Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1

Average Error: 33.1 → 0.4

Time: 10.4s

Precision: binary64

Cost: 960

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

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

↓

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

Java

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	33.1
Target	0.4
Herbie	0.4

\[{\left(\frac{x}{y}\right)}^{2} + {\left(\frac{z}{t}\right)}^{2} \]

Derivation

1. Initial program 33.1

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

2. Applied egg-rr 22.2

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

3. Applied egg-rr 4.5

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

4. Applied egg-rr 0.4

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

5. Final simplification 0.4

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

Alternatives

Alternative 1
Error	12.2
Cost	1996

\[\begin{array}{l} t_1 := \frac{z \cdot z}{t \cdot t}\\ t_2 := \frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{-310}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \end{array} \]

Alternative 2
Error	21.1
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{z}{t}}{\frac{t}{z}}\\ t_2 := \frac{x \cdot \frac{x}{y}}{y}\\ \mathbf{if}\;z \leq -9.555140259937095 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.0813613197454507 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.0118626641646008 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.52893545966354 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	21.0
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{if}\;z \leq -9.555140259937095 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.25811124578396 \cdot 10^{-160}:\\ \;\;\;\;\frac{x}{y \cdot \frac{y}{x}}\\ \mathbf{elif}\;z \leq -1.0118626641646008 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.52893545966354 \cdot 10^{-107}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	19.2
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{z}{t}}{\frac{t}{z}}\\ t_2 := \frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{if}\;z \leq -9.555140259937095 \cdot 10^{-89}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \mathbf{elif}\;z \leq -3.25811124578396 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.0118626641646008 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.52893545966354 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	26.2
Cost	448

\[\frac{z}{t} \cdot \frac{z}{t} \]

Alternative 6
Error	26.1
Cost	448

\[\frac{\frac{z}{t}}{\frac{t}{z}} \]

Reproduce

herbie shell --seed 2022300 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

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