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
    (fma.f64 y (-.f64 z x) x): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (-.f64 z x)) x)): 2 points increase in error, 0 points decrease in error
    (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 y (-.f64 z x)))): 0 points increase in error, 0 points decrease in error

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error12.1
Cost584
\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -1.4236426789482445 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.758377005603365 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 2
Error12.1
Cost584
\[\begin{array}{l} t_0 := y \cdot \left(z - x\right)\\ \mathbf{if}\;y \leq -32.57921626040976:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.758377005603365 \cdot 10^{-47}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error23.1
Cost456
\[\begin{array}{l} \mathbf{if}\;y \leq -1.4236426789482445 \cdot 10^{-19}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 6.758377005603365 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
Alternative 4
Error0.0
Cost448
\[x + y \cdot \left(z - x\right) \]
Alternative 5
Error34.2
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022291 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))