Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A

Average Error: 15.6 → 0.3

Time: 10.1s

Precision: binary64

Math

\[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]

↓

\[\begin{array}{l} t_0 := \sin \left(x \cdot 0.5\right)\\ \frac{t_0}{\frac{1}{\frac{2.6666666666666665}{\frac{\sin x}{t_0}}}} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))

↓

(FPCore (x)
 :precision binary64
 (let* ((t_0 (sin (* x 0.5))))
   (/ t_0 (/ 1.0 (/ 2.6666666666666665 (/ (sin x) t_0))))))

C

double code(double x) {
	return (((8.0 / 3.0) * sin((x * 0.5))) * sin((x * 0.5))) / sin(x);
}

↓

double code(double x) {
	double t_0 = sin((x * 0.5));
	return t_0 / (1.0 / (2.6666666666666665 / (sin(x) / t_0)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((8.0d0 / 3.0d0) * sin((x * 0.5d0))) * sin((x * 0.5d0))) / sin(x)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    t_0 = sin((x * 0.5d0))
    code = t_0 / (1.0d0 / (2.6666666666666665d0 / (sin(x) / t_0)))
end function

Java

public static double code(double x) {
	return (((8.0 / 3.0) * Math.sin((x * 0.5))) * Math.sin((x * 0.5))) / Math.sin(x);
}

↓

public static double code(double x) {
	double t_0 = Math.sin((x * 0.5));
	return t_0 / (1.0 / (2.6666666666666665 / (Math.sin(x) / t_0)));
}

Python

def code(x):
	return (((8.0 / 3.0) * math.sin((x * 0.5))) * math.sin((x * 0.5))) / math.sin(x)

↓

def code(x):
	t_0 = math.sin((x * 0.5))
	return t_0 / (1.0 / (2.6666666666666665 / (math.sin(x) / t_0)))

Julia

function code(x)
	return Float64(Float64(Float64(Float64(8.0 / 3.0) * sin(Float64(x * 0.5))) * sin(Float64(x * 0.5))) / sin(x))
end

↓

function code(x)
	t_0 = sin(Float64(x * 0.5))
	return Float64(t_0 / Float64(1.0 / Float64(2.6666666666666665 / Float64(sin(x) / t_0))))
end

MATLAB

function tmp = code(x)
	tmp = (((8.0 / 3.0) * sin((x * 0.5))) * sin((x * 0.5))) / sin(x);
end

↓

function tmp = code(x)
	t_0 = sin((x * 0.5));
	tmp = t_0 / (1.0 / (2.6666666666666665 / (sin(x) / t_0)));
end

Wolfram

code[x_] := N[(N[(N[(N[(8.0 / 3.0), $MachinePrecision] * N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Sin[x], $MachinePrecision]), $MachinePrecision]

↓

code[x_] := Block[{t$95$0 = N[Sin[N[(x * 0.5), $MachinePrecision]], $MachinePrecision]}, N[(t$95$0 / N[(1.0 / N[(2.6666666666666665 / N[(N[Sin[x], $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Error

Bits error versus x

Target

Original	15.6
Target	0.3
Herbie	0.3

\[\frac{\frac{8 \cdot \sin \left(x \cdot 0.5\right)}{3}}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}} \]

Derivation

1. Initial program 15.6

   \[\frac{\left(\frac{8}{3} \cdot \sin \left(x \cdot 0.5\right)\right) \cdot \sin \left(x \cdot 0.5\right)}{\sin x} \]

2. Simplified 15.6

   \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right) \cdot \left(2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)\right)}{\sin x}} \]

3. Applied associate-/l*_binary64 0.5

   \[\leadsto \color{blue}{\frac{\sin \left(x \cdot 0.5\right)}{\frac{\sin x}{2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)}}} \]

4. Applied clear-num_binary64 0.4

   \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\color{blue}{\frac{1}{\frac{2.6666666666666665 \cdot \sin \left(x \cdot 0.5\right)}{\sin x}}}} \]

5. Simplified 0.3

   \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{1}{\color{blue}{\frac{2.6666666666666665}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}}} \]

6. Final simplification 0.3

   \[\leadsto \frac{\sin \left(x \cdot 0.5\right)}{\frac{1}{\frac{2.6666666666666665}{\frac{\sin x}{\sin \left(x \cdot 0.5\right)}}}} \]

Reproduce

herbie shell --seed 2022131 
(FPCore (x)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, A"
  :precision binary64

  :herbie-target
  (/ (/ (* 8.0 (sin (* x 0.5))) 3.0) (/ (sin x) (sin (* x 0.5))))

  (/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x)))