Average Error: 0.0 → 0.0
Time: 3.1s
Precision: binary64
Cost: 6720
\[x + \left(y - x\right) \cdot z \]
↓
\[\mathsf{fma}\left(y - x, z, x\right) \]
(FPCore (x y z) :precision binary64 (+ x (* (- y x) z)))
↓
(FPCore (x y z) :precision binary64 (fma (- y x) z x))
double code(double x, double y, double z) {
	return x + ((y - x) * z);
}
↓
double code(double x, double y, double z) {
	return fma((y - x), z, x);
}

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

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

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

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, z, x\right)} \]
    Proof
    (fma.f64 (-.f64 y x) z x): 0 points increase in error, 0 points decrease in error
    (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (-.f64 y x) z) x)): 0 points increase in error, 0 points decrease in error
    (Rewrite<= +-commutative_binary64 (+.f64 x (*.f64 (-.f64 y x) z))): 0 points increase in error, 0 points decrease in error

  3. Final simplification0.0

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

Alternatives

Alternative 1
Error25.2
Cost917
\[\begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+109} \lor \neg \left(z \leq 3.8 \cdot 10^{+243}\right) \land z \leq 3.8 \cdot 10^{+272}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
Alternative 2
Error14.3
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-79} \lor \neg \left(z \leq 4.5 \cdot 10^{-119}\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 3
Error1.0
Cost585
\[\begin{array}{l} \mathbf{if}\;z \leq -215000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y - x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
Alternative 4
Error25.0
Cost456
\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-92}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-51}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
Alternative 5
Error0.0
Cost448
\[x + \left(y - x\right) \cdot z \]
Alternative 6
Error34.8
Cost64
\[x \]

Error

Reproduce

herbie shell --seed 2022343 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))