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

Average Error: 33.8 → 0.4

Time: 1.7min

Precision: binary64

Cost: 7300

Math

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

↓

\[{\left(\frac{x}{y}\right)}^{2} + \begin{array}{l} \mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (+ (pow (/ x y) 2.0) (if (!= z 0.0) (/ (/ z t) (/ t z)) (* (/ (/ 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) {
	double tmp;
	if (z != 0.0) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return pow((x / y), 2.0) + tmp;
}

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
    real(8) :: tmp
    if (z /= 0.0d0) then
        tmp = (z / t) / (t / z)
    else
        tmp = ((z / t) / t) * z
    end if
    code = ((x / y) ** 2.0d0) + tmp
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) {
	double tmp;
	if (z != 0.0) {
		tmp = (z / t) / (t / z);
	} else {
		tmp = ((z / t) / t) * z;
	}
	return Math.pow((x / y), 2.0) + tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if z != 0.0:
		tmp = (z / t) / (t / z)
	else:
		tmp = ((z / t) / t) * z
	return math.pow((x / y), 2.0) + tmp

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)
	tmp = 0.0
	if (z != 0.0)
		tmp = Float64(Float64(z / t) / Float64(t / z));
	else
		tmp = Float64(Float64(Float64(z / t) / t) * z);
	end
	return Float64((Float64(x / y) ^ 2.0) + tmp)
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z ~= 0.0)
		tmp = (z / t) / (t / z);
	else
		tmp = ((z / t) / t) * z;
	end
	tmp_2 = ((x / y) ^ 2.0) + tmp;
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[Power[N[(x / y), $MachinePrecision], 2.0], $MachinePrecision] + If[Unequal[z, 0.0], N[(N[(z / t), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z / t), $MachinePrecision] / t), $MachinePrecision] * z), $MachinePrecision]]), $MachinePrecision]

Target

Original	33.8
Target	0.4
Herbie	0.4

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

Derivation

1. Initial program 33.8

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

2. Simplified 0.4

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

3. Applied egg-rr 0.4

   \[\leadsto {\left(\frac{x}{y}\right)}^{2} + \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{z}{t}\right)}^{2}\\ } \end{array}} \]

4. Applied egg-rr 0.4

   \[\leadsto {\left(\frac{x}{y}\right)}^{2} + \begin{array}{l} \mathbf{if}\;z \ne 0:\\ \;\;\;\;\frac{\frac{z}{t}}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{z}{t}}{t} \cdot z\\ \end{array} \]

Alternatives

Alternative 1
Error	3.9
Cost	960

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

Alternative 2
Error	0.4
Cost	960

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

Reproduce

herbie shell --seed 2023033 
(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))))