Average Error: 0.6 → 0.6
Time: 16.4s
Precision: 64
\[\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\]
↓
\[e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}\]
\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)
↓
e^{\log \left(\cos^{-1} \left(\frac{1 - 5 \cdot \left(v \cdot v\right)}{v \cdot v - 1}\right)\right)}
double f(double v) {
        double r113658 = 1.0;
        double r113659 = 5.0;
        double r113660 = v;
        double r113661 = r113660 * r113660;
        double r113662 = r113659 * r113661;
        double r113663 = r113658 - r113662;
        double r113664 = r113661 - r113658;
        double r113665 = r113663 / r113664;
        double r113666 = acos(r113665);
        return r113666;
}
↓
double f(double v) {
        double r113667 = 1.0;
        double r113668 = 5.0;
        double r113669 = v;
        double r113670 = r113669 * r113669;
        double r113671 = r113668 * r113670;
        double r113672 = r113667 - r113671;
        double r113673 = r113670 - r113667;
        double r113674 = r113672 / r113673;
        double r113675 = acos(r113674);
        double r113676 = log(r113675);
        double r113677 = exp(r113676);
        return r113677;
}

Error

Bits error versus v

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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-exp-log0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019212 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))