Average Error: 0.0 → 0.0
Time: 23.1s
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 r2649195 = 2.0;
        double r2649196 = sqrt(r2649195);
        double r2649197 = 4.0;
        double r2649198 = r2649196 / r2649197;
        double r2649199 = 1.0;
        double r2649200 = 3.0;
        double r2649201 = v;
        double r2649202 = r2649201 * r2649201;
        double r2649203 = r2649200 * r2649202;
        double r2649204 = r2649199 - r2649203;
        double r2649205 = sqrt(r2649204);
        double r2649206 = r2649198 * r2649205;
        double r2649207 = r2649199 - r2649202;
        double r2649208 = r2649206 * r2649207;
        return r2649208;
}
↓
double f(double v) {
        double r2649209 = 1.0;
        double r2649210 = v;
        double r2649211 = r2649210 * r2649210;
        double r2649212 = 3.0;
        double r2649213 = r2649211 * r2649212;
        double r2649214 = r2649209 - r2649213;
        double r2649215 = sqrt(r2649214);
        double r2649216 = 2.0;
        double r2649217 = sqrt(r2649216);
        double r2649218 = 4.0;
        double r2649219 = r2649217 / r2649218;
        double r2649220 = r2649215 * r2649219;
        double r2649221 = r2649209 - r2649211;
        double r2649222 = r2649220 * r2649221;
        return r2649222;
}

Error

Bits error versus v

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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 2019153 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))