Average Error: 0.0 → 0.0
Time: 10.8s
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 r8334436 = 2.0;
        double r8334437 = sqrt(r8334436);
        double r8334438 = 4.0;
        double r8334439 = r8334437 / r8334438;
        double r8334440 = 1.0;
        double r8334441 = 3.0;
        double r8334442 = v;
        double r8334443 = r8334442 * r8334442;
        double r8334444 = r8334441 * r8334443;
        double r8334445 = r8334440 - r8334444;
        double r8334446 = sqrt(r8334445);
        double r8334447 = r8334439 * r8334446;
        double r8334448 = r8334440 - r8334443;
        double r8334449 = r8334447 * r8334448;
        return r8334449;
}
↓
double f(double v) {
        double r8334450 = 1.0;
        double r8334451 = v;
        double r8334452 = r8334451 * r8334451;
        double r8334453 = r8334450 - r8334452;
        double r8334454 = 3.0;
        double r8334455 = r8334452 * r8334454;
        double r8334456 = r8334450 - r8334455;
        double r8334457 = sqrt(r8334456);
        double r8334458 = 2.0;
        double r8334459 = sqrt(r8334458);
        double r8334460 = 4.0;
        double r8334461 = r8334459 / r8334460;
        double r8334462 = r8334457 * r8334461;
        double r8334463 = exp(r8334462);
        double r8334464 = log(r8334463);
        double r8334465 = r8334453 * r8334464;
        return r8334465;
}

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 
(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))))