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

Percentage Accurate: 87.9% → 99.9%

Time: 7.1s

Alternatives: 7

Speedup: 1.0×

• 21.2% 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: 87.9% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

2. Taylor expanded in x around inf 96.6%

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

3. Taylor expanded in y around 0 93.1%

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

   1. +-commutative 93.1%

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

   2. mul-1-neg 93.1%

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

   3. associate-/l* 93.7%

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

   4. sub-neg 93.7%

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

   5. *-lft-identity 93.7%

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

   6. associate-/l* 93.6%

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

   7. div-sub 99.8%

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

   8. sub-neg 99.8%

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

   9. metadata-eval 99.8%

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

   10. distribute-neg-in 99.8%

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

   11. associate-/l* 96.6%

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

   12. *-commutative 96.6%

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

   13. distribute-rgt-neg-in 96.6%

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

   14. distribute-frac-neg 96.6%

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

   15. *-commutative 96.6%

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

   16. associate-*r/ 100.0%

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

   17. *-commutative 100.0%

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

   18. distribute-rgt-neg-in 100.0%

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

   19. distribute-neg-in 100.0%

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

   20. metadata-eval 100.0%

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

   21. sub-neg 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -55000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -55000000000.0) (not (<= y 1.0)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -55000000000.0) || !(y <= 1.0)) {
		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 <= (-55000000000.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -55000000000.0) || !(y <= 1.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -55000000000.0) or not (y <= 1.0):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -55000000000.0) || !(y <= 1.0))
		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 <= -55000000000.0) || ~((y <= 1.0)))
		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, -55000000000.0], N[Not[LessEqual[y, 1.0]], $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 < -5.5e10 or 1 < y

   1. Initial program 82.0%

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

   2. Taylor expanded in x around inf 92.8%

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

   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 -5.5e10 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -55000000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -55000000000:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -55000000000.0)
   (- y (* y (/ x z)))
   (if (<= y 1.0) (+ y (/ x z)) (* y (- 1.0 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -55000000000.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = 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 (y <= (-55000000000.0d0)) then
        tmp = y - (y * (x / z))
    else if (y <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = 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 (y <= -55000000000.0) {
		tmp = y - (y * (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -55000000000.0:
		tmp = y - (y * (x / z))
	elif y <= 1.0:
		tmp = y + (x / z)
	else:
		tmp = y * (1.0 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -55000000000.0)
		tmp = Float64(y - Float64(y * Float64(x / z)));
	elseif (y <= 1.0)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -55000000000.0)
		tmp = y - (y * (x / z));
	elseif (y <= 1.0)
		tmp = y + (x / z);
	else
		tmp = y * (1.0 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -55000000000.0], N[(y - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e10

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 93.6%

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

   3. Taylor expanded in y around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. mul-1-neg 93.6%

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

      3. associate-/l* 100.0%

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

      4. sub-neg 100.0%

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

      5. *-lft-identity 100.0%

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

      6. associate-/l* 100.0%

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

      7. div-sub 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. distribute-neg-in 100.0%

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

      11. associate-/l* 93.6%

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

      12. *-commutative 93.6%

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

      13. distribute-rgt-neg-in 93.6%

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

      14. distribute-frac-neg 93.6%

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

      15. *-commutative 93.6%

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

      16. associate-*r/ 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. distribute-neg-in 100.0%

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

      20. metadata-eval 100.0%

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

      21. sub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. distribute-lft-neg-in 100.0%

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

      4. distribute-rgt-neg-out 100.0%

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

      5. *-lft-identity 100.0%

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

      6. distribute-rgt-neg-out 100.0%

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

      7. associate-*l/ 93.6%

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

      8. *-commutative 93.6%

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

      9. unsub-neg 93.6%

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

      10. associate-*r/ 100.0%

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

   8. Simplified 100.0%

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

   if -5.5e10 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 99.9%

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

   3. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if 1 < y

   1. Initial program 78.3%

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

   2. Taylor expanded in x around inf 92.0%

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

   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%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -55000000000:\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]

Alternative 4: 77.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+265}:\\ \;\;\;\;\frac{-y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+265) (/ (- (* y x)) z) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+265) {
		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 <= (-7.2d+265)) 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 <= -7.2e+265) {
		tmp = -(y * x) / z;
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+265:
		tmp = -(y * x) / z
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+265)
		tmp = Float64(Float64(-Float64(y * 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 <= -7.2e+265)
		tmp = -(y * x) / z;
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+265], N[((-N[(y * x), $MachinePrecision]) / z), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000005e265

   1. Initial program 84.9%

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

   2. Taylor expanded in y around inf 84.9%

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

   3. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. distribute-rgt-neg-out 84.9%

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

   5. Simplified 84.9%

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

   if -7.20000000000000005e265 < y

   1. Initial program 91.6%

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

   2. Taylor expanded in z around inf 75.5%

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

   3. Taylor expanded in x around 0 82.5%

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

      1. +-commutative 82.5%

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

   5. Simplified 82.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+265}:\\ \;\;\;\;\frac{-y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e-63) y (if (<= y 7.4e-26) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e-63) {
		tmp = y;
	} else if (y <= 7.4e-26) {
		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 <= (-4.1d-63)) then
        tmp = y
    else if (y <= 7.4d-26) 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 <= -4.1e-63) {
		tmp = y;
	} else if (y <= 7.4e-26) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e-63:
		tmp = y
	elif y <= 7.4e-26:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e-63)
		tmp = y;
	elseif (y <= 7.4e-26)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.1e-63)
		tmp = y;
	elseif (y <= 7.4e-26)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e-63], y, If[LessEqual[y, 7.4e-26], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999998e-63 or 7.3999999999999997e-26 < y

   1. Initial program 84.0%

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

   2. Taylor expanded in x around 0 54.2%

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

   if -4.0999999999999998e-63 < y < 7.3999999999999997e-26

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.6%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-63}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 78.2% 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 91.5%

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

2. Taylor expanded in z around inf 74.7%

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

3. Taylor expanded in x around 0 80.8%

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

   1. +-commutative 80.8%

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

5. Simplified 80.8%

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

6. Final simplification 80.8%

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

Alternative 7: 40.3% 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 91.5%

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

2. Taylor expanded in x around 0 39.8%

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

3. Final simplification 39.8%

   \[\leadsto y \]

Developer target: 93.7% 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 2023229 
(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))