Average Error: 0.0 → 0.0
Time: 21.6s
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 r188924 = 2.0;
        double r188925 = sqrt(r188924);
        double r188926 = 4.0;
        double r188927 = r188925 / r188926;
        double r188928 = 1.0;
        double r188929 = 3.0;
        double r188930 = v;
        double r188931 = r188930 * r188930;
        double r188932 = r188929 * r188931;
        double r188933 = r188928 - r188932;
        double r188934 = sqrt(r188933);
        double r188935 = r188927 * r188934;
        double r188936 = r188928 - r188931;
        double r188937 = r188935 * r188936;
        return r188937;
}
↓
double f(double v) {
        double r188938 = 2.0;
        double r188939 = sqrt(r188938);
        double r188940 = 4.0;
        double r188941 = r188939 / r188940;
        double r188942 = 1.0;
        double r188943 = 3.0;
        double r188944 = v;
        double r188945 = r188944 * r188944;
        double r188946 = r188943 * r188945;
        double r188947 = r188942 - r188946;
        double r188948 = sqrt(r188947);
        double r188949 = r188941 * r188948;
        double r188950 = exp(r188949);
        double r188951 = log(r188950);
        double r188952 = r188942 - r188945;
        double r188953 = r188951 * r188952;
        return r188953;
}

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 2019199 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))