Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left(1 - v \cdot v\right)\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left(1 - v \cdot v\right)\right)
double f(double v) {
        double r199288 = 2.0;
        double r199289 = sqrt(r199288);
        double r199290 = 4.0;
        double r199291 = r199289 / r199290;
        double r199292 = 1.0;
        double r199293 = 3.0;
        double r199294 = v;
        double r199295 = r199294 * r199294;
        double r199296 = r199293 * r199295;
        double r199297 = r199292 - r199296;
        double r199298 = sqrt(r199297);
        double r199299 = r199291 * r199298;
        double r199300 = r199292 - r199295;
        double r199301 = r199299 * r199300;
        return r199301;
}
↓
double f(double v) {
        double r199302 = 2.0;
        double r199303 = sqrt(r199302);
        double r199304 = 4.0;
        double r199305 = r199303 / r199304;
        double r199306 = 1.0;
        double r199307 = 3.0;
        double r199308 = v;
        double r199309 = r199308 * r199308;
        double r199310 = r199307 * r199309;
        double r199311 = r199306 - r199310;
        double r199312 = sqrt(r199311);
        double r199313 = r199306 - r199309;
        double r199314 = r199312 * r199313;
        double r199315 = r199305 * r199314;
        return r199315;
}

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 associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))