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

Average Error: 10.6 → 0.8

Time: 5.3s

Precision: binary64

Cost: 712

Math

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

↓

\[\begin{array}{l} t_0 := y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{if}\;y \leq -19383.412398030163:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7229580673675116 \cdot 10^{-6}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (- 1.0 (/ x z)))))
   (if (<= y -19383.412398030163)
     t_0
     (if (<= y 1.7229580673675116e-6) (+ y (/ x z)) t_0))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -19383.412398030163) {
		tmp = t_0;
	} else if (y <= 1.7229580673675116e-6) {
		tmp = y + (x / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (1.0d0 - (x / z))
    if (y <= (-19383.412398030163d0)) then
        tmp = t_0
    else if (y <= 1.7229580673675116d-6) then
        tmp = y + (x / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = y * (1.0 - (x / z));
	double tmp;
	if (y <= -19383.412398030163) {
		tmp = t_0;
	} else if (y <= 1.7229580673675116e-6) {
		tmp = y + (x / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = y * (1.0 - (x / z))
	tmp = 0
	if y <= -19383.412398030163:
		tmp = t_0
	elif y <= 1.7229580673675116e-6:
		tmp = y + (x / z)
	else:
		tmp = t_0
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(y * Float64(1.0 - Float64(x / z)))
	tmp = 0.0
	if (y <= -19383.412398030163)
		tmp = t_0;
	elseif (y <= 1.7229580673675116e-6)
		tmp = Float64(y + Float64(x / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = y * (1.0 - (x / z));
	tmp = 0.0;
	if (y <= -19383.412398030163)
		tmp = t_0;
	elseif (y <= 1.7229580673675116e-6)
		tmp = y + (x / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(1.0 - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -19383.412398030163], t$95$0, If[LessEqual[y, 1.7229580673675116e-6], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Target

Original	10.6
Target	0.0
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if y < -19383.4123980301629 or 1.7229580673675116e-6 < y

   1. Initial program 23.2

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

   2. Taylor expanded in y around 0 0.1

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

   3. Taylor expanded in y around inf 1.0

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

   if -19383.4123980301629 < y < 1.7229580673675116e-6

   1. Initial program 0.1

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

   2. Taylor expanded in x around 0 0.2

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

   3. Taylor expanded in y around 0 0.6

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19383.412398030163:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \mathbf{elif}\;y \leq 1.7229580673675116 \cdot 10^{-6}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \frac{x}{z}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	4.2
Cost	712

\[\begin{array}{l} t_0 := \frac{y}{z} \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -19383.412398030163:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.7229580673675116 \cdot 10^{-6}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	9.9
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq 2.282677092856716 \cdot 10^{+41}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;\frac{y \cdot \left(-x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3
Error	9.7
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq 2.282677092856716 \cdot 10^{+41}:\\ \;\;\;\;y + \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+106}:\\ \;\;\;\;y \cdot \frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4
Error	19.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3814539032587573 \cdot 10^{-83}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.4635196732403896 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 5
Error	8.9
Cost	320

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

Alternative 6
Error	31.3
Cost	64

\[y \]

Reproduce

herbie shell --seed 2022228 
(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))