Fuzzer 001

Average Error: 0.2 → 0.2

Time: 14.3s

Precision: 64

Math

\[\frac{a}{-\cos^{-1} a}\]

↓

\[-\frac{a}{\cos^{-1} a}\]

C

double f(double a) {
        double r2996366 = a;
        double r2996367 = acos(r2996366);
        double r2996368 = -r2996367;
        double r2996369 = r2996366 / r2996368;
        return r2996369;
}

↓

double f(double a) {
        double r2996370 = a;
        double r2996371 = acos(r2996370);
        double r2996372 = r2996370 / r2996371;
        double r2996373 = -r2996372;
        return r2996373;
}

Error

Bits error versus a

Derivation

1. Initial program 0.2

   \[\frac{a}{-\cos^{-1} a}\]
2. Using strategy rm

3. Applied clear-num 0.3

   \[\leadsto \color{blue}{\frac{1}{\frac{-\cos^{-1} a}{a}}}\]
4. Using strategy rm

5. Applied div-inv 0.4

   \[\leadsto \frac{1}{\color{blue}{\left(-\cos^{-1} a\right) \cdot \frac{1}{a}}}\]

6. Applied add-cube-cbrt 0.4

   \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\left(-\cos^{-1} a\right) \cdot \frac{1}{a}}\]

7. Applied times-frac 0.4

   \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{-\cos^{-1} a} \cdot \frac{\sqrt[3]{1}}{\frac{1}{a}}}\]

8. Simplified 0.4

   \[\leadsto \color{blue}{\frac{1}{-\cos^{-1} a}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{a}}\]

9. Simplified 0.4

   \[\leadsto \frac{1}{-\cos^{-1} a} \cdot \color{blue}{a}\]

10. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{-1 \cdot \frac{a}{\cos^{-1} a}}\]

11. Simplified 0.2

    \[\leadsto \color{blue}{-\frac{a}{\cos^{-1} a}}\]

12. Final simplification 0.2

    \[\leadsto -\frac{a}{\cos^{-1} a}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))