Average Error: 1.0 → 0.0
Time: 4.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r210636 = 4.0;
        double r210637 = 3.0;
        double r210638 = atan2(1.0, 0.0);
        double r210639 = r210637 * r210638;
        double r210640 = 1.0;
        double r210641 = v;
        double r210642 = r210641 * r210641;
        double r210643 = r210640 - r210642;
        double r210644 = r210639 * r210643;
        double r210645 = 2.0;
        double r210646 = 6.0;
        double r210647 = r210646 * r210642;
        double r210648 = r210645 - r210647;
        double r210649 = sqrt(r210648);
        double r210650 = r210644 * r210649;
        double r210651 = r210636 / r210650;
        return r210651;
}
↓
double f(double v) {
        double r210652 = 4.0;
        double r210653 = sqrt(r210652);
        double r210654 = 3.0;
        double r210655 = atan2(1.0, 0.0);
        double r210656 = r210654 * r210655;
        double r210657 = 1.0;
        double r210658 = v;
        double r210659 = r210658 * r210658;
        double r210660 = r210657 - r210659;
        double r210661 = r210656 * r210660;
        double r210662 = r210653 / r210661;
        double r210663 = 2.0;
        double r210664 = 6.0;
        double r210665 = r210664 * r210659;
        double r210666 = r210663 - r210665;
        double r210667 = sqrt(r210666);
        double r210668 = r210653 / r210667;
        double r210669 = r210662 * r210668;
        return r210669;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt1.0

    \[\leadsto \frac{\color{blue}{\sqrt{4} \cdot \sqrt{4}}}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]

  5. Final simplification0.0

    \[\leadsto \frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

Reproduce

herbie shell --seed 2020083 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))