Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \log \left(e^{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r131014 = 2.0;
        double r131015 = sqrt(r131014);
        double r131016 = 4.0;
        double r131017 = r131015 / r131016;
        double r131018 = 1.0;
        double r131019 = 3.0;
        double r131020 = v;
        double r131021 = r131020 * r131020;
        double r131022 = r131019 * r131021;
        double r131023 = r131018 - r131022;
        double r131024 = sqrt(r131023);
        double r131025 = r131017 * r131024;
        double r131026 = r131018 - r131021;
        double r131027 = r131025 * r131026;
        return r131027;
}
↓
double f(double v) {
        double r131028 = 2.0;
        double r131029 = sqrt(r131028);
        double r131030 = 4.0;
        double r131031 = r131029 / r131030;
        double r131032 = 1.0;
        double r131033 = 3.0;
        double r131034 = v;
        double r131035 = r131034 * r131034;
        double r131036 = r131033 * r131035;
        double r131037 = r131032 - r131036;
        double r131038 = sqrt(r131037);
        double r131039 = exp(r131038);
        double r131040 = log(r131039);
        double r131041 = r131031 * r131040;
        double r131042 = r131032 - r131035;
        double r131043 = r131041 * r131042;
        return r131043;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))