\[x + \frac{y \cdot y}{z} \]

↓

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

(FPCore (x y z) :precision binary64 (+ x (/ (* y y) z)))

↓

(FPCore (x y z) :precision binary64 (fma y (/ y z) x))

double code(double x, double y, double z) {
	return x + ((y * y) / z);
}

↓

double code(double x, double y, double z) {
	return fma(y, (y / z), x);
}

function code(x, y, z)
	return Float64(x + Float64(Float64(y * y) / z))
end

↓

function code(x, y, z)
	return fma(y, Float64(y / z), x)
end

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

↓

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

x + \frac{y \cdot y}{z}

↓

\mathsf{fma}\left(y, \frac{y}{z}, x\right)

Original	6.2
Target	0.1
Herbie	0.1

Derivation

Initial program 6.2
\[x + \frac{y \cdot y}{z} \]
Simplified0.1
\[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{y}{z}, x\right)} \]
Final simplification0.1
\[\leadsto \mathsf{fma}\left(y, \frac{y}{z}, x\right) \]

Alternatives

Alternative 1
Error	16.3
Cost	1096

\[\begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ \mathbf{if}\;t_0 \leq -3.15755589475137 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 3.679577947932958 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	11.9
Cost	1096

\[\begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ t_1 := \frac{y}{\frac{z}{y}}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	11.9
Cost	1096

\[\begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+129}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \end{array} \]

Alternative 4
Error	1.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+150}:\\ \;\;\;\;y \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+153}:\\ \;\;\;\;x + \frac{y \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \end{array} \]

Alternative 5
Error	0.1
Cost	448

\[x + y \cdot \frac{y}{z} \]

Alternative 6
Error	21.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :herbie-target
  (+ x (* y (/ y z)))

  (+ x (/ (* y y) z)))

Error

Target

Derivation

Alternatives

Error

Reproduce