Average Error: 0.0 → 0.0
Time: 17.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt{2} \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{1 - v \cdot v}{4}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\sqrt{2} \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{1 - v \cdot v}{4}\right)
double f(double v) {
        double r198091 = 2.0;
        double r198092 = sqrt(r198091);
        double r198093 = 4.0;
        double r198094 = r198092 / r198093;
        double r198095 = 1.0;
        double r198096 = 3.0;
        double r198097 = v;
        double r198098 = r198097 * r198097;
        double r198099 = r198096 * r198098;
        double r198100 = r198095 - r198099;
        double r198101 = sqrt(r198100);
        double r198102 = r198094 * r198101;
        double r198103 = r198095 - r198098;
        double r198104 = r198102 * r198103;
        return r198104;
}
↓
double f(double v) {
        double r198105 = 2.0;
        double r198106 = sqrt(r198105);
        double r198107 = 1.0;
        double r198108 = v;
        double r198109 = r198108 * r198108;
        double r198110 = 3.0;
        double r198111 = r198109 * r198110;
        double r198112 = r198107 - r198111;
        double r198113 = sqrt(r198112);
        double r198114 = r198107 - r198109;
        double r198115 = 4.0;
        double r198116 = r198114 / r198115;
        double r198117 = r198113 * r198116;
        double r198118 = r198106 * r198117;
        return r198118;
}

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. Simplified0.0

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

  4. Applied associate-*l*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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))))