Average Error: 0.5 → 0.5
Time: 6.9s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\sqrt{\pi} \cdot \left(\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right) \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\sqrt{\pi} \cdot \left(\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right) \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r200922 = 1.0;
        double r200923 = 5.0;
        double r200924 = v;
        double r200925 = r200924 * r200924;
        double r200926 = r200923 * r200925;
        double r200927 = r200922 - r200926;
        double r200928 = atan2(1.0, 0.0);
        double r200929 = t;
        double r200930 = r200928 * r200929;
        double r200931 = 2.0;
        double r200932 = 3.0;
        double r200933 = r200932 * r200925;
        double r200934 = r200922 - r200933;
        double r200935 = r200931 * r200934;
        double r200936 = sqrt(r200935);
        double r200937 = r200930 * r200936;
        double r200938 = r200922 - r200925;
        double r200939 = r200937 * r200938;
        double r200940 = r200927 / r200939;
        return r200940;
}
↓
double f(double v, double t) {
        double r200941 = 1.0;
        double r200942 = 5.0;
        double r200943 = v;
        double r200944 = r200943 * r200943;
        double r200945 = r200942 * r200944;
        double r200946 = r200941 - r200945;
        double r200947 = atan2(1.0, 0.0);
        double r200948 = sqrt(r200947);
        double r200949 = sqrt(r200948);
        double r200950 = r200949 * r200949;
        double r200951 = t;
        double r200952 = 2.0;
        double r200953 = 3.0;
        double r200954 = r200953 * r200944;
        double r200955 = r200941 - r200954;
        double r200956 = r200952 * r200955;
        double r200957 = sqrt(r200956);
        double r200958 = r200951 * r200957;
        double r200959 = r200950 * r200958;
        double r200960 = r200948 * r200959;
        double r200961 = r200941 - r200944;
        double r200962 = r200960 * r200961;
        double r200963 = r200946 / r200962;
        return r200963;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied associate-*l*0.5

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)} \cdot \left(1 - v \cdot v\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.8

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\color{blue}{\left(\sqrt{\pi} \cdot \sqrt{\pi}\right)} \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]

  6. Applied associate-*l*0.7

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\left(\sqrt{\pi} \cdot \left(\sqrt{\pi} \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right)} \cdot \left(1 - v \cdot v\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.7

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\sqrt{\pi} \cdot \left(\sqrt{\color{blue}{\sqrt{\pi} \cdot \sqrt{\pi}}} \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right) \cdot \left(1 - v \cdot v\right)}\]

  9. Applied sqrt-prod0.5

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\sqrt{\pi} \cdot \left(\color{blue}{\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right)} \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right) \cdot \left(1 - v \cdot v\right)}\]

  10. Final simplification0.5

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\sqrt{\pi} \cdot \left(\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right) \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)\right) \cdot \left(1 - v \cdot v\right)}\]

Reproduce

herbie shell --seed 2020033 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))