Average Error: 64.0 → 0
Time: 858.0ms
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 r75218 = 1.7e+308;
        double r75219 = t;
        double r75220 = r75218 * r75219;
        double r75221 = r75220 - r75218;
        return r75221;
}
↓
double f(double t) {
        double r75222 = 1.7e+308;
        double r75223 = t;
        double r75224 = -r75222;
        double r75225 = fma(r75222, r75223, r75224);
        return r75225;
}

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 2020035 +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))