Average Error: 0.2 → 0.2
Time: 11.7s
Precision: 64
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{-a}{\cos^{-1} a}\]
\frac{a}{-\cos^{-1} a}
↓
\frac{-a}{\cos^{-1} a}
double f(double a) {
        double r5118979 = a;
        double r5118980 = acos(r5118979);
        double r5118981 = -r5118980;
        double r5118982 = r5118979 / r5118981;
        return r5118982;
}
↓
double f(double a) {
        double r5118983 = a;
        double r5118984 = -r5118983;
        double r5118985 = acos(r5118983);
        double r5118986 = r5118984 / r5118985;
        return r5118986;
}

Error

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

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

  7. Applied add-cube-cbrt0.4

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

  8. Applied times-frac0.4

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

  9. Simplified0.4

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

  10. Simplified0.4

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

  11. Taylor expanded around 0 0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

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