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

Percentage Accurate: 88.4% → 99.7%

Time: 7.0s

Alternatives: 11

Speedup: 0.6×

• 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: 88.4% 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: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -430000 \lor \neg \left(y \leq 102000\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -430000.0) (not (<= y 102000.0)))
   (* y (- 1.0 (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -430000.0) || !(y <= 102000.0)) {
		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 <= (-430000.0d0)) .or. (.not. (y <= 102000.0d0))) 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 <= -430000.0) || !(y <= 102000.0)) {
		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 <= -430000.0) or not (y <= 102000.0):
		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 <= -430000.0) || !(y <= 102000.0))
		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 <= -430000.0) || ~((y <= 102000.0)))
		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, -430000.0], N[Not[LessEqual[y, 102000.0]], $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 < -4.3e5 or 102000 < y

   1. Initial program 76.8%

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

   3. Taylor expanded in y around inf 76.5%

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

      1. associate-/l* 99.6%

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

      2. div-sub 99.6%

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

      3. sub-neg 99.6%

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

      4. *-inverses 99.6%

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

      5. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   if -4.3e5 < y < 102000

   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 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -430000 \lor \neg \left(y \leq 102000\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{1 - y}{z}\\ t_1 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-29}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.00195:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ (- 1.0 y) z))) (t_1 (* y (- 1.0 (/ x z)))))
   (if (<= y -1.45e-6)
     t_1
     (if (<= y -1.22e-29)
       t_0
       (if (<= y -2.1e-85)
         t_1
         (if (<= y 0.00195) (/ x z) (if (<= y 12500.0) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((1.0 - y) / z);
	double t_1 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1.45e-6) {
		tmp = t_1;
	} else if (y <= -1.22e-29) {
		tmp = t_0;
	} else if (y <= -2.1e-85) {
		tmp = t_1;
	} else if (y <= 0.00195) {
		tmp = x / z;
	} else if (y <= 12500.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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 = x * ((1.0d0 - y) / z)
    t_1 = y * (1.0d0 - (x / z))
    if (y <= (-1.45d-6)) then
        tmp = t_1
    else if (y <= (-1.22d-29)) then
        tmp = t_0
    else if (y <= (-2.1d-85)) then
        tmp = t_1
    else if (y <= 0.00195d0) then
        tmp = x / z
    else if (y <= 12500.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((1.0 - y) / z);
	double t_1 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -1.45e-6) {
		tmp = t_1;
	} else if (y <= -1.22e-29) {
		tmp = t_0;
	} else if (y <= -2.1e-85) {
		tmp = t_1;
	} else if (y <= 0.00195) {
		tmp = x / z;
	} else if (y <= 12500.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((1.0 - y) / z)
	t_1 = y * (1.0 - (x / z))
	tmp = 0
	if y <= -1.45e-6:
		tmp = t_1
	elif y <= -1.22e-29:
		tmp = t_0
	elif y <= -2.1e-85:
		tmp = t_1
	elif y <= 0.00195:
		tmp = x / z
	elif y <= 12500.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(1.0 - y) / z))
	t_1 = Float64(y * Float64(1.0 - Float64(x / z)))
	tmp = 0.0
	if (y <= -1.45e-6)
		tmp = t_1;
	elseif (y <= -1.22e-29)
		tmp = t_0;
	elseif (y <= -2.1e-85)
		tmp = t_1;
	elseif (y <= 0.00195)
		tmp = Float64(x / z);
	elseif (y <= 12500.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((1.0 - y) / z);
	t_1 = y * (1.0 - (x / z));
	tmp = 0.0;
	if (y <= -1.45e-6)
		tmp = t_1;
	elseif (y <= -1.22e-29)
		tmp = t_0;
	elseif (y <= -2.1e-85)
		tmp = t_1;
	elseif (y <= 0.00195)
		tmp = x / z;
	elseif (y <= 12500.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e-6], t$95$1, If[LessEqual[y, -1.22e-29], t$95$0, If[LessEqual[y, -2.1e-85], t$95$1, If[LessEqual[y, 0.00195], N[(x / z), $MachinePrecision], If[LessEqual[y, 12500.0], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e-6 or -1.21999999999999996e-29 < y < -2.1e-85 or 12500 < y

   1. Initial program 78.3%

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

   3. Taylor expanded in y around inf 77.4%

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

      1. associate-/l* 98.9%

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

      2. div-sub 99.0%

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

      3. sub-neg 99.0%

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

      4. *-inverses 99.0%

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

      5. sub-neg 99.0%

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

   5. Simplified 99.0%

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

   if -1.4500000000000001e-6 < y < -1.21999999999999996e-29 or 0.0019499999999999999 < y < 12500

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.5%

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

      1. associate-/l* 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   if -2.1e-85 < y < 0.0019499999999999999

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.4%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-85}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 0.00195:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{-z}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+182}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+145}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y (- z)))))
   (if (<= y -5.2e+182)
     t_0
     (if (<= y -7e-6)
       y
       (if (<= y 3.9e-20)
         (/ x z)
         (if (<= y 1.6e+81) y (if (<= y 9.2e+145) t_0 (* z (/ y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / -z);
	double tmp;
	if (y <= -5.2e+182) {
		tmp = t_0;
	} else if (y <= -7e-6) {
		tmp = y;
	} else if (y <= 3.9e-20) {
		tmp = x / z;
	} else if (y <= 1.6e+81) {
		tmp = y;
	} else if (y <= 9.2e+145) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = x * (y / -z)
    if (y <= (-5.2d+182)) then
        tmp = t_0
    else if (y <= (-7d-6)) then
        tmp = y
    else if (y <= 3.9d-20) then
        tmp = x / z
    else if (y <= 1.6d+81) then
        tmp = y
    else if (y <= 9.2d+145) then
        tmp = t_0
    else
        tmp = z * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / -z);
	double tmp;
	if (y <= -5.2e+182) {
		tmp = t_0;
	} else if (y <= -7e-6) {
		tmp = y;
	} else if (y <= 3.9e-20) {
		tmp = x / z;
	} else if (y <= 1.6e+81) {
		tmp = y;
	} else if (y <= 9.2e+145) {
		tmp = t_0;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / -z)
	tmp = 0
	if y <= -5.2e+182:
		tmp = t_0
	elif y <= -7e-6:
		tmp = y
	elif y <= 3.9e-20:
		tmp = x / z
	elif y <= 1.6e+81:
		tmp = y
	elif y <= 9.2e+145:
		tmp = t_0
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / Float64(-z)))
	tmp = 0.0
	if (y <= -5.2e+182)
		tmp = t_0;
	elseif (y <= -7e-6)
		tmp = y;
	elseif (y <= 3.9e-20)
		tmp = Float64(x / z);
	elseif (y <= 1.6e+81)
		tmp = y;
	elseif (y <= 9.2e+145)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / -z);
	tmp = 0.0;
	if (y <= -5.2e+182)
		tmp = t_0;
	elseif (y <= -7e-6)
		tmp = y;
	elseif (y <= 3.9e-20)
		tmp = x / z;
	elseif (y <= 1.6e+81)
		tmp = y;
	elseif (y <= 9.2e+145)
		tmp = t_0;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / (-z)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.2e+182], t$95$0, If[LessEqual[y, -7e-6], y, If[LessEqual[y, 3.9e-20], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.6e+81], y, If[LessEqual[y, 9.2e+145], t$95$0, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.2e182 or 1.6e81 < y < 9.2e145

   1. Initial program 67.7%

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

   3. Taylor expanded in y around inf 67.7%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   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. sub-neg 99.9%

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

      4. *-inverses 99.9%

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

      5. sub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf 52.7%

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

      1. mul-1-neg 52.7%

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

      2. distribute-frac-neg2 52.7%

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

      3. associate-/l* 60.3%

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

   8. Simplified 60.3%

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

   if -5.2e182 < y < -6.99999999999999989e-6 or 3.90000000000000007e-20 < y < 1.6e81

   1. Initial program 88.8%

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

   3. Taylor expanded in x around 0 56.0%

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

   if -6.99999999999999989e-6 < y < 3.90000000000000007e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

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

   if 9.2e145 < y

   1. Initial program 67.3%

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

   3. Taylor expanded in x around 0 21.1%

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

      1. *-commutative 21.1%

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

      2. associate-/l* 69.8%

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

   5. Applied egg-rr 69.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-6}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+81}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+145}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{z} \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+163}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ x z) (- y))))
   (if (<= y -6.2e+163)
     t_0
     (if (<= y -8.2e-7)
       y
       (if (<= y 1.62e-18)
         (/ x z)
         (if (<= y 5.5e+80) y (if (<= y 4.2e+140) t_0 (* z (/ y z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x / z) * -y;
	double tmp;
	if (y <= -6.2e+163) {
		tmp = t_0;
	} else if (y <= -8.2e-7) {
		tmp = y;
	} else if (y <= 1.62e-18) {
		tmp = x / z;
	} else if (y <= 5.5e+80) {
		tmp = y;
	} else if (y <= 4.2e+140) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = (x / z) * -y
    if (y <= (-6.2d+163)) then
        tmp = t_0
    else if (y <= (-8.2d-7)) then
        tmp = y
    else if (y <= 1.62d-18) then
        tmp = x / z
    else if (y <= 5.5d+80) then
        tmp = y
    else if (y <= 4.2d+140) then
        tmp = t_0
    else
        tmp = z * (y / z)
    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 <= -6.2e+163) {
		tmp = t_0;
	} else if (y <= -8.2e-7) {
		tmp = y;
	} else if (y <= 1.62e-18) {
		tmp = x / z;
	} else if (y <= 5.5e+80) {
		tmp = y;
	} else if (y <= 4.2e+140) {
		tmp = t_0;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x / z) * -y
	tmp = 0
	if y <= -6.2e+163:
		tmp = t_0
	elif y <= -8.2e-7:
		tmp = y
	elif y <= 1.62e-18:
		tmp = x / z
	elif y <= 5.5e+80:
		tmp = y
	elif y <= 4.2e+140:
		tmp = t_0
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x / z) * Float64(-y))
	tmp = 0.0
	if (y <= -6.2e+163)
		tmp = t_0;
	elseif (y <= -8.2e-7)
		tmp = y;
	elseif (y <= 1.62e-18)
		tmp = Float64(x / z);
	elseif (y <= 5.5e+80)
		tmp = y;
	elseif (y <= 4.2e+140)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x / z) * -y;
	tmp = 0.0;
	if (y <= -6.2e+163)
		tmp = t_0;
	elseif (y <= -8.2e-7)
		tmp = y;
	elseif (y <= 1.62e-18)
		tmp = x / z;
	elseif (y <= 5.5e+80)
		tmp = y;
	elseif (y <= 4.2e+140)
		tmp = t_0;
	else
		tmp = z * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x / z), $MachinePrecision] * (-y)), $MachinePrecision]}, If[LessEqual[y, -6.2e+163], t$95$0, If[LessEqual[y, -8.2e-7], y, If[LessEqual[y, 1.62e-18], N[(x / z), $MachinePrecision], If[LessEqual[y, 5.5e+80], y, If[LessEqual[y, 4.2e+140], t$95$0, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.20000000000000057e163 or 5.49999999999999967e80 < y < 4.2000000000000004e140

   1. Initial program 74.4%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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* 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. mul-1-neg 55.3%

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

      3. *-commutative 55.3%

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

      4. distribute-frac-neg 55.3%

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

      5. associate-*r/ 62.7%

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

      6. distribute-rgt-neg-in 62.7%

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

      7. distribute-neg-frac2 62.7%

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

   8. Simplified 62.7%

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

   if -6.20000000000000057e163 < y < -8.1999999999999998e-7 or 1.62000000000000005e-18 < y < 5.49999999999999967e80

   1. Initial program 88.0%

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

   3. Taylor expanded in x around 0 57.2%

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

   if -8.1999999999999998e-7 < y < 1.62000000000000005e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

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

   if 4.2000000000000004e140 < y

   1. Initial program 61.6%

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

   3. Taylor expanded in x around 0 18.6%

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

      1. *-commutative 18.6%

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

      2. associate-/l* 67.1%

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

   5. Applied egg-rr 67.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+163}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.62 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+80}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+140}:\\ \;\;\;\;\frac{x}{z} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-111} \lor \neg \left(x \leq 5 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-111) (not (<= x 5e-81))) (* x (/ (- 1.0 y) z)) y))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-111) || !(x <= 5e-81)) {
		tmp = x * ((1.0 - y) / 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 ((x <= (-2.8d-111)) .or. (.not. (x <= 5d-81))) then
        tmp = x * ((1.0d0 - y) / z)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-111) || !(x <= 5e-81)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-111) or not (x <= 5e-81):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-111) || !(x <= 5e-81))
		tmp = Float64(x * Float64(Float64(1.0 - y) / z));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e-111) || ~((x <= 5e-81)))
		tmp = x * ((1.0 - y) / z);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-111], N[Not[LessEqual[x, 5e-81]], $MachinePrecision]], N[(x * N[(N[(1.0 - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999995e-111 or 4.99999999999999981e-81 < x

   1. Initial program 89.9%

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

   3. Taylor expanded in x around inf 74.9%

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

      1. associate-/l* 76.6%

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

      2. mul-1-neg 76.6%

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

      3. unsub-neg 76.6%

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

   5. Simplified 76.6%

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

   if -2.79999999999999995e-111 < x < 4.99999999999999981e-81

   1. Initial program 84.5%

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

   3. Taylor expanded in x around 0 78.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-111} \lor \neg \left(x \leq 5 \cdot 10^{-81}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-7} \lor \neg \left(y \leq 12500\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.6e-7) (not (<= y 12500.0)))
   (* y (- 1.0 (/ x z)))
   (/ (* x (- 1.0 y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.6e-7) || !(y <= 12500.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x * (1.0 - 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 <= (-7.6d-7)) .or. (.not. (y <= 12500.0d0))) then
        tmp = y * (1.0d0 - (x / z))
    else
        tmp = (x * (1.0d0 - y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.6e-7) || !(y <= 12500.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = (x * (1.0 - y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.6e-7) or not (y <= 12500.0):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = (x * (1.0 - y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.6e-7) || !(y <= 12500.0))
		tmp = Float64(y * Float64(1.0 - Float64(x / z)));
	else
		tmp = Float64(Float64(x * Float64(1.0 - y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.6e-7) || ~((y <= 12500.0)))
		tmp = y * (1.0 - (x / z));
	else
		tmp = (x * (1.0 - y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.6e-7], N[Not[LessEqual[y, 12500.0]], $MachinePrecision]], N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.60000000000000029e-7 or 12500 < y

   1. Initial program 77.2%

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

   3. Taylor expanded in y around inf 76.9%

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

      1. associate-/l* 99.6%

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

      2. div-sub 99.6%

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

      3. sub-neg 99.6%

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

      4. *-inverses 99.6%

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

      5. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   if -7.60000000000000029e-7 < y < 12500

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. mul-1-neg 71.5%

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

      2. unsub-neg 71.5%

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

   5. Simplified 71.5%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{-7} \lor \neg \left(y \leq 12500\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 - y\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 96.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq 76000:\\ \;\;\;\;\frac{x}{z} + t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (/ x z))))) (if (<= y 76000.0) (+ (/ x z) t_0) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= 76000.0) {
		tmp = (x / z) + t_0;
	} 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 <= 76000.0d0) then
        tmp = (x / z) + t_0
    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 <= 76000.0) {
		tmp = (x / z) + t_0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (1.0 - (x / z))
	tmp = 0
	if y <= 76000.0:
		tmp = (x / z) + t_0
	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 <= 76000.0)
		tmp = Float64(Float64(x / z) + t_0);
	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 <= 76000.0)
		tmp = (x / z) + t_0;
	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, 76000.0], N[(N[(x / z), $MachinePrecision] + t$95$0), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if y < 76000

   1. Initial program 92.7%

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

   3. Taylor expanded in y around 0 98.4%

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

   if 76000 < y

   1. Initial program 74.4%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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* 99.8%

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

      2. div-sub 99.8%

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

      3. sub-neg 99.8%

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

      4. *-inverses 99.8%

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

      5. sub-neg 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 76000:\\ \;\;\;\;\frac{x}{z} + y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-6} \lor \neg \left(y \leq 2.6 \cdot 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.4e-6) (not (<= y 2.6e-18))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-6) || !(y <= 2.6e-18)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.4d-6)) .or. (.not. (y <= 2.6d-18))) then
        tmp = z * (y / z)
    else
        tmp = x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.4e-6) || !(y <= 2.6e-18)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.4e-6) or not (y <= 2.6e-18):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.4e-6) || !(y <= 2.6e-18))
		tmp = Float64(z * Float64(y / z));
	else
		tmp = Float64(x / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.4e-6) || ~((y <= 2.6e-18)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.4e-6], N[Not[LessEqual[y, 2.6e-18]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.40000000000000006e-6 or 2.6e-18 < y

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 32.8%

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

      1. *-commutative 32.8%

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

      2. associate-/l* 51.3%

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

   5. Applied egg-rr 51.3%

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

   if -3.40000000000000006e-6 < y < 2.6e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-6} \lor \neg \left(y \leq 2.6 \cdot 10^{-18}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e-7) (* z (/ y z)) (if (<= y 1.15e-20) (/ x z) (/ z (/ z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-7) {
		tmp = z * (y / z);
	} else if (y <= 1.15e-20) {
		tmp = x / z;
	} else {
		tmp = z / (z / 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 <= (-8.5d-7)) then
        tmp = z * (y / z)
    else if (y <= 1.15d-20) then
        tmp = x / z
    else
        tmp = z / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-7) {
		tmp = z * (y / z);
	} else if (y <= 1.15e-20) {
		tmp = x / z;
	} else {
		tmp = z / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e-7:
		tmp = z * (y / z)
	elif y <= 1.15e-20:
		tmp = x / z
	else:
		tmp = z / (z / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e-7)
		tmp = Float64(z * Float64(y / z));
	elseif (y <= 1.15e-20)
		tmp = Float64(x / z);
	else
		tmp = Float64(z / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e-7)
		tmp = z * (y / z);
	elseif (y <= 1.15e-20)
		tmp = x / z;
	else
		tmp = z / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e-7], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-20], N[(x / z), $MachinePrecision], N[(z / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.50000000000000014e-7

   1. Initial program 79.8%

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

   3. Taylor expanded in x around 0 35.9%

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

      1. *-commutative 35.9%

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

      2. associate-/l* 49.6%

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

   5. Applied egg-rr 49.6%

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

   if -8.50000000000000014e-7 < y < 1.15e-20

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

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

   if 1.15e-20 < y

   1. Initial program 76.6%

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

   3. Taylor expanded in x around 0 29.8%

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

      1. *-commutative 29.8%

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

      2. associate-/l* 52.9%

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

   5. Applied egg-rr 52.9%

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

      1. clear-num 52.8%

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

      2. un-div-inv 53.2%

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

   7. Applied egg-rr 53.2%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e-7) y (if (<= y 8e-18) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-7) {
		tmp = y;
	} else if (y <= 8e-18) {
		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 <= (-8.5d-7)) then
        tmp = y
    else if (y <= 8d-18) 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 <= -8.5e-7) {
		tmp = y;
	} else if (y <= 8e-18) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e-7:
		tmp = y
	elif y <= 8e-18:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e-7)
		tmp = y;
	elseif (y <= 8e-18)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.5e-7)
		tmp = y;
	elseif (y <= 8e-18)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e-7], y, If[LessEqual[y, 8e-18], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000014e-7 or 8.0000000000000006e-18 < y

   1. Initial program 78.2%

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

   3. Taylor expanded in x around 0 48.6%

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

   if -8.50000000000000014e-7 < y < 8.0000000000000006e-18

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 70.5%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.3% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return y

Julia

function code(x, y, z)
	return y
end

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 88.2%

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

3. Taylor expanded in x around 0 39.9%

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

4. Final simplification 39.9%

   \[\leadsto y \]
5. Add Preprocessing

Developer target: 94.1% 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 2024080 
(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))