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

Average Error: 33.7 → 0.4

Time: 24.4s

Precision: binary64

Cost: 960

Math

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

↓

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

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

Target

Original	33.7
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 33.7

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

2. Simplified 0.4

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

   [Start] 33.7	\[ \frac{x \cdot x}{y \cdot y} + \frac{z \cdot z}{t \cdot t} \]
   rational.json-simplify-46 [=>] 29.6	\[ \color{blue}{\frac{\frac{x \cdot x}{y}}{y}} + \frac{z \cdot z}{t \cdot t} \]
   rational.json-simplify-49 [=>] 22.4	\[ \frac{\color{blue}{x \cdot \frac{x}{y}}}{y} + \frac{z \cdot z}{t \cdot t} \]
   rational.json-simplify-49 [=>] 19.2	\[ \color{blue}{\frac{x}{y} \cdot \frac{x}{y}} + \frac{z \cdot z}{t \cdot t} \]
   rational.json-simplify-46 [=>] 13.6	\[ \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\frac{\frac{z \cdot z}{t}}{t}} \]
   rational.json-simplify-49 [=>] 4.6	\[ \frac{x}{y} \cdot \frac{x}{y} + \frac{\color{blue}{z \cdot \frac{z}{t}}}{t} \]
   rational.json-simplify-49 [=>] 0.4	\[ \frac{x}{y} \cdot \frac{x}{y} + \color{blue}{\frac{z}{t} \cdot \frac{z}{t}} \]

3. Final simplification 0.4

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

Alternatives

Alternative 1
Error	29.6
Cost	960

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

Alternative 2
Error	16.6
Cost	960

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

Alternative 3
Error	7.8
Cost	960

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

Alternative 4
Error	7.8
Cost	960

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

Alternative 5
Error	4.1
Cost	960

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

Reproduce

herbie shell --seed 2023064 
(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))))