Average Error: 1.0 → 0.0
Time: 5.0s
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 r214067 = 4.0;
        double r214068 = 3.0;
        double r214069 = atan2(1.0, 0.0);
        double r214070 = r214068 * r214069;
        double r214071 = 1.0;
        double r214072 = v;
        double r214073 = r214072 * r214072;
        double r214074 = r214071 - r214073;
        double r214075 = r214070 * r214074;
        double r214076 = 2.0;
        double r214077 = 6.0;
        double r214078 = r214077 * r214073;
        double r214079 = r214076 - r214078;
        double r214080 = sqrt(r214079);
        double r214081 = r214075 * r214080;
        double r214082 = r214067 / r214081;
        return r214082;
}
↓
double f(double v) {
        double r214083 = 4.0;
        double r214084 = sqrt(r214083);
        double r214085 = 3.0;
        double r214086 = atan2(1.0, 0.0);
        double r214087 = r214085 * r214086;
        double r214088 = 1.0;
        double r214089 = v;
        double r214090 = r214089 * r214089;
        double r214091 = r214088 - r214090;
        double r214092 = r214087 * r214091;
        double r214093 = r214084 / r214092;
        double r214094 = 2.0;
        double r214095 = 6.0;
        double r214096 = r214095 * r214090;
        double r214097 = r214094 - r214096;
        double r214098 = sqrt(r214097);
        double r214099 = r214084 / r214098;
        double r214100 = r214093 * r214099;
        return r214100;
}

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 2020056 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))