Average Error: 0.6 → 0.6
Time: 52.3s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[\cos^{-1} \left(\sqrt[3]{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
\cos^{-1} \left(\sqrt[3]{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)
double f(double v) {
        double r8875079 = 1.0;
        double r8875080 = 5.0;
        double r8875081 = v;
        double r8875082 = r8875081 * r8875081;
        double r8875083 = r8875080 * r8875082;
        double r8875084 = r8875079 - r8875083;
        double r8875085 = r8875082 - r8875079;
        double r8875086 = r8875084 / r8875085;
        double r8875087 = acos(r8875086);
        return r8875087;
}
↓
double f(double v) {
        double r8875088 = 1.0;
        double r8875089 = v;
        double r8875090 = r8875089 * r8875089;
        double r8875091 = 5.0;
        double r8875092 = r8875090 * r8875091;
        double r8875093 = r8875088 - r8875092;
        double r8875094 = r8875090 - r8875088;
        double r8875095 = r8875093 / r8875094;
        double r8875096 = r8875095 * r8875095;
        double r8875097 = r8875095 * r8875096;
        double r8875098 = cbrt(r8875097);
        double r8875099 = acos(r8875098);
        return r8875099;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.6

    \[\leadsto \cos^{-1} \color{blue}{\left(\sqrt[3]{\left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1} \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right) \cdot \frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}}\right)}\]

  4. Final simplification0.6

    \[\leadsto \cos^{-1} \left(\sqrt[3]{\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \left(\frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1} \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{v \cdot v - 1}\right)}\right)\]

Reproduce

herbie shell --seed 2019168 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))