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

Average Error: 34.0 → 0.4

Time: 15.3s

Precision: binary64

Cost: 960

Math

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

↓

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

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) (/ x y)) (/ (/ z t) (/ t z))))

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

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

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

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(x / y)) + Float64(Float64(z / t) / Float64(t / z)))
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) * (x / y)) + ((z / t) / (t / z));
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[(x / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	34.0
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 34.0

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

2. Applied egg-rr 22.2

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

3. Applied egg-rr 4.6

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

4. Applied egg-rr 0.4

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

5. Final simplification 0.4

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

Alternatives

Alternative 1
Error	25.4
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{x}{\frac{y}{x}}}{y}\\ t_2 := \frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4100138135650045 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.2315823615469305 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.156033065017556 \cdot 10^{-240}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.303344355932839 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.374243096629574 \cdot 10^{-152}:\\ \;\;\;\;\frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{elif}\;x \leq 3.2497284217347205 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.052:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	22.8
Cost	1228

\[\begin{array}{l} t_1 := \frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{if}\;t \cdot t \leq 2 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t \cdot t \leq 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \cdot t \leq 10^{+131}:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.1
Cost	1228

\[\begin{array}{l} t_1 := \frac{\frac{x}{y}}{\frac{y}{x}}\\ \mathbf{if}\;t \cdot t \leq 2 \cdot 10^{-65}:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{elif}\;t \cdot t \leq 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \cdot t \leq 10^{+131}:\\ \;\;\;\;z \cdot \frac{z}{t \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	28.6
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{z \cdot z}{t}}{t}\\ t_2 := \frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7681698806191666 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+151}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	23.9
Cost	712

\[\begin{array}{l} t_1 := \frac{\frac{x}{\frac{y}{x}}}{y}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.599925610717672 \cdot 10^{+81}:\\ \;\;\;\;\frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	30.6
Cost	448

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

Reproduce

herbie shell --seed 2022291 
(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))))