SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Average Error: 0.0 → 0.0

Time: 7.2s

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 0.0

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

2. Simplified 0.0

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

   [Start] 0.0	\[ x + y \cdot \left(z - x\right) \]
   +-commutative [=>] 0.0	\[ \color{blue}{y \cdot \left(z - x\right) + x} \]
   fma-def [=>] 0.0	\[ \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	24.2
Cost	984

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -65000000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 2
Error	13.0
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	12.6
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.0056:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	24.1
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-197}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-165}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -135000 \lor \neg \left(y \leq 0.0126\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

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

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))