Average Error: 0.0 → 0.0
Time: 32.4s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \left(\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)\]
\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 \left(\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)
double f(double v) {
        double r6891278 = 2.0;
        double r6891279 = sqrt(r6891278);
        double r6891280 = 4.0;
        double r6891281 = r6891279 / r6891280;
        double r6891282 = 1.0;
        double r6891283 = 3.0;
        double r6891284 = v;
        double r6891285 = r6891284 * r6891284;
        double r6891286 = r6891283 * r6891285;
        double r6891287 = r6891282 - r6891286;
        double r6891288 = sqrt(r6891287);
        double r6891289 = r6891281 * r6891288;
        double r6891290 = r6891282 - r6891285;
        double r6891291 = r6891289 * r6891290;
        return r6891291;
}
↓
double f(double v) {
        double r6891292 = 1.0;
        double r6891293 = v;
        double r6891294 = r6891293 * r6891293;
        double r6891295 = r6891292 - r6891294;
        double r6891296 = 3.0;
        double r6891297 = r6891294 * r6891296;
        double r6891298 = r6891292 - r6891297;
        double r6891299 = sqrt(r6891298);
        double r6891300 = sqrt(r6891299);
        double r6891301 = r6891300 * r6891300;
        double r6891302 = 2.0;
        double r6891303 = sqrt(r6891302);
        double r6891304 = 4.0;
        double r6891305 = r6891303 / r6891304;
        double r6891306 = r6891301 * r6891305;
        double r6891307 = r6891295 * r6891306;
        return r6891307;
}

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-sqr-sqrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))