Average Error: 0.0 → 0.0
Time: 480.0ms
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 r800530 = x;
        double r800531 = r800530 * r800530;
        double r800532 = y;
        double r800533 = r800531 + r800532;
        double r800534 = r800533 + r800532;
        return r800534;
}
↓
double f(double x, double y) {
        double r800535 = y;
        double r800536 = x;
        double r800537 = fma(r800536, r800536, r800535);
        double r800538 = r800535 + r800537;
        return r800538;
}

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))