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

Average Accuracy: 47.7% → 99.3%

Time: 53.8s

Precision: binary64

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (pow (hypot (/ z t) (/ x y)) 2.0))

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 pow(hypot((z / t), (x / y)), 2.0);
}

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 Math.pow(Math.hypot((z / t), (x / y)), 2.0);
}

Python

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

↓

def code(x, y, z, t):
	return math.pow(math.hypot((z / t), (x / y)), 2.0)

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 hypot(Float64(z / t), Float64(x / y)) ^ 2.0
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 = hypot((z / t), (x / y)) ^ 2.0;
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[Power[N[Sqrt[N[(z / t), $MachinePrecision] ^ 2 + N[(x / y), $MachinePrecision] ^ 2], $MachinePrecision], 2.0], $MachinePrecision]

Target

Original	47.7%
Target	99.3%
Herbie	99.3%

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

Derivation

1. Initial program 47.7%

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

2. Simplified 99.3%

   \[\leadsto \color{blue}{{\left(\mathsf{hypot}\left(\frac{z}{t}, \frac{x}{y}\right)\right)}^{2}} \]
   Proof

Reproduce

herbie shell --seed 2023151 
(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))))