Main:bigenough2 from A

Average Error: 0.0 → 0.0

Time: 6.8s

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

Alternatives

Alternative 1
Error	26.4
Cost	2172

\[\begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+113}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+76}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -0.032:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-136}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{-153}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 460000000000:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+26}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+66}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+96}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+182}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2
Error	14.6
Cost	1376

\[\begin{array}{l} t_0 := \left(z + x\right) \cdot y\\ \mathbf{if}\;y \leq -0.0135:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-99}:\\ \;\;\;\;\left(1 + y\right) \cdot x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-136}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-121}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	14.6
Cost	1376

\[\begin{array}{l} t_0 := \left(z + x\right) \cdot y\\ \mathbf{if}\;y \leq -0.032:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-99}:\\ \;\;\;\;y \cdot x + x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{-136}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-190}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.16 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	18.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+89}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-15}:\\ \;\;\;\;\left(1 + y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 5
Error	0.0
Cost	576

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

Alternative 6
Error	24.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -0.032:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7
Error	0.0
Cost	448

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

Alternative 8
Error	34.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))