Average Error: 0.0 → 0.0
Time: 10.9s
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 r7236333 = 2.0;
        double r7236334 = sqrt(r7236333);
        double r7236335 = 4.0;
        double r7236336 = r7236334 / r7236335;
        double r7236337 = 1.0;
        double r7236338 = 3.0;
        double r7236339 = v;
        double r7236340 = r7236339 * r7236339;
        double r7236341 = r7236338 * r7236340;
        double r7236342 = r7236337 - r7236341;
        double r7236343 = sqrt(r7236342);
        double r7236344 = r7236336 * r7236343;
        double r7236345 = r7236337 - r7236340;
        double r7236346 = r7236344 * r7236345;
        return r7236346;
}
↓
double f(double v) {
        double r7236347 = 1.0;
        double r7236348 = v;
        double r7236349 = r7236348 * r7236348;
        double r7236350 = r7236347 - r7236349;
        double r7236351 = 3.0;
        double r7236352 = r7236349 * r7236351;
        double r7236353 = r7236347 - r7236352;
        double r7236354 = sqrt(r7236353);
        double r7236355 = 2.0;
        double r7236356 = sqrt(r7236355);
        double r7236357 = 4.0;
        double r7236358 = r7236356 / r7236357;
        double r7236359 = r7236354 * r7236358;
        double r7236360 = exp(r7236359);
        double r7236361 = log(r7236360);
        double r7236362 = r7236350 * r7236361;
        return r7236362;
}

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 2019171 +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))))