Average Error: 0.0 → 0.0
Time: 13.1s
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 r6269082 = 2.0;
        double r6269083 = sqrt(r6269082);
        double r6269084 = 4.0;
        double r6269085 = r6269083 / r6269084;
        double r6269086 = 1.0;
        double r6269087 = 3.0;
        double r6269088 = v;
        double r6269089 = r6269088 * r6269088;
        double r6269090 = r6269087 * r6269089;
        double r6269091 = r6269086 - r6269090;
        double r6269092 = sqrt(r6269091);
        double r6269093 = r6269085 * r6269092;
        double r6269094 = r6269086 - r6269089;
        double r6269095 = r6269093 * r6269094;
        return r6269095;
}
↓
double f(double v) {
        double r6269096 = 1.0;
        double r6269097 = v;
        double r6269098 = r6269097 * r6269097;
        double r6269099 = 3.0;
        double r6269100 = r6269098 * r6269099;
        double r6269101 = r6269096 - r6269100;
        double r6269102 = sqrt(r6269101);
        double r6269103 = 2.0;
        double r6269104 = sqrt(r6269103);
        double r6269105 = 4.0;
        double r6269106 = r6269104 / r6269105;
        double r6269107 = r6269102 * r6269106;
        double r6269108 = r6269096 - r6269098;
        double r6269109 = r6269107 * r6269108;
        return r6269109;
}

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