Average Error: 0.3 → 0.4
Time: 2.4s
Precision: 64
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{1}{-\cos^{-1} a} \cdot a\]
\frac{a}{-\cos^{-1} a}
↓
\frac{1}{-\cos^{-1} a} \cdot a
double f(double a) {
        double r116563 = a;
        double r116564 = acos(r116563);
        double r116565 = -r116564;
        double r116566 = r116563 / r116565;
        return r116566;
}
↓
double f(double a) {
        double r116567 = 1.0;
        double r116568 = a;
        double r116569 = acos(r116568);
        double r116570 = -r116569;
        double r116571 = r116567 / r116570;
        double r116572 = r116571 * r116568;
        return r116572;
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  3. Applied clear-num0.3

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

  5. Applied div-inv0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied times-frac0.5

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

  8. Simplified0.5

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  :precision binary64
  (/ a (- (acos a))))