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

Percentage Accurate: 87.7% → 99.9%

Time: 5.7s

Alternatives: 8

Speedup: 1.0×

• 20.4% 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: 87.7% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.3%

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

2. Taylor expanded in x around -inf 94.0%

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

   1. mul-1-neg 94.0%

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

   2. unsub-neg 94.0%

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

   3. associate-/l* 96.3%

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

   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%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ t_1 := -y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.16 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))) (t_1 (- (* y (/ x z)))))
   (if (<= y -1.16e+109)
     t_0
     (if (<= y -1.45e+57)
       t_1
       (if (<= y -6.2e-62)
         y
         (if (<= y 5e-15) (/ x z) (if (<= y 4e+203) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double t_1 = -(y * (x / z));
	double tmp;
	if (y <= -1.16e+109) {
		tmp = t_0;
	} else if (y <= -1.45e+57) {
		tmp = t_1;
	} else if (y <= -6.2e-62) {
		tmp = y;
	} else if (y <= 5e-15) {
		tmp = x / z;
	} else if (y <= 4e+203) {
		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 = z * (y / z)
    t_1 = -(y * (x / z))
    if (y <= (-1.16d+109)) then
        tmp = t_0
    else if (y <= (-1.45d+57)) then
        tmp = t_1
    else if (y <= (-6.2d-62)) then
        tmp = y
    else if (y <= 5d-15) then
        tmp = x / z
    else if (y <= 4d+203) 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 = z * (y / z);
	double t_1 = -(y * (x / z));
	double tmp;
	if (y <= -1.16e+109) {
		tmp = t_0;
	} else if (y <= -1.45e+57) {
		tmp = t_1;
	} else if (y <= -6.2e-62) {
		tmp = y;
	} else if (y <= 5e-15) {
		tmp = x / z;
	} else if (y <= 4e+203) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	t_1 = -(y * (x / z))
	tmp = 0
	if y <= -1.16e+109:
		tmp = t_0
	elif y <= -1.45e+57:
		tmp = t_1
	elif y <= -6.2e-62:
		tmp = y
	elif y <= 5e-15:
		tmp = x / z
	elif y <= 4e+203:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	t_1 = Float64(-Float64(y * Float64(x / z)))
	tmp = 0.0
	if (y <= -1.16e+109)
		tmp = t_0;
	elseif (y <= -1.45e+57)
		tmp = t_1;
	elseif (y <= -6.2e-62)
		tmp = y;
	elseif (y <= 5e-15)
		tmp = Float64(x / z);
	elseif (y <= 4e+203)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	t_1 = -(y * (x / z));
	tmp = 0.0;
	if (y <= -1.16e+109)
		tmp = t_0;
	elseif (y <= -1.45e+57)
		tmp = t_1;
	elseif (y <= -6.2e-62)
		tmp = y;
	elseif (y <= 5e-15)
		tmp = x / z;
	elseif (y <= 4e+203)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[y, -1.16e+109], t$95$0, If[LessEqual[y, -1.45e+57], t$95$1, If[LessEqual[y, -6.2e-62], y, If[LessEqual[y, 5e-15], N[(x / z), $MachinePrecision], If[LessEqual[y, 4e+203], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.16000000000000003e109 or 4.99999999999999999e-15 < y < 4e203

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 70.0%

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

   3. Taylor expanded in z around inf 38.2%

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

      1. associate-/l* 61.6%

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

      2. associate-/r/ 67.5%

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

   5. Applied egg-rr 67.5%

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

   if -1.16000000000000003e109 < y < -1.4500000000000001e57 or 4e203 < y

   1. Initial program 92.4%

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

   2. Taylor expanded in x around inf 77.2%

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

      1. associate-/l* 77.3%

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

      2. associate-/r/ 80.7%

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

      3. mul-1-neg 80.7%

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

      4. unsub-neg 80.7%

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

   4. Simplified 80.7%

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

   5. Taylor expanded in y around inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-*r/ 77.2%

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

      3. *-commutative 77.2%

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

      4. distribute-rgt-neg-out 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around 0 77.2%

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

      1. associate-*l/ 80.7%

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

      2. associate-*r* 80.7%

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

      3. neg-mul-1 80.7%

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

      4. *-commutative 80.7%

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

      5. distribute-neg-frac 80.7%

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

   10. Simplified 80.7%

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

   if -1.4500000000000001e57 < y < -6.1999999999999999e-62

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 71.6%

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

   if -6.1999999999999999e-62 < y < 4.99999999999999999e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+57}:\\ \;\;\;\;-y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;-y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 3: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+110}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+200}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (/ y z))))
   (if (<= y -2.35e+110)
     t_0
     (if (<= y -2.4e+60)
       (* x (/ (- y) z))
       (if (<= y -6e-62)
         y
         (if (<= y 6e-15)
           (/ x z)
           (if (<= y 8.5e+200) t_0 (* y (/ (- x) z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -2.35e+110) {
		tmp = t_0;
	} else if (y <= -2.4e+60) {
		tmp = x * (-y / z);
	} else if (y <= -6e-62) {
		tmp = y;
	} else if (y <= 6e-15) {
		tmp = x / z;
	} else if (y <= 8.5e+200) {
		tmp = t_0;
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (y / z)
    if (y <= (-2.35d+110)) then
        tmp = t_0
    else if (y <= (-2.4d+60)) then
        tmp = x * (-y / z)
    else if (y <= (-6d-62)) then
        tmp = y
    else if (y <= 6d-15) then
        tmp = x / z
    else if (y <= 8.5d+200) then
        tmp = t_0
    else
        tmp = y * (-x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y / z);
	double tmp;
	if (y <= -2.35e+110) {
		tmp = t_0;
	} else if (y <= -2.4e+60) {
		tmp = x * (-y / z);
	} else if (y <= -6e-62) {
		tmp = y;
	} else if (y <= 6e-15) {
		tmp = x / z;
	} else if (y <= 8.5e+200) {
		tmp = t_0;
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y / z)
	tmp = 0
	if y <= -2.35e+110:
		tmp = t_0
	elif y <= -2.4e+60:
		tmp = x * (-y / z)
	elif y <= -6e-62:
		tmp = y
	elif y <= 6e-15:
		tmp = x / z
	elif y <= 8.5e+200:
		tmp = t_0
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y / z))
	tmp = 0.0
	if (y <= -2.35e+110)
		tmp = t_0;
	elseif (y <= -2.4e+60)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (y <= -6e-62)
		tmp = y;
	elseif (y <= 6e-15)
		tmp = Float64(x / z);
	elseif (y <= 8.5e+200)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(Float64(-x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y / z);
	tmp = 0.0;
	if (y <= -2.35e+110)
		tmp = t_0;
	elseif (y <= -2.4e+60)
		tmp = x * (-y / z);
	elseif (y <= -6e-62)
		tmp = y;
	elseif (y <= 6e-15)
		tmp = x / z;
	elseif (y <= 8.5e+200)
		tmp = t_0;
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.35e+110], t$95$0, If[LessEqual[y, -2.4e+60], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-62], y, If[LessEqual[y, 6e-15], N[(x / z), $MachinePrecision], If[LessEqual[y, 8.5e+200], t$95$0, N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.3499999999999999e110 or 6e-15 < y < 8.5e200

   1. Initial program 70.7%

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

   2. Taylor expanded in y around inf 70.0%

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

   3. Taylor expanded in z around inf 38.2%

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

      1. associate-/l* 61.6%

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

      2. associate-/r/ 67.5%

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

   5. Applied egg-rr 67.5%

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

   if -2.3499999999999999e110 < y < -2.4e60

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf 74.2%

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

      1. associate-/l* 82.4%

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

      2. associate-/r/ 82.2%

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

      3. mul-1-neg 82.2%

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

      4. unsub-neg 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. associate-*r/ 82.2%

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

      3. *-commutative 82.2%

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

      4. distribute-rgt-neg-out 82.2%

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

   7. Simplified 82.2%

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

   if -2.4e60 < y < -6.0000000000000002e-62

   1. Initial program 96.0%

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

   2. Taylor expanded in x around 0 71.6%

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

   if -6.0000000000000002e-62 < y < 6e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.0%

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

   if 8.5e200 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.5%

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

      1. associate-/l* 73.3%

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

      2. associate-/r/ 79.5%

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

      3. mul-1-neg 79.5%

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

      4. unsub-neg 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in y around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-*r/ 73.3%

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

      3. *-commutative 73.3%

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

      4. distribute-rgt-neg-out 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in y around 0 79.5%

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

      1. associate-*l/ 79.5%

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

      2. associate-*r* 79.5%

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

      3. neg-mul-1 79.5%

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

      4. *-commutative 79.5%

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

      5. distribute-neg-frac 79.5%

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

   10. Simplified 79.5%

       \[\leadsto \color{blue}{y \cdot \frac{-x}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-62}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+200}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]

Alternative 4: 77.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \frac{x}{z}\\ \mathbf{if}\;y \leq -1.78 \cdot 10^{+106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+202}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ y (/ x z))))
   (if (<= y -1.78e+106)
     t_0
     (if (<= y -1.75e+59)
       (* x (/ (- y) z))
       (if (<= y 8.5e+202) t_0 (* y (/ (- x) z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -1.78e+106) {
		tmp = t_0;
	} else if (y <= -1.75e+59) {
		tmp = x * (-y / z);
	} else if (y <= 8.5e+202) {
		tmp = t_0;
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y + (x / z)
    if (y <= (-1.78d+106)) then
        tmp = t_0
    else if (y <= (-1.75d+59)) then
        tmp = x * (-y / z)
    else if (y <= 8.5d+202) then
        tmp = t_0
    else
        tmp = y * (-x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x / z);
	double tmp;
	if (y <= -1.78e+106) {
		tmp = t_0;
	} else if (y <= -1.75e+59) {
		tmp = x * (-y / z);
	} else if (y <= 8.5e+202) {
		tmp = t_0;
	} else {
		tmp = y * (-x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x / z)
	tmp = 0
	if y <= -1.78e+106:
		tmp = t_0
	elif y <= -1.75e+59:
		tmp = x * (-y / z)
	elif y <= 8.5e+202:
		tmp = t_0
	else:
		tmp = y * (-x / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x / z))
	tmp = 0.0
	if (y <= -1.78e+106)
		tmp = t_0;
	elseif (y <= -1.75e+59)
		tmp = Float64(x * Float64(Float64(-y) / z));
	elseif (y <= 8.5e+202)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(Float64(-x) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x / z);
	tmp = 0.0;
	if (y <= -1.78e+106)
		tmp = t_0;
	elseif (y <= -1.75e+59)
		tmp = x * (-y / z);
	elseif (y <= 8.5e+202)
		tmp = t_0;
	else
		tmp = y * (-x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.78e+106], t$95$0, If[LessEqual[y, -1.75e+59], N[(x * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+202], t$95$0, N[(y * N[((-x) / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.77999999999999995e106 or -1.75e59 < y < 8.5000000000000003e202

   1. Initial program 87.8%

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

   2. Taylor expanded in x around -inf 93.8%

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

      1. mul-1-neg 93.8%

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

      2. unsub-neg 93.8%

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

      3. associate-/l* 96.6%

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

      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%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 85.9%

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

      1. mul-1-neg 85.9%

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

      2. distribute-frac-neg 85.9%

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

   7. Simplified 85.9%

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

   if -1.77999999999999995e106 < y < -1.75e59

   1. Initial program 82.8%

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

   2. Taylor expanded in x around inf 74.2%

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

      1. associate-/l* 82.4%

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

      2. associate-/r/ 82.2%

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

      3. mul-1-neg 82.2%

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

      4. unsub-neg 82.2%

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

   4. Simplified 82.2%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. mul-1-neg 74.2%

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

      2. associate-*r/ 82.2%

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

      3. *-commutative 82.2%

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

      4. distribute-rgt-neg-out 82.2%

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

   7. Simplified 82.2%

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

   if 8.5000000000000003e202 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.5%

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

      1. associate-/l* 73.3%

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

      2. associate-/r/ 79.5%

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

      3. mul-1-neg 79.5%

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

      4. unsub-neg 79.5%

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

   4. Simplified 79.5%

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

   5. Taylor expanded in y around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-*r/ 73.3%

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

      3. *-commutative 73.3%

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

      4. distribute-rgt-neg-out 73.3%

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

   7. Simplified 73.3%

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

   8. Taylor expanded in y around 0 79.5%

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

      1. associate-*l/ 79.5%

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

      2. associate-*r* 79.5%

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

      3. neg-mul-1 79.5%

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

      4. *-commutative 79.5%

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

      5. distribute-neg-frac 79.5%

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

   10. Simplified 79.5%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.78 \cdot 10^{+106}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+202}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \end{array} \]

Alternative 5: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+30) (not (<= y 2.15e-13)))
   (* y (- 1.0 (/ x z)))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+30) || !(y <= 2.15e-13)) {
		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 <= (-5.5d+30)) .or. (.not. (y <= 2.15d-13))) 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 <= -5.5e+30) || !(y <= 2.15e-13)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+30) or not (y <= 2.15e-13):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+30) || !(y <= 2.15e-13))
		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 <= -5.5e+30) || ~((y <= 2.15e-13)))
		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, -5.5e+30], N[Not[LessEqual[y, 2.15e-13]], $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 < -5.50000000000000025e30 or 2.1499999999999999e-13 < y

   1. Initial program 75.9%

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

   2. Taylor expanded in x around -inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

      3. associate-/l* 92.3%

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

      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%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in y around inf 99.4%

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

   if -5.50000000000000025e30 < y < 2.1499999999999999e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in x around -inf 100.0%

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

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. distribute-frac-neg 98.9%

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

   7. Simplified 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+30} \lor \neg \left(y \leq 2.15 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]

Alternative 6: 63.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-62} \lor \neg \left(y \leq 1.25 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e-62) (not (<= y 1.25e-13))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-62) || !(y <= 1.25e-13)) {
		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 <= (-5d-62)) .or. (.not. (y <= 1.25d-13))) 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 <= -5e-62) || !(y <= 1.25e-13)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e-62) or not (y <= 1.25e-13):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e-62) || !(y <= 1.25e-13))
		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 <= -5e-62) || ~((y <= 1.25e-13)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e-62], N[Not[LessEqual[y, 1.25e-13]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e-62 or 1.24999999999999997e-13 < y

   1. Initial program 79.1%

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

   2. Taylor expanded in y around inf 76.2%

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

   3. Taylor expanded in z around inf 40.2%

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

      1. associate-/l* 56.0%

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

      2. associate-/r/ 59.1%

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

   5. Applied egg-rr 59.1%

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

   if -5.0000000000000002e-62 < y < 1.24999999999999997e-13

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-62} \lor \neg \left(y \leq 1.25 \cdot 10^{-13}\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 7: 60.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-64}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e-64) y (if (<= y 6.5e-15) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e-64) {
		tmp = y;
	} else if (y <= 6.5e-15) {
		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 <= (-7d-64)) then
        tmp = y
    else if (y <= 6.5d-15) 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 <= -7e-64) {
		tmp = y;
	} else if (y <= 6.5e-15) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7e-64:
		tmp = y
	elif y <= 6.5e-15:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e-64)
		tmp = y;
	elseif (y <= 6.5e-15)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7e-64)
		tmp = y;
	elseif (y <= 6.5e-15)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e-64], y, If[LessEqual[y, 6.5e-15], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000006e-64 or 6.49999999999999991e-15 < y

   1. Initial program 79.1%

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

   2. Taylor expanded in x around 0 56.0%

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

   if -7.0000000000000006e-64 < y < 6.49999999999999991e-15

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-64}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 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 88.3%

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

2. Taylor expanded in x around 0 42.8%

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

3. Final simplification 42.8%

   \[\leadsto y \]

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 2023332 
(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))