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

Percentage Accurate: 88.8% → 99.8%

Time: 7.6s

Alternatives: 10

Speedup: 1.0×

• 20.0% 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: 88.8% 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: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+15} \lor \neg \left(y \leq 420000000\right):\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.15e+15) (not (<= y 420000000.0)))
   (- y (* y (/ x z)))
   (/ (+ x (* y (- z x))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.15e+15) || !(y <= 420000000.0)) {
		tmp = y - (y * (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 <= (-3.15d+15)) .or. (.not. (y <= 420000000.0d0))) then
        tmp = y - (y * (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 <= -3.15e+15) || !(y <= 420000000.0)) {
		tmp = y - (y * (x / z));
	} else {
		tmp = (x + (y * (z - x))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.15e+15) or not (y <= 420000000.0):
		tmp = y - (y * (x / z))
	else:
		tmp = (x + (y * (z - x))) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.15e+15) || !(y <= 420000000.0))
		tmp = Float64(y - Float64(y * 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 <= -3.15e+15) || ~((y <= 420000000.0)))
		tmp = y - (y * (x / z));
	else
		tmp = (x + (y * (z - x))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.15e+15], N[Not[LessEqual[y, 420000000.0]], $MachinePrecision]], N[(y - N[(y * 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 < -3.15e15 or 4.2e8 < y

   1. Initial program 77.2%

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

   2. Taylor expanded in x around inf 93.4%

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

   3. Taylor expanded in y around inf 93.4%

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

      1. associate-*r* 93.4%

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

      2. mul-1-neg 93.4%

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

   5. Simplified 93.4%

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

   6. Taylor expanded in y around 0 99.9%

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

      1. distribute-lft-in 99.9%

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

      2. mul-1-neg 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. unsub-neg 99.9%

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

      5. *-rgt-identity 99.9%

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

   8. Simplified 99.9%

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

   if -3.15e15 < y < 4.2e8

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+15} \lor \neg \left(y \leq 420000000\right):\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \left(z - x\right)}{z}\\ \end{array} \]

Alternative 2: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+242}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -2.25e-20)
     t_0
     (if (<= y 2.9e-81)
       (/ x z)
       (if (<= y 1.45e-46)
         y
         (if (<= y 7.2e-27) (/ x z) (if (<= y 2.5e+242) t_0 y)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -2.25e-20) {
		tmp = t_0;
	} else if (y <= 2.9e-81) {
		tmp = x / z;
	} else if (y <= 1.45e-46) {
		tmp = y;
	} else if (y <= 7.2e-27) {
		tmp = x / z;
	} else if (y <= 2.5e+242) {
		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 = z * (y / z)
    if (y <= (-2.25d-20)) then
        tmp = t_0
    else if (y <= 2.9d-81) then
        tmp = x / z
    else if (y <= 1.45d-46) then
        tmp = y
    else if (y <= 7.2d-27) then
        tmp = x / z
    else if (y <= 2.5d+242) 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 = z * (y / z);
	double tmp;
	if (y <= -2.25e-20) {
		tmp = t_0;
	} else if (y <= 2.9e-81) {
		tmp = x / z;
	} else if (y <= 1.45e-46) {
		tmp = y;
	} else if (y <= 7.2e-27) {
		tmp = x / z;
	} else if (y <= 2.5e+242) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -2.25e-20:
		tmp = t_0
	elif y <= 2.9e-81:
		tmp = x / z
	elif y <= 1.45e-46:
		tmp = y
	elif y <= 7.2e-27:
		tmp = x / z
	elif y <= 2.5e+242:
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -2.25e-20)
		tmp = t_0;
	elseif (y <= 2.9e-81)
		tmp = Float64(x / z);
	elseif (y <= 1.45e-46)
		tmp = y;
	elseif (y <= 7.2e-27)
		tmp = Float64(x / z);
	elseif (y <= 2.5e+242)
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -2.25e-20)
		tmp = t_0;
	elseif (y <= 2.9e-81)
		tmp = x / z;
	elseif (y <= 1.45e-46)
		tmp = y;
	elseif (y <= 7.2e-27)
		tmp = x / z;
	elseif (y <= 2.5e+242)
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.25e-20], t$95$0, If[LessEqual[y, 2.9e-81], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.45e-46], y, If[LessEqual[y, 7.2e-27], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.5e+242], t$95$0, y]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2500000000000001e-20 or 7.1999999999999997e-27 < y < 2.5000000000000002e242

   1. Initial program 82.1%

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

   2. Taylor expanded in z around inf 46.6%

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

   3. Taylor expanded in x around 0 40.6%

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

      1. *-commutative 40.6%

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

   5. Simplified 40.6%

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

      1. *-un-lft-identity 40.6%

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

      2. times-frac 58.9%

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

      3. /-rgt-identity 58.9%

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

   7. Applied egg-rr 58.9%

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

   if -2.2500000000000001e-20 < y < 2.89999999999999989e-81 or 1.45000000000000002e-46 < y < 7.1999999999999997e-27

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.0%

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

   if 2.89999999999999989e-81 < y < 1.45000000000000002e-46 or 2.5000000000000002e242 < y

   1. Initial program 80.9%

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

   2. Taylor expanded in x around 0 69.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-46}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+242}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+67} \lor \neg \left(x \leq 3.9 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.5e+67) (not (<= x 3.9e+40)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.5e+67) || !(x <= 3.9e+40)) {
		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 <= (-2.5d+67)) .or. (.not. (x <= 3.9d+40))) 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 <= -2.5e+67) || !(x <= 3.9e+40)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.5e+67) or not (x <= 3.9e+40):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.5e+67) || !(x <= 3.9e+40))
		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 <= -2.5e+67) || ~((x <= 3.9e+40)))
		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, -2.5e+67], N[Not[LessEqual[x, 3.9e+40]], $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 < -2.49999999999999988e67 or 3.9000000000000001e40 < x

   1. Initial program 91.3%

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

   2. Taylor expanded in x around inf 86.0%

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

      1. associate-/l* 87.7%

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

      2. associate-/r/ 87.7%

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

      3. mul-1-neg 87.7%

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

      4. unsub-neg 87.7%

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

   4. Simplified 87.7%

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

   if -2.49999999999999988e67 < x < 3.9000000000000001e40

   1. Initial program 88.6%

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

   2. Taylor expanded in z around inf 79.3%

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

   3. Taylor expanded in x around 0 90.6%

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

      1. +-commutative 90.6%

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

   5. Simplified 90.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+67} \lor \neg \left(x \leq 3.9 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 4: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -235000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -235000.0) (not (<= y 1.0))) (- y (* y (/ x z))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -235000.0) || !(y <= 1.0)) {
		tmp = y - (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 <= (-235000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y - (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 <= -235000.0) || !(y <= 1.0)) {
		tmp = y - (y * (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -235000.0) or not (y <= 1.0):
		tmp = y - (y * (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -235000.0) || !(y <= 1.0))
		tmp = Float64(y - 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 <= -235000.0) || ~((y <= 1.0)))
		tmp = y - (y * (x / z));
	else
		tmp = y + (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -235000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y - N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -235000 or 1 < y

   1. Initial program 78.0%

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

   2. Taylor expanded in x around inf 93.6%

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

   3. Taylor expanded in y around inf 92.8%

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

      1. associate-*r* 92.8%

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

      2. mul-1-neg 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in y around 0 99.1%

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

      1. distribute-lft-in 99.2%

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

      2. mul-1-neg 99.2%

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

      3. distribute-rgt-neg-in 99.2%

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

      4. unsub-neg 99.2%

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

      5. *-rgt-identity 99.2%

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

   8. Simplified 99.2%

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

   if -235000 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 99.7%

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

   3. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

   5. Simplified 99.7%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -235000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y - y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 5: 81.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 40000000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 40000000000.0)
   (+ y (/ x z))
   (if (<= y 2.6e+50) (* x (/ (- y) z)) (- y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 40000000000.0) {
		tmp = y + (x / z);
	} else if (y <= 2.6e+50) {
		tmp = x * (-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 <= 40000000000.0d0) then
        tmp = y + (x / z)
    else if (y <= 2.6d+50) then
        tmp = x * (-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 <= 40000000000.0) {
		tmp = y + (x / z);
	} else if (y <= 2.6e+50) {
		tmp = x * (-y / z);
	} else {
		tmp = y - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 40000000000.0:
		tmp = y + (x / z)
	elif y <= 2.6e+50:
		tmp = x * (-y / z)
	else:
		tmp = y - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 40000000000.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 2.6e+50)
		tmp = Float64(x * Float64(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 <= 40000000000.0)
		tmp = y + (x / z);
	elseif (y <= 2.6e+50)
		tmp = x * (-y / z);
	else
		tmp = y - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 40000000000.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+50], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 4e10

   1. Initial program 94.4%

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

   2. Taylor expanded in z around inf 85.3%

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

   3. Taylor expanded in x around 0 90.9%

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

      1. +-commutative 90.9%

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

   5. Simplified 90.9%

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

   if 4e10 < y < 2.6000000000000002e50

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-/l* 78.2%

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

      2. associate-/r/ 78.4%

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

      3. mul-1-neg 78.4%

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

      4. unsub-neg 78.4%

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

   4. Simplified 78.4%

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

   5. Taylor expanded in y around inf 78.4%

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

      1. neg-mul-1 78.4%

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

      2. distribute-neg-frac 78.4%

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

   7. Simplified 78.4%

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

   if 2.6000000000000002e50 < y

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 37.6%

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

   3. Taylor expanded in x around 0 60.4%

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

      1. +-commutative 60.4%

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

   5. Simplified 60.4%

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

      1. +-commutative 60.4%

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

      2. add-cube-cbrt 59.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} + \frac{x}{z} \]

      3. fma-def 59.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \frac{x}{z}\right)} \]

      4. frac-2neg 59.1%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \color{blue}{\frac{-x}{-z}}\right) \]

      5. distribute-frac-neg 59.1%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \color{blue}{-\frac{x}{-z}}\right) \]

      6. add-sqr-sqrt 27.3%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}\right) \]

      7. sqrt-unprod 61.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}\right) \]

      8. sqr-neg 61.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\sqrt{\color{blue}{z \cdot z}}}\right) \]

      9. sqrt-unprod 34.4%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}\right) \]

      10. add-sqr-sqrt 65.5%

          \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{z}}\right) \]

      11. fma-neg 65.5%

          \[\leadsto \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y} - \frac{x}{z}} \]

      12. add-cube-cbrt 66.8%

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

   7. Applied egg-rr 66.8%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 40000000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;y - \frac{x}{z}\\ \end{array} \]

Alternative 6: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.7%

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

2. Taylor expanded in x around inf 97.0%

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

3. Final simplification 97.0%

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

Alternative 7: 59.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-22) y (if (<= y 2.8e-81) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-22) {
		tmp = y;
	} else if (y <= 2.8e-81) {
		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 <= (-3.8d-22)) then
        tmp = y
    else if (y <= 2.8d-81) 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 <= -3.8e-22) {
		tmp = y;
	} else if (y <= 2.8e-81) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e-22:
		tmp = y
	elif y <= 2.8e-81:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-22)
		tmp = y;
	elseif (y <= 2.8e-81)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-22)
		tmp = y;
	elseif (y <= 2.8e-81)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e-22], y, If[LessEqual[y, 2.8e-81], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000023e-22 or 2.7999999999999999e-81 < y

   1. Initial program 82.7%

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

   2. Taylor expanded in x around 0 57.4%

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

   if -3.80000000000000023e-22 < y < 2.7999999999999999e-81

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 80.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 81.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < 1

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 85.6%

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

   3. Taylor expanded in x around 0 91.3%

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

      1. +-commutative 91.3%

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

   5. Simplified 91.3%

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

   if 1 < y

   1. Initial program 78.0%

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

   2. Taylor expanded in z around inf 35.6%

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

   3. Taylor expanded in x around 0 53.8%

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

      1. +-commutative 53.8%

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

   5. Simplified 53.8%

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

      1. +-commutative 53.8%

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

      2. add-cube-cbrt 52.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} + \frac{x}{z} \]

      3. fma-def 52.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \frac{x}{z}\right)} \]

      4. frac-2neg 52.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \color{blue}{\frac{-x}{-z}}\right) \]

      5. distribute-frac-neg 52.6%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, \color{blue}{-\frac{x}{-z}}\right) \]

      6. add-sqr-sqrt 25.8%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}\right) \]

      7. sqrt-unprod 56.5%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}\right) \]

      8. sqr-neg 56.5%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\sqrt{\color{blue}{z \cdot z}}}\right) \]

      9. sqrt-unprod 31.0%

         \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}\right) \]

      10. add-sqr-sqrt 60.1%

          \[\leadsto \mathsf{fma}\left(\sqrt[3]{y} \cdot \sqrt[3]{y}, \sqrt[3]{y}, -\frac{x}{\color{blue}{z}}\right) \]

      11. fma-neg 60.1%

          \[\leadsto \color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y} - \frac{x}{z}} \]

      12. add-cube-cbrt 61.2%

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

   7. Applied egg-rr 61.2%

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

4. Final simplification 82.7%

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

Alternative 9: 78.3% 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 89.7%

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

2. Taylor expanded in z around inf 71.4%

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

3. Taylor expanded in x around 0 80.6%

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

   1. +-commutative 80.6%

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

5. Simplified 80.6%

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

6. Final simplification 80.6%

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

Alternative 10: 40.7% 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 89.7%

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

2. Taylor expanded in x around 0 43.2%

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

3. Final simplification 43.2%

   \[\leadsto y \]

Developer target: 94.5% 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 2023185 
(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))