Average Error: 0.3 → 0.4
Time: 11.6s
Precision: 64
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\frac{\frac{1}{-\cos^{-1} a}}{\frac{1}{a}}\]
\frac{a}{-\cos^{-1} a}
↓
\frac{\frac{1}{-\cos^{-1} a}}{\frac{1}{a}}
double f(double a) {
        double r174046 = a;
        double r174047 = acos(r174046);
        double r174048 = -r174047;
        double r174049 = r174046 / r174048;
        return r174049;
}
↓
double f(double a) {
        double r174050 = 1.0;
        double r174051 = a;
        double r174052 = acos(r174051);
        double r174053 = -r174052;
        double r174054 = r174050 / r174053;
        double r174055 = r174050 / r174051;
        double r174056 = r174054 / r174055;
        return r174056;
}

Error

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  3. Applied clear-num0.4

    \[\leadsto \color{blue}{\frac{1}{\frac{-\cos^{-1} a}{a}}}\]
  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 associate-/r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019212 
(FPCore (a)
  :name "Fuzzer 001"
  :precision binary64
  (/ a (- (acos a))))