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

Average Accuracy: 99.9% → 99.9%

Time: 10.8s

Precision: binary64

Cost: 19584

Math

\[\left(x + \cos y\right) - z \cdot \sin y \]

↓

\[\mathsf{fma}\left(\sin y, -z, x + \cos y\right) \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ x (cos y)) (* z (sin y))))

↓

(FPCore (x y z) :precision binary64 (fma (sin y) (- z) (+ x (cos y))))

C

double code(double x, double y, double z) {
	return (x + cos(y)) - (z * sin(y));
}

↓

double code(double x, double y, double z) {
	return fma(sin(y), -z, (x + cos(y)));
}

Julia

function code(x, y, z)
	return Float64(Float64(x + cos(y)) - Float64(z * sin(y)))
end

↓

function code(x, y, z)
	return fma(sin(y), Float64(-z), Float64(x + cos(y)))
end

Wolfram

code[x_, y_, z_] := N[(N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(z * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[Sin[y], $MachinePrecision] * (-z) + N[(x + N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[\left(x + \cos y\right) - z \cdot \sin y \]

2. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, -z, x + \cos y\right)} \]
   Proof

   [Start] 99.9	\[ \left(x + \cos y\right) - z \cdot \sin y \]
   cancel-sign-sub-inv [=>] 99.9	\[ \color{blue}{\left(x + \cos y\right) + \left(-z\right) \cdot \sin y} \]
   +-commutative [=>] 99.9	\[ \color{blue}{\left(-z\right) \cdot \sin y + \left(x + \cos y\right)} \]
   *-commutative [=>] 99.9	\[ \color{blue}{\sin y \cdot \left(-z\right)} + \left(x + \cos y\right) \]
   fma-def [=>] 99.9	\[ \color{blue}{\mathsf{fma}\left(\sin y, -z, x + \cos y\right)} \]

3. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\sin y, -z, x + \cos y\right) \]

Alternatives

Alternative 1
Accuracy	90.0%
Cost	13384

\[\begin{array}{l} \mathbf{if}\;x \leq -60000000:\\ \;\;\;\;x + \cos y\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;\cos y - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	99.9%
Cost	13248

\[\left(x + \cos y\right) - \sin y \cdot z \]

Alternative 3
Accuracy	68.1%
Cost	6992

\[\begin{array}{l} \mathbf{if}\;y \leq -28:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+47}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+114}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+152}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\cos y\\ \end{array} \]

Alternative 4
Accuracy	82.7%
Cost	6921

\[\begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+113} \lor \neg \left(z \leq 7.2 \cdot 10^{+152}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5
Accuracy	80.9%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -0.115 \lor \neg \left(y \leq 1.15 \cdot 10^{-20}\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 6
Accuracy	70.4%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -3300 \lor \neg \left(y \leq 7.3 \cdot 10^{+37}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) + y \cdot \left(y \cdot -0.5 - z\right)\\ \end{array} \]

Alternative 7
Accuracy	70.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -28:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+45}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 8
Accuracy	66.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-99}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-37}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9
Accuracy	63.0%
Cost	388

\[\begin{array}{l} \mathbf{if}\;z \leq 5.5 \cdot 10^{+233}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 10
Accuracy	61.4%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.9:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11
Accuracy	62.5%
Cost	192

\[x + 1 \]

Alternative 12
Accuracy	22.0%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023140 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))