Average Error: 1.0 → 0.0
Time: 6.8s
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 r199951 = 4.0;
        double r199952 = 3.0;
        double r199953 = atan2(1.0, 0.0);
        double r199954 = r199952 * r199953;
        double r199955 = 1.0;
        double r199956 = v;
        double r199957 = r199956 * r199956;
        double r199958 = r199955 - r199957;
        double r199959 = r199954 * r199958;
        double r199960 = 2.0;
        double r199961 = 6.0;
        double r199962 = r199961 * r199957;
        double r199963 = r199960 - r199962;
        double r199964 = sqrt(r199963);
        double r199965 = r199959 * r199964;
        double r199966 = r199951 / r199965;
        return r199966;
}
↓
double f(double v) {
        double r199967 = 4.0;
        double r199968 = sqrt(r199967);
        double r199969 = 3.0;
        double r199970 = atan2(1.0, 0.0);
        double r199971 = r199969 * r199970;
        double r199972 = 1.0;
        double r199973 = v;
        double r199974 = r199973 * r199973;
        double r199975 = r199972 - r199974;
        double r199976 = r199971 * r199975;
        double r199977 = r199968 / r199976;
        double r199978 = 2.0;
        double r199979 = 6.0;
        double r199980 = r199979 * r199974;
        double r199981 = r199978 - r199980;
        double r199982 = sqrt(r199981);
        double r199983 = r199968 / r199982;
        double r199984 = r199977 * r199983;
        return r199984;
}

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 2020045 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))