Average Error: 6.4 → 0.1
Time: 3.7s
Precision: binary64
\[x + \frac{y \cdot y}{z} \]
↓
\[\mathsf{fma}\left(y, \frac{y}{z}, x\right) \]
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);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original6.4
Target0.1
Herbie0.1
\[x + y \cdot \frac{y}{z} \]

Derivation

  1. Initial program 6.4

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2021307 
(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)))