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

Percentage Accurate: 87.4% → 99.9%

Time: 6.7s

Alternatives: 10

Speedup: 0.5×

• 20.7% 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: 87.4% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} + t\_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - x, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (/ x z)))))
   (if (<= y -2e-63)
     (+ (/ x z) t_0)
     (if (<= y 5e+16) (/ (fma y (- z x) x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -2e-63) {
		tmp = (x / z) + t_0;
	} else if (y <= 5e+16) {
		tmp = fma(y, (z - x), x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - Float64(x / z)))
	tmp = 0.0
	if (y <= -2e-63)
		tmp = Float64(Float64(x / z) + t_0);
	elseif (y <= 5e+16)
		tmp = Float64(fma(y, Float64(z - x), x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-63], N[(N[(x / z), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[y, 5e+16], N[(N[(y * N[(z - x), $MachinePrecision] + x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000013e-63

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 99.9%

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

   if -2.00000000000000013e-63 < y < 5e16

   1. Initial program 100.0%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   2. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   if 5e16 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 76.1%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+16}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - x, x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{+133}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))))
   (if (<= y -1.36e+133)
     t_0
     (if (<= y -1.08e+73)
       (* y (/ x (- z)))
       (if (<= y 1.65e-5) t_0 (- y (/ x z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -1.36e+133) {
		tmp = t_0;
	} else if (y <= -1.08e+73) {
		tmp = y * (x / -z);
	} else if (y <= 1.65e-5) {
		tmp = t_0;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y + (x / z)
    if (y <= (-1.36d+133)) then
        tmp = t_0
    else if (y <= (-1.08d+73)) then
        tmp = y * (x / -z)
    else if (y <= 1.65d-5) then
        tmp = t_0
    else
        tmp = y - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -1.36e+133) {
		tmp = t_0;
	} else if (y <= -1.08e+73) {
		tmp = y * (x / -z);
	} else if (y <= 1.65e-5) {
		tmp = t_0;
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	tmp = 0
	if y <= -1.36e+133:
		tmp = t_0
	elif y <= -1.08e+73:
		tmp = y * (x / -z)
	elif y <= 1.65e-5:
		tmp = t_0
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -1.36e+133)
		tmp = t_0;
	elseif (y <= -1.08e+73)
		tmp = Float64(y * Float64(x / Float64(-z)));
	elseif (y <= 1.65e-5)
		tmp = t_0;
	else
		tmp = Float64(y - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	tmp = 0.0;
	if (y <= -1.36e+133)
		tmp = t_0;
	elseif (y <= -1.08e+73)
		tmp = y * (x / -z);
	elseif (y <= 1.65e-5)
		tmp = t_0;
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.36e+133], t$95$0, If[LessEqual[y, -1.08e+73], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-5], t$95$0, N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3600000000000001e133 or -1.08e73 < y < 1.6500000000000001e-5

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0 96.3%

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

   4. Taylor expanded in x around 0 88.7%

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

   5. Taylor expanded in y around 0 88.7%

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

      1. +-commutative 88.7%

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

   7. Simplified 88.7%

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

   if -1.3600000000000001e133 < y < -1.08e73

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 87.2%

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

   4. Taylor expanded in z around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. distribute-lft-neg-out 59.7%

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

      3. *-commutative 59.7%

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

   6. Simplified 59.7%

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

      1. frac-2neg 59.7%

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

      2. distribute-frac-neg2 59.7%

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

      3. distribute-rgt-neg-out 59.7%

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

      4. remove-double-neg 59.7%

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

      5. associate-*r/ 72.3%

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

   8. Applied egg-rr 72.3%

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

   if 1.6500000000000001e-5 < y

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in x around 0 52.3%

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

      1. *-rgt-identity 52.3%

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

      2. add-sqr-sqrt 19.9%

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

      3. sqrt-unprod 67.9%

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

      4. sqr-neg 67.9%

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

      5. sqrt-unprod 44.7%

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

      6. add-sqr-sqrt 67.7%

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

      7. distribute-frac-neg 67.7%

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

      8. sub-neg 67.7%

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

      9. add-sqr-sqrt 40.2%

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

      10. cancel-sign-sub-inv 40.2%

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

   6. Applied egg-rr 40.2%

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

      1. distribute-lft-neg-out 40.2%

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

      2. rem-square-sqrt 67.7%

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

      3. sub-neg 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+133}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+42} \lor \neg \left(y \leq 10^{+14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.8e+42) (not (<= y 1e+14)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+42) || !(y <= 1e+14)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-4.8d+42)) .or. (.not. (y <= 1d+14))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = (x + (y * (z - x))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.8e+42) || !(y <= 1e+14)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.8e+42) or not (y <= 1e+14):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.8e+42) || !(y <= 1e+14))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.8e+42) || ~((y <= 1e+14)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.8e+42], N[Not[LessEqual[y, 1e+14]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999997e42 or 1e14 < y

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. associate-/l* 99.9%

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

      2. div-sub 99.9%

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

      3. *-inverses 99.9%

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

   5. Simplified 99.9%

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

   if -4.7999999999999997e42 < y < 1e14

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+42} \lor \neg \left(y \leq 10^{+14}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} + t\_0\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (/ x z)))))
   (if (<= y -1e-63)
     (+ (/ x z) t_0)
     (if (<= y 3200000000000.0) (/ (+ x (* y (- z x))) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1e-63) {
		tmp = (x / z) + t_0;
	} else if (y <= 3200000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = t_0;
	}
	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 * (1.0d0 - (x / z))
    if (y <= (-1d-63)) then
        tmp = (x / z) + t_0
    else if (y <= 3200000000000.0d0) then
        tmp = (x + (y * (z - x))) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1e-63) {
		tmp = (x / z) + t_0;
	} else if (y <= 3200000000000.0) {
		tmp = (x + (y * (z - x))) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - (x / z))
	tmp = 0
	if y <= -1e-63:
		tmp = (x / z) + t_0
	elif y <= 3200000000000.0:
		tmp = (x + (y * (z - x))) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - Float64(x / z)))
	tmp = 0.0
	if (y <= -1e-63)
		tmp = Float64(Float64(x / z) + t_0);
	elseif (y <= 3200000000000.0)
		tmp = Float64(Float64(x + Float64(y * Float64(z - x))) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - (x / z));
	tmp = 0.0;
	if (y <= -1e-63)
		tmp = (x / z) + t_0;
	elseif (y <= 3200000000000.0)
		tmp = (x + (y * (z - x))) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-63], N[(N[(x / z), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[y, 3200000000000.0], N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000007e-63

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 99.9%

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

   if -1.00000000000000007e-63 < y < 3.2e12

   1. Initial program 100.0%

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

   if 3.2e12 < y

   1. Initial program 76.1%

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

   3. Taylor expanded in y around inf 76.1%

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

      1. associate-/l* 100.0%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -32.0) (not (<= y 1.65e-5)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -32.0) || !(y <= 1.65e-5)) {
		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 <= (-32.0d0)) .or. (.not. (y <= 1.65d-5))) 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 <= -32.0) || !(y <= 1.65e-5)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -32.0) or not (y <= 1.65e-5):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -32.0) || !(y <= 1.65e-5))
		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 <= -32.0) || ~((y <= 1.65e-5)))
		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, -32.0], N[Not[LessEqual[y, 1.65e-5]], $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 < -32 or 1.6500000000000001e-5 < y

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 74.4%

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

      1. associate-/l* 99.4%

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

      2. div-sub 99.4%

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

      3. *-inverses 99.4%

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

   5. Simplified 99.4%

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

   if -32 < y < 1.6500000000000001e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 94.7%

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

   4. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

      1. +-commutative 99.0%

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

   7. Simplified 99.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -32 \lor \neg \left(y \leq 1.65 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3600000000 \lor \neg \left(x \leq 4.3 \cdot 10^{+124}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3600000000.0) (not (<= x 4.3e+124)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3600000000.0) || !(x <= 4.3e+124)) {
		tmp = x * ((1.0 - 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 ((x <= (-3600000000.0d0)) .or. (.not. (x <= 4.3d+124))) then
        tmp = x * ((1.0d0 - 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 ((x <= -3600000000.0) || !(x <= 4.3e+124)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3600000000.0) or not (x <= 4.3e+124):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3600000000.0) || !(x <= 4.3e+124))
		tmp = Float64(x * Float64(Float64(1.0 - 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 ((x <= -3600000000.0) || ~((x <= 4.3e+124)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3600000000.0], N[Not[LessEqual[x, 4.3e+124]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e9 or 4.3e124 < x

   1. Initial program 85.7%

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

   3. Taylor expanded in x around inf 78.3%

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

      1. associate-/l* 84.1%

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

      2. mul-1-neg 84.1%

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

      3. unsub-neg 84.1%

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

   5. Simplified 84.1%

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

   if -3.6e9 < x < 4.3e124

   1. Initial program 86.3%

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

   3. Taylor expanded in y around 0 99.3%

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

   4. Taylor expanded in x around 0 84.5%

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

   5. Taylor expanded in y around 0 84.5%

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

      1. +-commutative 84.5%

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

   7. Simplified 84.5%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3600000000 \lor \neg \left(x \leq 4.3 \cdot 10^{+124}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-33} \lor \neg \left(y \leq 2.9 \cdot 10^{-32}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-33) (not (<= y 2.9e-32))) y (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-33) || !(y <= 2.9e-32)) {
		tmp = y;
	} 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 <= (-3.4d-33)) .or. (.not. (y <= 2.9d-32))) then
        tmp = y
    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 <= -3.4e-33) || !(y <= 2.9e-32)) {
		tmp = y;
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-33) or not (y <= 2.9e-32):
		tmp = y
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-33) || !(y <= 2.9e-32))
		tmp = y;
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-33) || ~((y <= 2.9e-32)))
		tmp = y;
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-33], N[Not[LessEqual[y, 2.9e-32]], $MachinePrecision]], y, N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4000000000000001e-33 or 2.89999999999999996e-32 < y

   1. Initial program 77.5%

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

   3. Taylor expanded in x around 0 53.3%

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

   if -3.4000000000000001e-33 < y < 2.89999999999999996e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-33} \lor \neg \left(y \leq 2.9 \cdot 10^{-32}\right):\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.65e-5) (+ y (/ x z)) (- y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.65e-5) {
		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 <= 1.65d-5) 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 <= 1.65e-5) {
		tmp = y + (x / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.65e-5:
		tmp = y + (x / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.65e-5)
		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 <= 1.65e-5)
		tmp = y + (x / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.65e-5], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.6500000000000001e-5

   1. Initial program 89.6%

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

   3. Taylor expanded in y around 0 96.6%

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

   4. Taylor expanded in x around 0 83.7%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. +-commutative 83.7%

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

   7. Simplified 83.7%

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

   if 1.6500000000000001e-5 < y

   1. Initial program 77.7%

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

   3. Taylor expanded in y around 0 85.5%

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

   4. Taylor expanded in x around 0 52.3%

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

      1. *-rgt-identity 52.3%

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

      2. add-sqr-sqrt 19.9%

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

      3. sqrt-unprod 67.9%

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

      4. sqr-neg 67.9%

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

      5. sqrt-unprod 44.7%

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

      6. add-sqr-sqrt 67.7%

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

      7. distribute-frac-neg 67.7%

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

      8. sub-neg 67.7%

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

      9. add-sqr-sqrt 40.2%

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

      10. cancel-sign-sub-inv 40.2%

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

   6. Applied egg-rr 40.2%

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

      1. distribute-lft-neg-out 40.2%

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

      2. rem-square-sqrt 67.7%

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

      3. sub-neg 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-5}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.8% 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 86.1%

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

3. Taylor expanded in y around 0 93.3%

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

4. Taylor expanded in x around 0 74.4%

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

5. Taylor expanded in y around 0 74.4%

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

   1. +-commutative 74.4%

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

7. Simplified 74.4%

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

8. Final simplification 74.4%

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

Alternative 10: 40.8% 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 86.1%

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

3. Taylor expanded in x around 0 43.5%

   \[\leadsto \color{blue}{y} \]
4. Add Preprocessing

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 2024096 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (- (+ y (/ x z)) (/ y (/ z x)))

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