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

Percentage Accurate: 88.1% → 99.9%

Time: 8.5s

Alternatives: 9

Speedup: 1.0×

• 21.3% 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: 88.1% 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

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

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(1.0 - y) * Float64(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[(1.0 - y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in x around 0 95.1%

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

   1. +-commutative 95.1%

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

   2. mul-1-neg 95.1%

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

   3. unsub-neg 95.1%

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

5. Applied egg-rr 95.1%

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

6. Taylor expanded in z around 0 94.1%

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

   1. *-commutative 94.1%

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

   2. associate-*r/ 99.9%

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

8. Simplified 99.9%

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

Alternative 2: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{-z}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+164}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x (- z)))))
   (if (<= y -4.5e+83)
     t_0
     (if (<= y 900000000.0)
       (+ y (/ x z))
       (if (<= y 3.2e+164) t_0 (* z (/ y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / -z);
	double tmp;
	if (y <= -4.5e+83) {
		tmp = t_0;
	} else if (y <= 900000000.0) {
		tmp = y + (x / z);
	} else if (y <= 3.2e+164) {
		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 = y * (x / -z)
    if (y <= (-4.5d+83)) then
        tmp = t_0
    else if (y <= 900000000.0d0) then
        tmp = y + (x / z)
    else if (y <= 3.2d+164) 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 = y * (x / -z);
	double tmp;
	if (y <= -4.5e+83) {
		tmp = t_0;
	} else if (y <= 900000000.0) {
		tmp = y + (x / z);
	} else if (y <= 3.2e+164) {
		tmp = t_0;
	} else {
		tmp = z * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / -z)
	tmp = 0
	if y <= -4.5e+83:
		tmp = t_0
	elif y <= 900000000.0:
		tmp = y + (x / z)
	elif y <= 3.2e+164:
		tmp = t_0
	else:
		tmp = z * (y / z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / Float64(-z)))
	tmp = 0.0
	if (y <= -4.5e+83)
		tmp = t_0;
	elseif (y <= 900000000.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 3.2e+164)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / -z);
	tmp = 0.0;
	if (y <= -4.5e+83)
		tmp = t_0;
	elseif (y <= 900000000.0)
		tmp = y + (x / z);
	elseif (y <= 3.2e+164)
		tmp = t_0;
	else
		tmp = z * (y / 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, -4.5e+83], t$95$0, If[LessEqual[y, 900000000.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+164], t$95$0, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999999e83 or 9e8 < y < 3.1999999999999998e164

   1. Initial program 83.0%

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

   3. Taylor expanded in y around inf 83.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - x\right)}{z}} \]
   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. *-inverses 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x around inf 68.3%

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

      1. mul-1-neg 68.3%

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

      2. distribute-frac-neg2 68.3%

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

   8. Simplified 68.3%

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

   if -4.4999999999999999e83 < y < 9e8

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 93.5%

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

   4. Taylor expanded in x around 0 94.2%

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

      1. +-commutative 94.2%

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

   6. Simplified 94.2%

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

   if 3.1999999999999998e164 < y

   1. Initial program 49.3%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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* 71.8%

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

   5. Applied egg-rr 71.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{elif}\;y \leq 900000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+164}:\\ \;\;\;\;y \cdot \frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{-z}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+84}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1700000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+164}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y (- z)))))
   (if (<= y -8.5e+84)
     t_0
     (if (<= y 1700000000.0)
       (+ y (/ x z))
       (if (<= y 3e+164) t_0 (* z (/ y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / -z);
	double tmp;
	if (y <= -8.5e+84) {
		tmp = t_0;
	} else if (y <= 1700000000.0) {
		tmp = y + (x / z);
	} else if (y <= 3e+164) {
		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 <= (-8.5d+84)) then
        tmp = t_0
    else if (y <= 1700000000.0d0) then
        tmp = y + (x / z)
    else if (y <= 3d+164) 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 <= -8.5e+84) {
		tmp = t_0;
	} else if (y <= 1700000000.0) {
		tmp = y + (x / z);
	} else if (y <= 3e+164) {
		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 <= -8.5e+84:
		tmp = t_0
	elif y <= 1700000000.0:
		tmp = y + (x / z)
	elif y <= 3e+164:
		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 <= -8.5e+84)
		tmp = t_0;
	elseif (y <= 1700000000.0)
		tmp = Float64(y + Float64(x / z));
	elseif (y <= 3e+164)
		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 <= -8.5e+84)
		tmp = t_0;
	elseif (y <= 1700000000.0)
		tmp = y + (x / z);
	elseif (y <= 3e+164)
		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, -8.5e+84], t$95$0, If[LessEqual[y, 1700000000.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+164], t$95$0, N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000008e84 or 1.7e9 < y < 3.00000000000000001e164

   1. Initial program 83.0%

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

   3. Taylor expanded in x around inf 60.0%

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

      1. associate-/l* 59.0%

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

      2. mul-1-neg 59.0%

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

      3. unsub-neg 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in y around inf 59.0%

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

      1. neg-mul-1 59.0%

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

   8. Simplified 59.0%

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

   if -8.5000000000000008e84 < y < 1.7e9

   1. Initial program 99.2%

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

   3. Taylor expanded in z around inf 93.5%

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

   4. Taylor expanded in x around 0 94.2%

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

      1. +-commutative 94.2%

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

   6. Simplified 94.2%

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

   if 3.00000000000000001e164 < y

   1. Initial program 49.3%

      \[\frac{x + y \cdot \left(z - x\right)}{z} \]
   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* 71.8%

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

   5. Applied egg-rr 71.8%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 1700000000:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+164}:\\ \;\;\;\;x \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -50 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -50.0) (not (<= y 1.0))) (* y (- 1.0 (/ x z))) (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -50.0) || !(y <= 1.0)) {
		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 <= (-50.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -50.0) || !(y <= 1.0)) {
		tmp = y * (1.0 - (x / z));
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -50.0) or not (y <= 1.0):
		tmp = y * (1.0 - (x / z))
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -50.0) || !(y <= 1.0))
		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 <= -50.0) || ~((y <= 1.0)))
		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, -50.0], N[Not[LessEqual[y, 1.0]], $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 < -50 or 1 < y

   1. Initial program 79.5%

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

   3. Taylor expanded in y around inf 78.1%

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

      1. associate-/l* 98.4%

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

      2. div-sub 98.4%

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

      3. *-inverses 98.4%

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

   5. Simplified 98.4%

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

   if -50 < y < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.3%

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

   4. Taylor expanded in x around 0 99.3%

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

      1. +-commutative 99.3%

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

   6. Simplified 99.3%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+25} \lor \neg \left(x \leq 2.9 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.6e+25) (not (<= x 2.9e+144)))
   (* x (/ (- 1.0 y) z))
   (+ y (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.6e+25) || !(x <= 2.9e+144)) {
		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 <= (-5.6d+25)) .or. (.not. (x <= 2.9d+144))) 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 <= -5.6e+25) || !(x <= 2.9e+144)) {
		tmp = x * ((1.0 - y) / z);
	} else {
		tmp = y + (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.6e+25) or not (x <= 2.9e+144):
		tmp = x * ((1.0 - y) / z)
	else:
		tmp = y + (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.6e+25) || !(x <= 2.9e+144))
		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 <= -5.6e+25) || ~((x <= 2.9e+144)))
		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, -5.6e+25], N[Not[LessEqual[x, 2.9e+144]], $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 < -5.6000000000000003e25 or 2.89999999999999998e144 < x

   1. Initial program 85.0%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. associate-/l* 89.9%

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

      2. mul-1-neg 89.9%

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

      3. unsub-neg 89.9%

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

   5. Simplified 89.9%

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

   if -5.6000000000000003e25 < x < 2.89999999999999998e144

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf 75.1%

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

   4. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

   6. Simplified 82.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+25} \lor \neg \left(x \leq 2.9 \cdot 10^{+144}\right):\\ \;\;\;\;x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-7} \lor \neg \left(y \leq 0.00033\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-7) (not (<= y 0.00033))) (* z (/ y z)) (/ x z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-7) || !(y <= 0.00033)) {
		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 <= (-1.8d-7)) .or. (.not. (y <= 0.00033d0))) 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 <= -1.8e-7) || !(y <= 0.00033)) {
		tmp = z * (y / z);
	} else {
		tmp = x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-7) or not (y <= 0.00033):
		tmp = z * (y / z)
	else:
		tmp = x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-7) || !(y <= 0.00033))
		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 <= -1.8e-7) || ~((y <= 0.00033)))
		tmp = z * (y / z);
	else
		tmp = x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-7], N[Not[LessEqual[y, 0.00033]], $MachinePrecision]], N[(z * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999997e-7 or 3.3e-4 < y

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 31.6%

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

      1. *-commutative 31.6%

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

      2. associate-/l* 49.9%

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

   5. Applied egg-rr 49.9%

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

   if -1.79999999999999997e-7 < y < 3.3e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-7} \lor \neg \left(y \leq 0.00033\right):\\ \;\;\;\;z \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 0.00033:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-7) y (if (<= y 0.00033) (/ x z) y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-7) {
		tmp = y;
	} else if (y <= 0.00033) {
		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 <= (-1.4d-7)) then
        tmp = y
    else if (y <= 0.00033d0) 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 <= -1.4e-7) {
		tmp = y;
	} else if (y <= 0.00033) {
		tmp = x / z;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-7:
		tmp = y
	elif y <= 0.00033:
		tmp = x / z
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-7)
		tmp = y;
	elseif (y <= 0.00033)
		tmp = Float64(x / z);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-7)
		tmp = y;
	elseif (y <= 0.00033)
		tmp = x / z;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-7], y, If[LessEqual[y, 0.00033], N[(x / z), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-7 or 3.3e-4 < y

   1. Initial program 79.7%

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

   3. Taylor expanded in x around 0 46.0%

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

   if -1.4000000000000001e-7 < y < 3.3e-4

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.7%

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

Alternative 8: 77.4% 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 89.6%

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

3. Taylor expanded in z around inf 66.5%

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

4. Taylor expanded in x around 0 73.9%

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

   1. +-commutative 73.9%

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

6. Simplified 73.9%

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

7. Final simplification 73.9%

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

Alternative 9: 40.1% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

Derivation

1. Initial program 89.6%

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

3. Taylor expanded in x around 0 35.4%

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

Developer Target 1: 93.9% 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 2024131 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (/ x z)) (/ y (/ z x))))

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