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

Percentage Accurate: 88.1% → 99.9%

Time: 8.5s

Alternatives: 13

Speedup: 0.8×

• 20.3% 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: 88.1% 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, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 840000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-209)
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (if (<= y 840000000000.0) (/ (+ x (* y (- z x))) z) (/ y (/ z (- z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-209) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else if (y <= 840000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y / (z / (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 <= (-2d-209)) then
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    else if (y <= 840000000000.0d0) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = y / (z / (z - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-209) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else if (y <= 840000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y / (z / (z - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e-209:
		tmp = (x / z) + (y * (1.0 - (x / z)))
	elif y <= 840000000000.0:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = y / (z / (z - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e-209)
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	elseif (y <= 840000000000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = Float64(y / Float64(z / Float64(z - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e-209)
		tmp = (x / z) + (y * (1.0 - (x / z)));
	elseif (y <= 840000000000.0)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = y / (z / (z - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e-209], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 840000000000.0], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e-209

   1. Initial program 85.9%

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

   2. Taylor expanded in y around 0 100.0%

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

   if -2.0000000000000001e-209 < y < 8.4e11

   1. Initial program 99.9%

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

   if 8.4e11 < y

   1. Initial program 74.3%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 840000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \]

Alternative 2: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00058:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+155)
   y
   (if (<= y -1.9e+79)
     (/ x z)
     (if (<= y -1.85e-13) y (if (<= y 0.00058) (/ x z) (* z (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+155) {
		tmp = y;
	} else if (y <= -1.9e+79) {
		tmp = x / z;
	} else if (y <= -1.85e-13) {
		tmp = y;
	} else if (y <= 0.00058) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-6.5d+155)) then
        tmp = y
    else if (y <= (-1.9d+79)) then
        tmp = x / z
    else if (y <= (-1.85d-13)) then
        tmp = y
    else if (y <= 0.00058d0) then
        tmp = x / z
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+155) {
		tmp = y;
	} else if (y <= -1.9e+79) {
		tmp = x / z;
	} else if (y <= -1.85e-13) {
		tmp = y;
	} else if (y <= 0.00058) {
		tmp = x / z;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+155:
		tmp = y
	elif y <= -1.9e+79:
		tmp = x / z
	elif y <= -1.85e-13:
		tmp = y
	elif y <= 0.00058:
		tmp = x / z
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+155)
		tmp = y;
	elseif (y <= -1.9e+79)
		tmp = Float64(x / z);
	elseif (y <= -1.85e-13)
		tmp = y;
	elseif (y <= 0.00058)
		tmp = Float64(x / z);
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+155)
		tmp = y;
	elseif (y <= -1.9e+79)
		tmp = x / z;
	elseif (y <= -1.85e-13)
		tmp = y;
	elseif (y <= 0.00058)
		tmp = x / z;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+155], y, If[LessEqual[y, -1.9e+79], N[(x / z), $MachinePrecision], If[LessEqual[y, -1.85e-13], y, If[LessEqual[y, 0.00058], N[(x / z), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.50000000000000046e155 or -1.9000000000000001e79 < y < -1.84999999999999994e-13

   1. Initial program 65.9%

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

   2. Taylor expanded in x around 0 75.7%

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

   if -6.50000000000000046e155 < y < -1.9000000000000001e79 or -1.84999999999999994e-13 < y < 5.8e-4

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.7%

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

   if 5.8e-4 < y

   1. Initial program 75.6%

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

   2. Taylor expanded in x around 0 28.2%

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

      1. associate-/l* 44.4%

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

      2. associate-/r/ 49.2%

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

   4. Applied egg-rr 49.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00058:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 840000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+19)
   (* y (- 1.0 (/ x z)))
   (if (<= y 840000000000.0) (/ (+ x (* y (- z x))) z) (/ y (/ z (- z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+19) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 840000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y / (z / (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 <= (-3.4d+19)) then
        tmp = y * (1.0d0 - (x / z))
    else if (y <= 840000000000.0d0) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = y / (z / (z - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+19) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 840000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = y / (z / (z - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+19:
		tmp = y * (1.0 - (x / z))
	elif y <= 840000000000.0:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = y / (z / (z - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+19)
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	elseif (y <= 840000000000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = Float64(y / Float64(z / Float64(z - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+19)
		tmp = y * (1.0 - (x / z));
	elseif (y <= 840000000000.0)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = y / (z / (z - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+19], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 840000000000.0], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4e19

   1. Initial program 68.7%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in y around inf 99.9%

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

   if -3.4e19 < y < 8.4e11

   1. Initial program 99.9%

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

   if 8.4e11 < y

   1. Initial program 74.3%

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

   2. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+19}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 840000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \]

Alternative 4: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-309)
   (+ (/ x z) (* y (- 1.0 (/ x z))))
   (+ y (* x (- (/ 1.0 z) (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-309) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1d-309)) then
        tmp = (x / z) + (y * (1.0d0 - (x / z)))
    else
        tmp = y + (x * ((1.0d0 / z) - (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-309) {
		tmp = (x / z) + (y * (1.0 - (x / z)));
	} else {
		tmp = y + (x * ((1.0 / z) - (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e-309:
		tmp = (x / z) + (y * (1.0 - (x / z)))
	else:
		tmp = y + (x * ((1.0 / z) - (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-309)
		tmp = Float64(Float64(x / z) + Float64(y * Float64(1.0 - Float64(x / z))));
	else
		tmp = Float64(y + Float64(x * Float64(Float64(1.0 / z) - Float64(y / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e-309)
		tmp = (x / z) + (y * (1.0 - (x / z)));
	else
		tmp = y + (x * ((1.0 / z) - (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e-309], N[(N[(x / z), $MachinePrecision] + N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * N[(N[(1.0 / z), $MachinePrecision] - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.000000000000002e-309

   1. Initial program 88.6%

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

   2. Taylor expanded in y around 0 100.0%

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

   if -1.000000000000002e-309 < y

   1. Initial program 88.7%

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

   2. Taylor expanded in x around 0 98.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot \left(\frac{1}{z} - \frac{y}{z}\right)\\ \end{array} \]

Alternative 5: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+156} \lor \neg \left(y \leq -3.8 \cdot 10^{+87}\right) \land y \leq 1.65 \cdot 10^{+122}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+156) (and (not (<= y -3.8e+87)) (<= y 1.65e+122)))
   (+ y (/ x z))
   (* y (/ (- x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+156) || (!(y <= -3.8e+87) && (y <= 1.65e+122))) {
		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 <= (-6.2d+156)) .or. (.not. (y <= (-3.8d+87))) .and. (y <= 1.65d+122)) 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 <= -6.2e+156) || (!(y <= -3.8e+87) && (y <= 1.65e+122))) {
		tmp = y + (x / z);
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+156) or (not (y <= -3.8e+87) and (y <= 1.65e+122)):
		tmp = y + (x / z)
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+156) || (!(y <= -3.8e+87) && (y <= 1.65e+122)))
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y * Float64(Float64(-x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+156) || (~((y <= -3.8e+87)) && (y <= 1.65e+122)))
		tmp = y + (x / z);
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+156], And[N[Not[LessEqual[y, -3.8e+87]], $MachinePrecision], LessEqual[y, 1.65e+122]]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000004e156 or -3.80000000000000011e87 < y < 1.6499999999999999e122

   1. Initial program 91.8%

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

   2. Taylor expanded in x around 0 98.3%

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

   3. Taylor expanded in y around 0 91.1%

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

   if -6.2000000000000004e156 < y < -3.80000000000000011e87 or 1.6499999999999999e122 < y

   1. Initial program 75.6%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. associate-/l* 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 68.9%

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

      1. neg-mul-1 68.9%

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

      2. distribute-neg-frac 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in y around 0 61.4%

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

      1. mul-1-neg 61.4%

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

      2. associate-*r/ 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

      4. distribute-frac-neg 68.9%

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

   10. Simplified 68.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+156} \lor \neg \left(y \leq -3.8 \cdot 10^{+87}\right) \land y \leq 1.65 \cdot 10^{+122}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]

Alternative 6: 76.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+157}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+121}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))))
   (if (<= y -2.1e+157)
     t_0
     (if (<= y -1.95e+89)
       (* y (/ (- x) z))
       (if (<= y 1.12e+121) t_0 (/ y (/ (- z) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -2.1e+157) {
		tmp = t_0;
	} else if (y <= -1.95e+89) {
		tmp = y * (-x / z);
	} else if (y <= 1.12e+121) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y + (x / z)
    if (y <= (-2.1d+157)) then
        tmp = t_0
    else if (y <= (-1.95d+89)) then
        tmp = y * (-x / z)
    else if (y <= 1.12d+121) then
        tmp = t_0
    else
        tmp = y / (-z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -2.1e+157) {
		tmp = t_0;
	} else if (y <= -1.95e+89) {
		tmp = y * (-x / z);
	} else if (y <= 1.12e+121) {
		tmp = t_0;
	} else {
		tmp = y / (-z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	tmp = 0
	if y <= -2.1e+157:
		tmp = t_0
	elif y <= -1.95e+89:
		tmp = y * (-x / z)
	elif y <= 1.12e+121:
		tmp = t_0
	else:
		tmp = y / (-z / x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -2.1e+157)
		tmp = t_0;
	elseif (y <= -1.95e+89)
		tmp = Float64(y * Float64(Float64(-x) / z));
	elseif (y <= 1.12e+121)
		tmp = t_0;
	else
		tmp = Float64(y / Float64(Float64(-z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	tmp = 0.0;
	if (y <= -2.1e+157)
		tmp = t_0;
	elseif (y <= -1.95e+89)
		tmp = y * (-x / z);
	elseif (y <= 1.12e+121)
		tmp = t_0;
	else
		tmp = y / (-z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+157], t$95$0, If[LessEqual[y, -1.95e+89], N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+121], t$95$0, N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e157 or -1.95000000000000005e89 < y < 1.12e121

   1. Initial program 91.8%

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

   2. Taylor expanded in x around 0 98.3%

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

   3. Taylor expanded in y around 0 91.1%

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

   if -2.1e157 < y < -1.95000000000000005e89

   1. Initial program 99.7%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. associate-/l* 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around 0 85.6%

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

      1. neg-mul-1 85.6%

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

      2. distribute-neg-frac 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in y around 0 85.4%

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

      1. mul-1-neg 85.4%

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

      2. associate-*r/ 85.7%

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

      3. distribute-rgt-neg-in 85.7%

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

      4. distribute-frac-neg 85.7%

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

   10. Simplified 85.7%

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

   if 1.12e121 < y

   1. Initial program 67.7%

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

   2. Taylor expanded in y around inf 67.7%

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

      1. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 63.5%

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

      1. neg-mul-1 63.5%

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

      2. distribute-neg-frac 63.5%

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

   7. Simplified 63.5%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+157}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+121}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \end{array} \]

Alternative 7: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00075:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+155)
   y
   (if (<= y -2.1e+78)
     (/ x z)
     (if (<= y -5.2e-13) y (if (<= y 0.00075) (/ x z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+155) {
		tmp = y;
	} else if (y <= -2.1e+78) {
		tmp = x / z;
	} else if (y <= -5.2e-13) {
		tmp = y;
	} else if (y <= 0.00075) {
		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 <= (-6.5d+155)) then
        tmp = y
    else if (y <= (-2.1d+78)) then
        tmp = x / z
    else if (y <= (-5.2d-13)) then
        tmp = y
    else if (y <= 0.00075d0) 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 <= -6.5e+155) {
		tmp = y;
	} else if (y <= -2.1e+78) {
		tmp = x / z;
	} else if (y <= -5.2e-13) {
		tmp = y;
	} else if (y <= 0.00075) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e+155:
		tmp = y
	elif y <= -2.1e+78:
		tmp = x / z
	elif y <= -5.2e-13:
		tmp = y
	elif y <= 0.00075:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+155)
		tmp = y;
	elseif (y <= -2.1e+78)
		tmp = Float64(x / z);
	elseif (y <= -5.2e-13)
		tmp = y;
	elseif (y <= 0.00075)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e+155)
		tmp = y;
	elseif (y <= -2.1e+78)
		tmp = x / z;
	elseif (y <= -5.2e-13)
		tmp = y;
	elseif (y <= 0.00075)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e+155], y, If[LessEqual[y, -2.1e+78], N[(x / z), $MachinePrecision], If[LessEqual[y, -5.2e-13], y, If[LessEqual[y, 0.00075], N[(x / z), $MachinePrecision], y]]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.50000000000000046e155 or -2.1000000000000001e78 < y < -5.2000000000000001e-13 or 7.5000000000000002e-4 < y

   1. Initial program 71.4%

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

   2. Taylor expanded in x around 0 58.0%

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

   if -6.50000000000000046e155 < y < -2.1000000000000001e78 or -5.2000000000000001e-13 < y < 7.5000000000000002e-4

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+155}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00075:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+145} \lor \neg \left(x \leq 3.1 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+145) (not (<= x 3.1e+68)))
   (* (/ x z) (- 1.0 y))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+145) || !(x <= 3.1e+68)) {
		tmp = (x / z) * (1.0 - y);
	} 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 ((x <= (-1.7d+145)) .or. (.not. (x <= 3.1d+68))) then
        tmp = (x / z) * (1.0d0 - y)
    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 ((x <= -1.7e+145) || !(x <= 3.1e+68)) {
		tmp = (x / z) * (1.0 - y);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+145) or not (x <= 3.1e+68):
		tmp = (x / z) * (1.0 - y)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+145) || !(x <= 3.1e+68))
		tmp = Float64(Float64(x / z) * Float64(1.0 - y));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.7e+145) || ~((x <= 3.1e+68)))
		tmp = (x / z) * (1.0 - y);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+145], N[Not[LessEqual[x, 3.1e+68]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e145 or 3.0999999999999998e68 < x

   1. Initial program 87.5%

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

   2. Taylor expanded in x around inf 85.4%

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

      1. associate-/l* 93.1%

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

      2. mul-1-neg 93.1%

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

      3. unsub-neg 93.1%

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

   4. Simplified 93.1%

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

      1. div-inv 93.1%

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

      2. clear-num 93.2%

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

   6. Applied egg-rr 93.2%

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

   if -1.7e145 < x < 3.0999999999999998e68

   1. Initial program 89.2%

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

   2. Taylor expanded in x around 0 96.5%

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

   3. Taylor expanded in y around 0 88.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+145} \lor \neg \left(x \leq 3.1 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 9: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.52) (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 <= -1.52) || !(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 <= (-1.52d0)) .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 <= -1.52) || !(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 <= -1.52) 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 <= -1.52) || !(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 <= -1.52) || ~((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, -1.52], 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 < -1.52 or 1 < y

   1. Initial program 73.5%

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

   2. Taylor expanded in y around 0 93.5%

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

   3. Taylor expanded in y around inf 99.0%

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

   if -1.52 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.7%

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

   3. Taylor expanded in y around 0 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 10: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.52)
   (* y (- 1.0 (/ x z)))
   (if (<= y 1.0) (+ y (/ x z)) (/ y (/ z (- z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.52) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y / (z / (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 <= (-1.52d0)) then
        tmp = y * (1.0d0 - (x / z))
    else if (y <= 1.0d0) then
        tmp = y + (x / z)
    else
        tmp = y / (z / (z - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.52) {
		tmp = y * (1.0 - (x / z));
	} else if (y <= 1.0) {
		tmp = y + (x / z);
	} else {
		tmp = y / (z / (z - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.52:
		tmp = y * (1.0 - (x / z))
	elif y <= 1.0:
		tmp = y + (x / z)
	else:
		tmp = y / (z / (z - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.52)
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	elseif (y <= 1.0)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(y / Float64(z / Float64(z - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.52)
		tmp = y * (1.0 - (x / z));
	elseif (y <= 1.0)
		tmp = y + (x / z);
	else
		tmp = y / (z / (z - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.52], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.52

   1. Initial program 72.2%

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

   2. Taylor expanded in y around 0 99.9%

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

   3. Taylor expanded in y around inf 99.0%

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

   if -1.52 < y < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 99.7%

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

   3. Taylor expanded in y around 0 98.8%

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

   if 1 < y

   1. Initial program 74.7%

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

   2. Taylor expanded in y around inf 73.8%

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

      1. associate-/l* 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \end{array} \]

Alternative 11: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+146}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.4e+146) (+ y (/ x z)) (* z (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.4e+146) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 6.4d+146) then
        tmp = y + (x / z)
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.4e+146) {
		tmp = y + (x / z);
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.4e+146:
		tmp = y + (x / z)
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.4e+146)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.4e+146)
		tmp = y + (x / z);
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.4e+146], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.3999999999999999e146

   1. Initial program 91.3%

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

   2. Taylor expanded in x around 0 97.6%

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

   3. Taylor expanded in y around 0 86.8%

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

   if 6.3999999999999999e146 < y

   1. Initial program 67.3%

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

   2. Taylor expanded in x around 0 15.3%

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

      1. associate-/l* 41.3%

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

      2. associate-/r/ 54.7%

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

   4. Applied egg-rr 54.7%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{+146}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]

Alternative 12: 81.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0 97.8%

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

   3. Taylor expanded in y around 0 92.2%

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

   if 1 < y

   1. Initial program 74.7%

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

   2. Taylor expanded in x around 0 96.3%

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

   3. Taylor expanded in y around 0 43.3%

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

      1. +-commutative 43.3%

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

      2. *-un-lft-identity 43.3%

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

      3. fma-def 43.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(1, y, \frac{x}{z}\right)} \]

      4. frac-2neg 43.3%

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

      5. distribute-frac-neg 43.3%

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

      6. add-sqr-sqrt 28.6%

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

      7. sqrt-unprod 52.7%

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

      8. sqr-neg 52.7%

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

      9. sqrt-unprod 21.0%

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

      10. add-sqr-sqrt 57.8%

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

      11. fma-neg 57.8%

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

      12. *-un-lft-identity 57.8%

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

   5. Applied egg-rr 57.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 13: 40.9% 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 88.7%

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

2. Taylor expanded in x around 0 35.4%

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

3. Final simplification 35.4%

   \[\leadsto y \]

Developer target: 94.2% 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 2023240 
(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))