Average Error: 0.0 → 0.0
Time: 500.0ms
Precision: 64
\[\left(x \cdot x + y\right) + y\]
↓
\[y + \mathsf{fma}\left(x, x, y\right)\]
\left(x \cdot x + y\right) + y
↓
y + \mathsf{fma}\left(x, x, y\right)
double f(double x, double y) {
        double r97769 = x;
        double r97770 = r97769 * r97769;
        double r97771 = y;
        double r97772 = r97770 + r97771;
        double r97773 = r97772 + r97771;
        return r97773;
}
↓
double f(double x, double y) {
        double r97774 = y;
        double r97775 = x;
        double r97776 = fma(r97775, r97775, r97774);
        double r97777 = r97774 + r97776;
        return r97777;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0.0
\[\left(y + y\right) + x \cdot x\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2"
  :precision binary64

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

  (+ (+ (* x x) y) y))