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

Percentage Accurate: 87.9% → 99.9%

Time: 8.4s

Alternatives: 9

Speedup: 1.0×

• 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: 87.9% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.3%

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

3. Taylor expanded in x around -inf 95.9%

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

   1. mul-1-neg 95.9%

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

   2. unsub-neg 95.9%

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

   3. associate-/l* 95.6%

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

   4. associate-/r/ 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

5. Simplified 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 76.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{\frac{-z}{x}}\\ t_1 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 220:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ y (/ (- z) x))) (t_1 (+ y (/ x z))))
   (if (<= y -6.8e+174)
     t_0
     (if (<= y -2.5e+46)
       t_1
       (if (<= y -2.9e+20)
         t_0
         (if (<= y 220.0)
           t_1
           (if (<= y 2e+106)
             t_0
             (if (<= y 1.04e+136)
               (/ z (/ z y))
               (if (<= y 1.85e+195) t_0 y)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y / (-z / x);
	double t_1 = y + (x / z);
	double tmp;
	if (y <= -6.8e+174) {
		tmp = t_0;
	} else if (y <= -2.5e+46) {
		tmp = t_1;
	} else if (y <= -2.9e+20) {
		tmp = t_0;
	} else if (y <= 220.0) {
		tmp = t_1;
	} else if (y <= 2e+106) {
		tmp = t_0;
	} else if (y <= 1.04e+136) {
		tmp = z / (z / y);
	} else if (y <= 1.85e+195) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / (-z / x)
    t_1 = y + (x / z)
    if (y <= (-6.8d+174)) then
        tmp = t_0
    else if (y <= (-2.5d+46)) then
        tmp = t_1
    else if (y <= (-2.9d+20)) then
        tmp = t_0
    else if (y <= 220.0d0) then
        tmp = t_1
    else if (y <= 2d+106) then
        tmp = t_0
    else if (y <= 1.04d+136) then
        tmp = z / (z / y)
    else if (y <= 1.85d+195) then
        tmp = t_0
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y / (-z / x);
	double t_1 = y + (x / z);
	double tmp;
	if (y <= -6.8e+174) {
		tmp = t_0;
	} else if (y <= -2.5e+46) {
		tmp = t_1;
	} else if (y <= -2.9e+20) {
		tmp = t_0;
	} else if (y <= 220.0) {
		tmp = t_1;
	} else if (y <= 2e+106) {
		tmp = t_0;
	} else if (y <= 1.04e+136) {
		tmp = z / (z / y);
	} else if (y <= 1.85e+195) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y / (-z / x)
	t_1 = y + (x / z)
	tmp = 0
	if y <= -6.8e+174:
		tmp = t_0
	elif y <= -2.5e+46:
		tmp = t_1
	elif y <= -2.9e+20:
		tmp = t_0
	elif y <= 220.0:
		tmp = t_1
	elif y <= 2e+106:
		tmp = t_0
	elif y <= 1.04e+136:
		tmp = z / (z / y)
	elif y <= 1.85e+195:
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y / Float64(Float64(-z) / x))
	t_1 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -6.8e+174)
		tmp = t_0;
	elseif (y <= -2.5e+46)
		tmp = t_1;
	elseif (y <= -2.9e+20)
		tmp = t_0;
	elseif (y <= 220.0)
		tmp = t_1;
	elseif (y <= 2e+106)
		tmp = t_0;
	elseif (y <= 1.04e+136)
		tmp = Float64(z / Float64(z / y));
	elseif (y <= 1.85e+195)
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y / (-z / x);
	t_1 = y + (x / z);
	tmp = 0.0;
	if (y <= -6.8e+174)
		tmp = t_0;
	elseif (y <= -2.5e+46)
		tmp = t_1;
	elseif (y <= -2.9e+20)
		tmp = t_0;
	elseif (y <= 220.0)
		tmp = t_1;
	elseif (y <= 2e+106)
		tmp = t_0;
	elseif (y <= 1.04e+136)
		tmp = z / (z / y);
	elseif (y <= 1.85e+195)
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y / N[((-z) / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+174], t$95$0, If[LessEqual[y, -2.5e+46], t$95$1, If[LessEqual[y, -2.9e+20], t$95$0, If[LessEqual[y, 220.0], t$95$1, If[LessEqual[y, 2e+106], t$95$0, If[LessEqual[y, 1.04e+136], N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+195], t$95$0, y]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.8000000000000002e174 or -2.5000000000000001e46 < y < -2.9e20 or 220 < y < 2.00000000000000018e106 or 1.04e136 < y < 1.85e195

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 84.1%

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

      1. associate-/l* 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in z around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. neg-mul-1 76.7%

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

   8. Simplified 76.7%

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

   if -6.8000000000000002e174 < y < -2.5000000000000001e46 or -2.9e20 < y < 220

   1. Initial program 96.1%

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

   3. Taylor expanded in x around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. associate-/l* 98.7%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 96.4%

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

      1. mul-1-neg 96.4%

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

      2. distribute-frac-neg 96.4%

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

   8. Simplified 96.4%

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

   9. Taylor expanded in y around 0 96.4%

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

       1. +-commutative 96.4%

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

   11. Simplified 96.4%

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

   if 2.00000000000000018e106 < y < 1.04e136

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 63.7%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 76.0%

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

   5. Applied egg-rr 76.0%

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

      1. *-commutative 76.0%

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

      2. clear-num 75.9%

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

      3. un-div-inv 84.0%

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

   7. Applied egg-rr 84.0%

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

   if 1.85e195 < y

   1. Initial program 54.2%

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

   3. Taylor expanded in x around 0 62.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq 220:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+195}:\\ \;\;\;\;\frac{y}{\frac{-z}{x}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 170:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+195}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) (/ z y))))
   (if (<= y -3.5e+174)
     t_0
     (if (<= y 170.0)
       (+ y (/ x z))
       (if (<= y 2.4e+106)
         t_0
         (if (<= y 1.08e+136) (/ z (/ z y)) (if (<= y 6e+195) t_0 y)))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / (z / y);
	double tmp;
	if (y <= -3.5e+174) {
		tmp = t_0;
	} else if (y <= 170.0) {
		tmp = y + (x / z);
	} else if (y <= 2.4e+106) {
		tmp = t_0;
	} else if (y <= 1.08e+136) {
		tmp = z / (z / y);
	} else if (y <= 6e+195) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = -x / (z / y)
    if (y <= (-3.5d+174)) then
        tmp = t_0
    else if (y <= 170.0d0) then
        tmp = y + (x / z)
    else if (y <= 2.4d+106) then
        tmp = t_0
    else if (y <= 1.08d+136) then
        tmp = z / (z / y)
    else if (y <= 6d+195) then
        tmp = t_0
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / (z / y);
	double tmp;
	if (y <= -3.5e+174) {
		tmp = t_0;
	} else if (y <= 170.0) {
		tmp = y + (x / z);
	} else if (y <= 2.4e+106) {
		tmp = t_0;
	} else if (y <= 1.08e+136) {
		tmp = z / (z / y);
	} else if (y <= 6e+195) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / (z / y)
	tmp = 0
	if y <= -3.5e+174:
		tmp = t_0
	elif y <= 170.0:
		tmp = y + (x / z)
	elif y <= 2.4e+106:
		tmp = t_0
	elif y <= 1.08e+136:
		tmp = z / (z / y)
	elif y <= 6e+195:
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / Float64(z / y))
	tmp = 0.0
	if (y <= -3.5e+174)
		tmp = t_0;
	elseif (y <= 170.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 2.4e+106)
		tmp = t_0;
	elseif (y <= 1.08e+136)
		tmp = Float64(z / Float64(z / y));
	elseif (y <= 6e+195)
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / (z / y);
	tmp = 0.0;
	if (y <= -3.5e+174)
		tmp = t_0;
	elseif (y <= 170.0)
		tmp = y + (x / z);
	elseif (y <= 2.4e+106)
		tmp = t_0;
	elseif (y <= 1.08e+136)
		tmp = z / (z / y);
	elseif (y <= 6e+195)
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+174], t$95$0, If[LessEqual[y, 170.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+106], t$95$0, If[LessEqual[y, 1.08e+136], N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+195], t$95$0, y]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.5000000000000001e174 or 170 < y < 2.4000000000000001e106 or 1.07999999999999994e136 < y < 6.0000000000000001e195

   1. Initial program 83.9%

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

   3. Taylor expanded in y around inf 81.8%

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

      1. associate-/l* 97.7%

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

   5. Simplified 97.7%

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

   6. Taylor expanded in z around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. associate-/l* 69.2%

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

   8. Simplified 69.2%

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

   if -3.5000000000000001e174 < y < 170

   1. Initial program 96.3%

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

   3. Taylor expanded in x around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. associate-/l* 98.2%

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

      4. associate-/r/ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 92.6%

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

      1. mul-1-neg 92.6%

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

      2. distribute-frac-neg 92.6%

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

   8. Simplified 92.6%

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

   9. Taylor expanded in y around 0 92.6%

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

       1. +-commutative 92.6%

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

   11. Simplified 92.6%

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

   if 2.4000000000000001e106 < y < 1.07999999999999994e136

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0 63.7%

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

      1. associate-/l* 76.1%

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

      2. associate-/r/ 76.0%

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

   5. Applied egg-rr 76.0%

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

      1. *-commutative 76.0%

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

      2. clear-num 75.9%

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

      3. un-div-inv 84.0%

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

   7. Applied egg-rr 84.0%

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

   if 6.0000000000000001e195 < y

   1. Initial program 54.2%

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

   3. Taylor expanded in x around 0 62.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+174}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 170:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+195}:\\ \;\;\;\;\frac{-x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.00023)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.00023)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 0.00023d0))) 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 <= -1.0) || !(y <= 0.00023)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.00023):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.00023))
		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 <= -1.0) || ~((y <= 0.00023)))
		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, -1.0], N[Not[LessEqual[y, 0.00023]], $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 or 2.3000000000000001e-4 < y

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 78.4%

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

      1. associate-/l* 98.9%

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

   5. Simplified 98.9%

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

      1. clear-num 98.7%

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

      2. associate-/r/ 98.8%

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

      3. clear-num 98.8%

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

      4. div-sub 98.8%

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

      5. *-inverses 98.8%

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

   7. Applied egg-rr 98.8%

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

   if -1 < y < 2.3000000000000001e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-frac-neg 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in y around 0 99.3%

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

       1. +-commutative 99.3%

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

   11. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.00023\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{elif}\;y \leq 0.00023:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0)
   (/ y (/ z (- z x)))
   (if (<= y 0.00023) (+ y (/ x z)) (* y (- 1.0 (/ x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = y / (z / (z - x));
	} else if (y <= 0.00023) {
		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 <= (-1.0d0)) then
        tmp = y / (z / (z - x))
    else if (y <= 0.00023d0) 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 <= -1.0) {
		tmp = y / (z / (z - x));
	} else if (y <= 0.00023) {
		tmp = y + (x / z);
	} else {
		tmp = y * (1.0 - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = y / (z / (z - x))
	elif y <= 0.00023:
		tmp = y + (x / z)
	else:
		tmp = y * (1.0 - (x / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(y / Float64(z / Float64(z - x)));
	elseif (y <= 0.00023)
		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 <= -1.0)
		tmp = y / (z / (z - x));
	elseif (y <= 0.00023)
		tmp = y + (x / z);
	else
		tmp = y * (1.0 - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00023], 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 < -1

   1. Initial program 83.1%

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

   3. Taylor expanded in y around inf 83.1%

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

      1. associate-/l* 99.9%

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

   5. Simplified 99.9%

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

   if -1 < y < 2.3000000000000001e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in x around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. associate-/l* 100.0%

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

      4. associate-/r/ 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. distribute-frac-neg 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in y around 0 99.3%

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

       1. +-commutative 99.3%

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

   11. Simplified 99.3%

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

   if 2.3000000000000001e-4 < y

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. associate-/l* 97.9%

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

   5. Simplified 97.9%

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

      1. clear-num 97.7%

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

      2. associate-/r/ 97.9%

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

      3. clear-num 98.0%

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

      4. div-sub 98.0%

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

      5. *-inverses 98.0%

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

   7. Applied egg-rr 98.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\frac{y}{\frac{z}{z - x}}\\ \mathbf{elif}\;y \leq 0.00023:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-103) y (if (<= y 3.8e-11) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-103) {
		tmp = y;
	} else if (y <= 3.8e-11) {
		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 <= (-4d-103)) then
        tmp = y
    else if (y <= 3.8d-11) 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 <= -4e-103) {
		tmp = y;
	} else if (y <= 3.8e-11) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e-103:
		tmp = y
	elif y <= 3.8e-11:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-103)
		tmp = y;
	elseif (y <= 3.8e-11)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e-103)
		tmp = y;
	elseif (y <= 3.8e-11)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e-103], y, If[LessEqual[y, 3.8e-11], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999983e-103 or 3.7999999999999998e-11 < y

   1. Initial program 81.7%

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

   3. Taylor expanded in x around 0 44.5%

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

   if -3.99999999999999983e-103 < y < 3.7999999999999998e-11

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 78.5%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-103}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.6e-34) (* z (/ y z)) (if (<= y 3.6e-9) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.6e-34) {
		tmp = z * (y / z);
	} else if (y <= 3.6e-9) {
		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 <= (-8.6d-34)) then
        tmp = z * (y / z)
    else if (y <= 3.6d-9) 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 <= -8.6e-34) {
		tmp = z * (y / z);
	} else if (y <= 3.6e-9) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.6e-34:
		tmp = z * (y / z)
	elif y <= 3.6e-9:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.6e-34)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 3.6e-9)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.6e-34)
		tmp = z * (y / z);
	elseif (y <= 3.6e-9)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.6e-34], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-9], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5999999999999999e-34

   1. Initial program 84.8%

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

   3. Taylor expanded in x around 0 33.7%

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

      1. associate-/l* 46.1%

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

      2. associate-/r/ 58.1%

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

   5. Applied egg-rr 58.1%

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

   if -8.5999999999999999e-34 < y < 3.6e-9

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.6%

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

   if 3.6e-9 < y

   1. Initial program 76.2%

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

   3. Taylor expanded in x around 0 41.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-34}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.9e+147) (* z (/ y z)) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.9e+147) {
		tmp = z * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.9d+147)) then
        tmp = z * (y / z)
    else
        tmp = y + (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.9e+147) {
		tmp = z * (y / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.9e+147:
		tmp = z * (y / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.9e+147)
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(y + Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.9e+147)
		tmp = z * (y / z);
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.9e+147], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.9000000000000001e147

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 18.7%

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

      1. associate-/l* 34.3%

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

      2. associate-/r/ 55.5%

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

   5. Applied egg-rr 55.5%

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

   if -5.9000000000000001e147 < y

   1. Initial program 90.7%

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

   3. Taylor expanded in x around -inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

      3. associate-/l* 97.5%

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

      4. associate-/r/ 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. distribute-frac-neg 77.0%

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

   8. Simplified 77.0%

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

   9. Taylor expanded in y around 0 77.0%

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

       1. +-commutative 77.0%

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

   11. Simplified 77.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+147}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.1% 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 89.3%

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

3. Taylor expanded in x around 0 36.1%

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

4. Final simplification 36.1%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024029 
(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))