Average Error: 0.0 → 0.0
Time: 18.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r5486032 = 2.0;
        double r5486033 = sqrt(r5486032);
        double r5486034 = 4.0;
        double r5486035 = r5486033 / r5486034;
        double r5486036 = 1.0;
        double r5486037 = 3.0;
        double r5486038 = v;
        double r5486039 = r5486038 * r5486038;
        double r5486040 = r5486037 * r5486039;
        double r5486041 = r5486036 - r5486040;
        double r5486042 = sqrt(r5486041);
        double r5486043 = r5486035 * r5486042;
        double r5486044 = r5486036 - r5486039;
        double r5486045 = r5486043 * r5486044;
        return r5486045;
}
↓
double f(double v) {
        double r5486046 = 1.0;
        double r5486047 = v;
        double r5486048 = r5486047 * r5486047;
        double r5486049 = 3.0;
        double r5486050 = r5486048 * r5486049;
        double r5486051 = r5486046 - r5486050;
        double r5486052 = sqrt(r5486051);
        double r5486053 = 2.0;
        double r5486054 = sqrt(r5486053);
        double r5486055 = 4.0;
        double r5486056 = r5486054 / r5486055;
        double r5486057 = r5486052 * r5486056;
        double r5486058 = r5486046 - r5486048;
        double r5486059 = r5486057 * r5486058;
        return r5486059;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))