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

Average Error: 33.8 → 0.3

Time: 12.1s

Precision: binary64

Cost: 960

Math

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

↓

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

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

Target

Original	33.8
Target	0.4
Herbie	0.3

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

Derivation

1. Initial program 33.8

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

2. Applied egg-rr 22.3

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

3. Applied egg-rr 4.3

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

4. Applied egg-rr 0.4

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

5. Applied egg-rr 0.3

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

6. Final simplification 0.3

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

Alternatives

Alternative 1
Error	21.0
Cost	2008

\[\begin{array}{l} t_1 := \frac{\frac{z \cdot z}{t}}{t}\\ t_2 := \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 100000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{\frac{z}{t}}}\\ \end{array} \]

Alternative 2
Error	20.8
Cost	2008

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{x}{y}\\ t_2 := \frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 10^{-112}:\\ \;\;\;\;\frac{\frac{z \cdot z}{t}}{t}\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 100000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+284}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{\frac{z}{t}}}\\ \end{array} \]

Alternative 3
Error	20.2
Cost	1748

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{x}{y}\\ \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 10^{-112}:\\ \;\;\;\;\frac{\frac{z \cdot z}{t}}{t}\\ \mathbf{elif}\;z \cdot z \leq 4 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot z \leq 100000000000:\\ \;\;\;\;\frac{z \cdot \frac{z}{t}}{t}\\ \mathbf{elif}\;z \cdot z \leq 5 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{z}{t}\\ \end{array} \]

Alternative 4
Error	25.9
Cost	1504

\[\begin{array}{l} t_1 := \frac{z}{\frac{t}{\frac{z}{t}}}\\ t_2 := \frac{x \cdot \frac{x}{y}}{y}\\ \mathbf{if}\;t \leq -1.4248214323341543 \cdot 10^{+212}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.054514293863566 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.211966111000501 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8602931252697267 \cdot 10^{+161}:\\ \;\;\;\;\frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	26.0
Cost	1504

\[\begin{array}{l} t_1 := \frac{z}{\frac{t}{\frac{z}{t}}}\\ t_2 := \frac{x \cdot \frac{x}{y}}{y}\\ t_3 := \frac{x}{\frac{y}{\frac{x}{y}}}\\ \mathbf{if}\;t \leq -1.4248214323341543 \cdot 10^{+212}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.054514293863566 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.211966111000501 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.8602931252697267 \cdot 10^{+161}:\\ \;\;\;\;\frac{z}{t \cdot \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	29.8
Cost	448

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

Alternative 7
Error	29.8
Cost	448

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

Reproduce

herbie shell --seed 2022228 
(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))))