Average Error: 0.0 → 0.0
Time: 9.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}}\right)\]
\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 r2593268 = 2.0;
        double r2593269 = sqrt(r2593268);
        double r2593270 = 4.0;
        double r2593271 = r2593269 / r2593270;
        double r2593272 = 1.0;
        double r2593273 = 3.0;
        double r2593274 = v;
        double r2593275 = r2593274 * r2593274;
        double r2593276 = r2593273 * r2593275;
        double r2593277 = r2593272 - r2593276;
        double r2593278 = sqrt(r2593277);
        double r2593279 = r2593271 * r2593278;
        double r2593280 = r2593272 - r2593275;
        double r2593281 = r2593279 * r2593280;
        return r2593281;
}
↓
double f(double v) {
        double r2593282 = 1.0;
        double r2593283 = v;
        double r2593284 = r2593283 * r2593283;
        double r2593285 = r2593282 - r2593284;
        double r2593286 = 3.0;
        double r2593287 = r2593284 * r2593286;
        double r2593288 = r2593282 - r2593287;
        double r2593289 = sqrt(r2593288);
        double r2593290 = 2.0;
        double r2593291 = sqrt(r2593290);
        double r2593292 = 4.0;
        double r2593293 = r2593291 / r2593292;
        double r2593294 = r2593289 * r2593293;
        double r2593295 = exp(r2593294);
        double r2593296 = log(r2593295);
        double r2593297 = r2593285 * r2593296;
        return r2593297;
}

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))))