Average Error: 64.0 → 0
Time: 2.8s
Precision: 64
\[1.8999999999999999 \le t \le 2.10000000000000009\]
\[1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}\]
↓
\[1.6999999999999999 \cdot 10^{308} \cdot \left(t + -1\right)\]
1.6999999999999999 \cdot 10^{308} \cdot t - 1.6999999999999999 \cdot 10^{308}
↓
1.6999999999999999 \cdot 10^{308} \cdot \left(t + -1\right)
double f(double t) {
        double r38422 = 1.7e+308;
        double r38423 = t;
        double r38424 = r38422 * r38423;
        double r38425 = r38424 - r38422;
        return r38425;
}
↓
double f(double t) {
        double r38426 = 1.7e+308;
        double r38427 = t;
        double r38428 = -1.0;
        double r38429 = r38427 + r38428;
        double r38430 = r38426 * r38429;
        return r38430;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 add-cube-cbrt64.0

    \[\leadsto 1.6999999999999999 \cdot 10^{308} \cdot t - \color{blue}{\left(\sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}\right) \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}}\]

  4. Applied prod-diff1.6

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.6999999999999999 \cdot 10^{308}, t, -\sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \left(\sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{1.6999999999999999 \cdot 10^{308}}, \sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}, \sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \left(\sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}\right)\right)}\]

  5. Simplified0

    \[\leadsto \color{blue}{1.6999999999999999 \cdot 10^{308} \cdot \left(t + -1\right)} + \mathsf{fma}\left(-\sqrt[3]{1.6999999999999999 \cdot 10^{308}}, \sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}, \sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \left(\sqrt[3]{1.6999999999999999 \cdot 10^{308}} \cdot \sqrt[3]{1.6999999999999999 \cdot 10^{308}}\right)\right)\]

  6. Simplified0

    \[\leadsto 1.6999999999999999 \cdot 10^{308} \cdot \left(t + -1\right) + \color{blue}{0}\]

  7. Final simplification0

    \[\leadsto 1.6999999999999999 \cdot 10^{308} \cdot \left(t + -1\right)\]

Reproduce

herbie shell --seed 2020047 +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))