Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(1 - v \cdot v\right) \cdot \log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}}\right)
double f(double v) {
        double r6587334 = 2.0;
        double r6587335 = sqrt(r6587334);
        double r6587336 = 4.0;
        double r6587337 = r6587335 / r6587336;
        double r6587338 = 1.0;
        double r6587339 = 3.0;
        double r6587340 = v;
        double r6587341 = r6587340 * r6587340;
        double r6587342 = r6587339 * r6587341;
        double r6587343 = r6587338 - r6587342;
        double r6587344 = sqrt(r6587343);
        double r6587345 = r6587337 * r6587344;
        double r6587346 = r6587338 - r6587341;
        double r6587347 = r6587345 * r6587346;
        return r6587347;
}
↓
double f(double v) {
        double r6587348 = 1.0;
        double r6587349 = v;
        double r6587350 = r6587349 * r6587349;
        double r6587351 = r6587348 - r6587350;
        double r6587352 = 3.0;
        double r6587353 = r6587350 * r6587352;
        double r6587354 = r6587348 - r6587353;
        double r6587355 = sqrt(r6587354);
        double r6587356 = 2.0;
        double r6587357 = sqrt(r6587356);
        double r6587358 = 4.0;
        double r6587359 = r6587357 / r6587358;
        double r6587360 = r6587355 * r6587359;
        double r6587361 = exp(r6587360);
        double r6587362 = log(r6587361);
        double r6587363 = r6587351 * r6587362;
        return r6587363;
}

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

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

Reproduce

herbie shell --seed 2019152 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))