Average Error: 0.0 → 0.0
Time: 21.2s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\sqrt{2}}{4} \cdot \left(\frac{\sqrt{1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}} \cdot \left(1 - v \cdot v\right)\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\frac{\sqrt{2}}{4} \cdot \left(\frac{\sqrt{1 - \left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right)}}{\sqrt{1 + 3 \cdot \left(v \cdot v\right)}} \cdot \left(1 - v \cdot v\right)\right)
double f(double v) {
        double r6133047 = 2.0;
        double r6133048 = sqrt(r6133047);
        double r6133049 = 4.0;
        double r6133050 = r6133048 / r6133049;
        double r6133051 = 1.0;
        double r6133052 = 3.0;
        double r6133053 = v;
        double r6133054 = r6133053 * r6133053;
        double r6133055 = r6133052 * r6133054;
        double r6133056 = r6133051 - r6133055;
        double r6133057 = sqrt(r6133056);
        double r6133058 = r6133050 * r6133057;
        double r6133059 = r6133051 - r6133054;
        double r6133060 = r6133058 * r6133059;
        return r6133060;
}
↓
double f(double v) {
        double r6133061 = 2.0;
        double r6133062 = sqrt(r6133061);
        double r6133063 = 4.0;
        double r6133064 = r6133062 / r6133063;
        double r6133065 = 1.0;
        double r6133066 = 3.0;
        double r6133067 = v;
        double r6133068 = r6133067 * r6133067;
        double r6133069 = r6133066 * r6133068;
        double r6133070 = r6133069 * r6133069;
        double r6133071 = r6133065 - r6133070;
        double r6133072 = sqrt(r6133071);
        double r6133073 = r6133065 + r6133069;
        double r6133074 = sqrt(r6133073);
        double r6133075 = r6133072 / r6133074;
        double r6133076 = r6133065 - r6133068;
        double r6133077 = r6133075 * r6133076;
        double r6133078 = r6133064 * r6133077;
        return r6133078;
}

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 associate-*l*0.0

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

  5. Applied flip--0.0

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

  6. Applied sqrt-div0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))