. (.not. (y <= 4.2d-6))) then
        tmp = y / (z / (z - x))
    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 <= -27000000.0) || !(y <= 4.2e-6)) {
		tmp = y / (z / (z - x));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -27000000.0) or not (y <= 4.2e-6):
		tmp = y / (z / (z - x))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -27000000.0) || !(y <= 4.2e-6))
		tmp = Float64(y / Float64(z / Float64(z - x)));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -27000000.0) || ~((y <= 4.2e-6)))
		tmp = y / (z / (z - x));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -27000000.0], N[Not[LessEqual[y, 4.2e-6]], $MachinePrecision]], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e7 or 4.1999999999999996e-6 < y

   1. Initial program 72.5%

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

   3. Taylor expanded in y around inf 71.6%

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

      1. associate-/l* 99.1%

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

   5. Simplified 99.1%

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

   if -2.7e7 < y < 4.1999999999999996e-6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-frac-neg 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in y around 0 99.3%

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

       1. +-commutative 99.3%

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

   11. Simplified 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27000000 \lor \neg \left(y \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-45} \lor \neg \left(y \leq 1.9 \cdot 10^{-54}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.15e-45) (not (<= y 1.9e-54))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e-45) || !(y <= 1.9e-54)) {
		tmp = z * (y / z);
	} else {
		tmp = 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 <= (-2.15d-45)) .or. (.not. (y <= 1.9d-54))) then
        tmp = z * (y / z)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.15e-45) || !(y <= 1.9e-54)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.15e-45) or not (y <= 1.9e-54):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.15e-45) || !(y <= 1.9e-54))
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.15e-45) || ~((y <= 1.9e-54)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.15e-45], N[Not[LessEqual[y, 1.9e-54]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1499999999999999e-45 or 1.9000000000000001e-54 < y

   1. Initial program 76.4%

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

   3. Taylor expanded in x around 0 34.8%

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

      1. associate-/l* 51.4%

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

      2. associate-/r/ 54.1%

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

   5. Applied egg-rr 54.1%

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

   if -2.1499999999999999e-45 < y < 1.9000000000000001e-54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.0%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-45} \lor \neg \left(y \leq 1.9 \cdot 10^{-54}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -52000000:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -52000000.0) y (if (<= z 5.1e+64) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -52000000.0) {
		tmp = y;
	} else if (z <= 5.1e+64) {
		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 (z <= (-52000000.0d0)) then
        tmp = y
    else if (z <= 5.1d+64) 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 (z <= -52000000.0) {
		tmp = y;
	} else if (z <= 5.1e+64) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -52000000.0:
		tmp = y
	elif z <= 5.1e+64:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -52000000.0)
		tmp = y;
	elseif (z <= 5.1e+64)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -52000000.0)
		tmp = y;
	elseif (z <= 5.1e+64)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -52000000.0], y, If[LessEqual[z, 5.1e+64], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e7 or 5.10000000000000024e64 < z

   1. Initial program 69.0%

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

   3. Taylor expanded in x around 0 71.4%

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

   if -5.2e7 < z < 5.10000000000000024e64

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 51.7%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -52000000:\\ \;\;\;\;y\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.9% 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 85.3%

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

3. Taylor expanded in x around -inf 95.2%

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

   1. mul-1-neg 95.2%

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

   2. unsub-neg 95.2%

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

   3. associate-/l* 96.3%

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

   4. associate-/r/ 100.0%

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

   5. sub-neg 100.0%

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

   6. metadata-eval 100.0%

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

5. Simplified 100.0%

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

6. Taylor expanded in y around 0 76.4%

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

   1. mul-1-neg 76.4%

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

   2. distribute-frac-neg 76.4%

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

8. Simplified 76.4%

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

9. Taylor expanded in y around 0 76.4%

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

    1. +-commutative 76.4%

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

11. Simplified 76.4%

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

12. Final simplification 76.4%

    \[\leadsto y + \frac{x}{z} \]
13. Add Preprocessing

Alternative 10: 41.3% 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 85.3%

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

3. Taylor expanded in x around 0 43.1%

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

4. Final simplification 43.1%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.4% 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 2024027 
(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))