Average Error: 1.0 → 0.0
Time: 11.4s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r6015805 = 4.0;
        double r6015806 = 3.0;
        double r6015807 = atan2(1.0, 0.0);
        double r6015808 = r6015806 * r6015807;
        double r6015809 = 1.0;
        double r6015810 = v;
        double r6015811 = r6015810 * r6015810;
        double r6015812 = r6015809 - r6015811;
        double r6015813 = r6015808 * r6015812;
        double r6015814 = 2.0;
        double r6015815 = 6.0;
        double r6015816 = r6015815 * r6015811;
        double r6015817 = r6015814 - r6015816;
        double r6015818 = sqrt(r6015817);
        double r6015819 = r6015813 * r6015818;
        double r6015820 = r6015805 / r6015819;
        return r6015820;
}
↓
double f(double v) {
        double r6015821 = 4.0;
        double r6015822 = atan2(1.0, 0.0);
        double r6015823 = 3.0;
        double r6015824 = r6015822 * r6015823;
        double r6015825 = 1.0;
        double r6015826 = v;
        double r6015827 = r6015826 * r6015826;
        double r6015828 = r6015825 - r6015827;
        double r6015829 = r6015824 * r6015828;
        double r6015830 = r6015821 / r6015829;
        double r6015831 = 2.0;
        double r6015832 = 6.0;
        double r6015833 = r6015832 * r6015827;
        double r6015834 = r6015831 - r6015833;
        double r6015835 = sqrt(r6015834);
        double r6015836 = r6015830 / r6015835;
        return r6015836;
}

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 associate-/r*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))