Average Error: 0.4 → 0.3
Time: 1.8m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\left(1 - v \cdot v\right) \cdot t}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\left(1 - v \cdot v\right) \cdot t}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v, double t) {
        double r9559936 = 1.0;
        double r9559937 = 5.0;
        double r9559938 = v;
        double r9559939 = r9559938 * r9559938;
        double r9559940 = r9559937 * r9559939;
        double r9559941 = r9559936 - r9559940;
        double r9559942 = atan2(1.0, 0.0);
        double r9559943 = t;
        double r9559944 = r9559942 * r9559943;
        double r9559945 = 2.0;
        double r9559946 = 3.0;
        double r9559947 = r9559946 * r9559939;
        double r9559948 = r9559936 - r9559947;
        double r9559949 = r9559945 * r9559948;
        double r9559950 = sqrt(r9559949);
        double r9559951 = r9559944 * r9559950;
        double r9559952 = r9559936 - r9559939;
        double r9559953 = r9559951 * r9559952;
        double r9559954 = r9559941 / r9559953;
        return r9559954;
}
↓
double f(double v, double t) {
        double r9559955 = 1.0;
        double r9559956 = v;
        double r9559957 = r9559956 * r9559956;
        double r9559958 = 5.0;
        double r9559959 = r9559957 * r9559958;
        double r9559960 = r9559955 - r9559959;
        double r9559961 = atan2(1.0, 0.0);
        double r9559962 = r9559960 / r9559961;
        double r9559963 = r9559955 - r9559957;
        double r9559964 = t;
        double r9559965 = r9559963 * r9559964;
        double r9559966 = r9559962 / r9559965;
        double r9559967 = 2.0;
        double r9559968 = 6.0;
        double r9559969 = r9559957 * r9559968;
        double r9559970 = r9559967 - r9559969;
        double r9559971 = sqrt(r9559970);
        double r9559972 = r9559966 / r9559971;
        return r9559972;
}

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 0.4

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\left(1 - v \cdot v\right) \cdot t}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]

Reproduce

herbie shell --seed 2019130 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))