Average Error: 0.0 → 0.0
Time: 3.0s
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 r149033 = 2.0;
        double r149034 = sqrt(r149033);
        double r149035 = 4.0;
        double r149036 = r149034 / r149035;
        double r149037 = 1.0;
        double r149038 = 3.0;
        double r149039 = v;
        double r149040 = r149039 * r149039;
        double r149041 = r149038 * r149040;
        double r149042 = r149037 - r149041;
        double r149043 = sqrt(r149042);
        double r149044 = r149036 * r149043;
        double r149045 = r149037 - r149040;
        double r149046 = r149044 * r149045;
        return r149046;
}
↓
double f(double v) {
        double r149047 = 2.0;
        double r149048 = sqrt(r149047);
        double r149049 = 4.0;
        double r149050 = r149048 / r149049;
        double r149051 = 1.0;
        double r149052 = 3.0;
        double r149053 = v;
        double r149054 = r149053 * r149053;
        double r149055 = r149052 * r149054;
        double r149056 = r149051 - r149055;
        double r149057 = sqrt(r149056);
        double r149058 = r149050 * r149057;
        double r149059 = r149051 - r149054;
        double r149060 = r149058 * r149059;
        return r149060;
}

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 2020064 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))