Average Error: 0.0 → 0.0
Time: 30.8s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \left(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)\]
\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(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)
double f(double v) {
        double r8126202 = 2.0;
        double r8126203 = sqrt(r8126202);
        double r8126204 = 4.0;
        double r8126205 = r8126203 / r8126204;
        double r8126206 = 1.0;
        double r8126207 = 3.0;
        double r8126208 = v;
        double r8126209 = r8126208 * r8126208;
        double r8126210 = r8126207 * r8126209;
        double r8126211 = r8126206 - r8126210;
        double r8126212 = sqrt(r8126211);
        double r8126213 = r8126205 * r8126212;
        double r8126214 = r8126206 - r8126209;
        double r8126215 = r8126213 * r8126214;
        return r8126215;
}
↓
double f(double v) {
        double r8126216 = 1.0;
        double r8126217 = v;
        double r8126218 = r8126217 * r8126217;
        double r8126219 = r8126216 - r8126218;
        double r8126220 = 3.0;
        double r8126221 = r8126218 * r8126220;
        double r8126222 = r8126216 - r8126221;
        double r8126223 = sqrt(r8126222);
        double r8126224 = exp(r8126223);
        double r8126225 = log(r8126224);
        double r8126226 = 2.0;
        double r8126227 = sqrt(r8126226);
        double r8126228 = 4.0;
        double r8126229 = r8126227 / r8126228;
        double r8126230 = r8126225 * r8126229;
        double r8126231 = r8126219 * r8126230;
        return r8126231;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(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))))