Average Error: 64.0 → 0
Time: 557.0ms
Precision: 64
\[1.8999999999999999 \le t \le 2.10000000000000009\]
\[1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}\]
↓
\[\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)\]
1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}
↓
\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)
double f(double t) {
        double r75730 = 1.7e+308;
        double r75731 = t;
        double r75732 = r75730 * r75731;
        double r75733 = r75732 - r75730;
        return r75733;
}
↓
double f(double t) {
        double r75734 = 1.7e+308;
        double r75735 = t;
        double r75736 = -r75734;
        double r75737 = fma(r75734, r75735, r75736);
        return r75737;
}

Error

Bits error versus t

Target

Original64.0
Target0
Herbie0
\[\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)\]

Derivation

  1. Initial program 64.0

    \[1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}\]
  2. Using strategy rm

  3. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -1.6999999999999999 \cdot 10^{308}\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (t)
  :name "fma_test2"
  :precision binary64
  :pre (<= 1.9 t 2.1)

  :herbie-target
  (fma 1.7e+308 t (- 1.7e+308))

  (- (* 1.7e+308 t) 1.7e+308))