Average Error: 0.6 → 0.6
Time: 5.2s
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 r151142 = 1.0;
        double r151143 = 5.0;
        double r151144 = v;
        double r151145 = r151144 * r151144;
        double r151146 = r151143 * r151145;
        double r151147 = r151142 - r151146;
        double r151148 = r151145 - r151142;
        double r151149 = r151147 / r151148;
        double r151150 = acos(r151149);
        return r151150;
}
↓
double f(double v) {
        double r151151 = 1.0;
        double r151152 = 5.0;
        double r151153 = v;
        double r151154 = r151153 * r151153;
        double r151155 = r151152 * r151154;
        double r151156 = r151151 - r151155;
        double r151157 = r151154 - r151151;
        double r151158 = r151156 / r151157;
        double r151159 = acos(r151158);
        double r151160 = log(r151159);
        double r151161 = exp(r151160);
        return r151161;
}

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-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 2020064 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 1"
  :precision binary64
  (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))