SynthBasics:oscSampleBasedAux from YampaSynth-0.2

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Precision: binary64

Cost: 6720

• 20.2% of points produce a very large (infinite) output. You may want to add a precondition.

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 100.0%

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

2. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]
   Step-by-step derivation

   [Start] 100.0%	\[ x + y \cdot \left(z - x\right) \]
   +-commutative [=>] 100.0%	\[ \color{blue}{y \cdot \left(z - x\right) + x} \]
   fma-def [=>] 100.0%	\[ \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]

3. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	100.0%
Cost	6720

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

Alternative 2
Accuracy	61.4%
Cost	1180

\[\begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+61}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2300000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+46}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3
Accuracy	86.4%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+62} \lor \neg \left(x \leq 2.1 \cdot 10^{+70}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 4
Accuracy	74.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -100000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Accuracy	86.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+70}:\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot x\\ \end{array} \]

Alternative 6
Accuracy	61.0%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-65}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 7
Accuracy	100.0%
Cost	448

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

Alternative 8
Accuracy	36.4%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023256 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))