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

Average Accuracy: 99.9% → 99.9%

Time: 11.1s

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	99.9%
Cost	13248

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

Alternative 2
Accuracy	99.4%
Cost	7113

\[\begin{array}{l} \mathbf{if}\;z \leq -246000 \lor \neg \left(z \leq 7.4 \cdot 10^{-6}\right):\\ \;\;\;\;\left(x + 1\right) - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 3
Accuracy	70.7%
Cost	6992

\[\begin{array}{l} \mathbf{if}\;x \leq -0.017:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-278}:\\ \;\;\;\;\cos y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-254}:\\ \;\;\;\;1 - y \cdot z\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-6}:\\ \;\;\;\;\cos y\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 4
Accuracy	84.8%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+106} \lor \neg \left(z \leq 4.9 \cdot 10^{+126}\right):\\ \;\;\;\;1 - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 5
Accuracy	93.4%
Cost	6985

\[\begin{array}{l} \mathbf{if}\;z \leq -15500000000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+18}\right):\\ \;\;\;\;x - \sin y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 6
Accuracy	82.0%
Cost	6921

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+107} \lor \neg \left(z \leq 2.6 \cdot 10^{+175}\right):\\ \;\;\;\;\sin y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \cos y\\ \end{array} \]

Alternative 7
Accuracy	80.4%
Cost	6857

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \lor \neg \left(y \leq 14500\right):\\ \;\;\;\;x + \cos y\\ \mathbf{else}:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \end{array} \]

Alternative 8
Accuracy	69.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -260:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;y \leq 39000:\\ \;\;\;\;1 + \left(x - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 9
Accuracy	65.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-6} \lor \neg \left(x \leq 2 \cdot 10^{-96}\right):\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;1 - y \cdot z\\ \end{array} \]

Alternative 10
Accuracy	60.4%
Cost	520

\[\begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-279}:\\ \;\;\;\;x + 1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-304}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 1\\ \end{array} \]

Alternative 11
Accuracy	60.1%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -0.8:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.0006:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12
Accuracy	60.8%
Cost	192

\[x + 1 \]

Alternative 13
Accuracy	21.7%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023133 
(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))))