Average Error: 0.0 → 0.0
Time: 12.8s
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 r8299654 = 2.0;
        double r8299655 = sqrt(r8299654);
        double r8299656 = 4.0;
        double r8299657 = r8299655 / r8299656;
        double r8299658 = 1.0;
        double r8299659 = 3.0;
        double r8299660 = v;
        double r8299661 = r8299660 * r8299660;
        double r8299662 = r8299659 * r8299661;
        double r8299663 = r8299658 - r8299662;
        double r8299664 = sqrt(r8299663);
        double r8299665 = r8299657 * r8299664;
        double r8299666 = r8299658 - r8299661;
        double r8299667 = r8299665 * r8299666;
        return r8299667;
}
↓
double f(double v) {
        double r8299668 = 1.0;
        double r8299669 = v;
        double r8299670 = r8299669 * r8299669;
        double r8299671 = 3.0;
        double r8299672 = r8299670 * r8299671;
        double r8299673 = r8299668 - r8299672;
        double r8299674 = sqrt(r8299673);
        double r8299675 = 2.0;
        double r8299676 = sqrt(r8299675);
        double r8299677 = 4.0;
        double r8299678 = r8299676 / r8299677;
        double r8299679 = r8299674 * r8299678;
        double r8299680 = r8299668 - r8299670;
        double r8299681 = r8299679 * r8299680;
        return r8299681;
}

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 2019192 
(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))))