Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r294964 = 2.0;
        double r294965 = sqrt(r294964);
        double r294966 = 4.0;
        double r294967 = r294965 / r294966;
        double r294968 = 1.0;
        double r294969 = 3.0;
        double r294970 = v;
        double r294971 = r294970 * r294970;
        double r294972 = r294969 * r294971;
        double r294973 = r294968 - r294972;
        double r294974 = sqrt(r294973);
        double r294975 = r294967 * r294974;
        double r294976 = r294968 - r294971;
        double r294977 = r294975 * r294976;
        return r294977;
}
↓
double f(double v) {
        double r294978 = 2.0;
        double r294979 = sqrt(r294978);
        double r294980 = 4.0;
        double r294981 = r294979 / r294980;
        double r294982 = 1.0;
        double r294983 = 3.0;
        double r294984 = v;
        double r294985 = r294984 * r294984;
        double r294986 = r294983 * r294985;
        double r294987 = r294982 - r294986;
        double r294988 = sqrt(r294987);
        double r294989 = r294981 * r294988;
        double r294990 = exp(r294989);
        double r294991 = log(r294990);
        double r294992 = r294982 - r294985;
        double r294993 = r294991 * r294992;
        return r294993;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)} \cdot \left(1 - v \cdot v\right)\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))