Average Error: 0.0 → 0.0
Time: 5.2s
Precision: binary64
Cost: 6720
\[x + y \cdot \left(z - x\right) \]
↓
\[\mathsf{fma}\left(y, z - x, x\right) \]
(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))
↓
(FPCore (x y z) :precision binary64 (fma y (- z x) x))
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);
}

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

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]

x + y \cdot \left(z - x\right)
↓
\mathsf{fma}\left(y, z - x, x\right)

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, z - x, x\right)} \]
    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 simplification0.0

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

Alternatives

Alternative 1
Error23.8
Cost1312
\[\begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+155}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.42 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-33}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+172}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 2
Error12.5
Cost848
\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error12.5
Cost848
\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -8.2 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 0.0132:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 4
Error23.9
Cost720
\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-33}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 5
Error0.0
Cost704
\[x + y \cdot \left(x + \left(z - \left(x + x\right)\right)\right) \]
Alternative 6
Error0.9
Cost585
\[\begin{array}{l} \mathbf{if}\;y \leq -31500 \lor \neg \left(y \leq 0.015\right):\\ \;\;\;\;y \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
Alternative 7
Error0.0
Cost448
\[x + y \cdot \left(z - x\right) \]
Alternative 8
Error34.7
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022354 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))