SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.02% → 0.01%

Time: 5.6s

Precision: binary64

Cost: 6720

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (fma y (- z x) x))

C

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

↓

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

Julia

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.02

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

2. Simplified 0.01

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

   [Start] 0.02	\[ x + y \cdot \left(z - x\right) \]
   +-commutative [=>] 0.02	\[ \color{blue}{y \cdot \left(z - x\right) + x} \]
   fma-def [=>] 0.01	\[ \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

3. Final simplification 0.01

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

Alternatives

Alternative 1
Error	41.15%
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-106}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 120000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	27.21%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+32} \lor \neg \left(x \leq 4.3 \cdot 10^{-107}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Error	21.01%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+49} \lor \neg \left(x \leq 255000\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z - x\right)\\ \end{array} \]

Alternative 4
Error	1.55%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -34 \lor \neg \left(y \leq 2.5 \cdot 10^{-5}\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 5
Error	0.02%
Cost	576

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

Alternative 6
Error	39.99%
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 51000:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7
Error	0.02%
Cost	448

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

Alternative 8
Error	54.25%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))