Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r12732114 = 2.0;
        double r12732115 = sqrt(r12732114);
        double r12732116 = 4.0;
        double r12732117 = r12732115 / r12732116;
        double r12732118 = 1.0;
        double r12732119 = 3.0;
        double r12732120 = v;
        double r12732121 = r12732120 * r12732120;
        double r12732122 = r12732119 * r12732121;
        double r12732123 = r12732118 - r12732122;
        double r12732124 = sqrt(r12732123);
        double r12732125 = r12732117 * r12732124;
        double r12732126 = r12732118 - r12732121;
        double r12732127 = r12732125 * r12732126;
        return r12732127;
}
↓
double f(double v) {
        double r12732128 = 2.0;
        double r12732129 = sqrt(r12732128);
        double r12732130 = 4.0;
        double r12732131 = r12732129 / r12732130;
        double r12732132 = 1.0;
        double r12732133 = 3.0;
        double r12732134 = v;
        double r12732135 = r12732134 * r12732134;
        double r12732136 = r12732133 * r12732135;
        double r12732137 = r12732132 - r12732136;
        double r12732138 = sqrt(r12732137);
        double r12732139 = r12732131 * r12732138;
        double r12732140 = r12732132 - r12732135;
        double r12732141 = r12732139 * r12732140;
        return r12732141;
}

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

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

Reproduce

herbie shell --seed 2019173 
(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))))