Average Error: 0.5 → 0.3
Time: 2.7m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{2 \cdot \left(1 - \left(v \cdot v\right) \cdot 3\right)}}}{1 - v \cdot v}\]
\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{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{t}}{\sqrt{2 \cdot \left(1 - \left(v \cdot v\right) \cdot 3\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r41824102 = 1.0;
        double r41824103 = 5.0;
        double r41824104 = v;
        double r41824105 = r41824104 * r41824104;
        double r41824106 = r41824103 * r41824105;
        double r41824107 = r41824102 - r41824106;
        double r41824108 = atan2(1.0, 0.0);
        double r41824109 = t;
        double r41824110 = r41824108 * r41824109;
        double r41824111 = 2.0;
        double r41824112 = 3.0;
        double r41824113 = r41824112 * r41824105;
        double r41824114 = r41824102 - r41824113;
        double r41824115 = r41824111 * r41824114;
        double r41824116 = sqrt(r41824115);
        double r41824117 = r41824110 * r41824116;
        double r41824118 = r41824102 - r41824105;
        double r41824119 = r41824117 * r41824118;
        double r41824120 = r41824107 / r41824119;
        return r41824120;
}
↓
double f(double v, double t) {
        double r41824121 = 1.0;
        double r41824122 = v;
        double r41824123 = r41824122 * r41824122;
        double r41824124 = 5.0;
        double r41824125 = r41824123 * r41824124;
        double r41824126 = r41824121 - r41824125;
        double r41824127 = atan2(1.0, 0.0);
        double r41824128 = r41824126 / r41824127;
        double r41824129 = t;
        double r41824130 = r41824128 / r41824129;
        double r41824131 = 2.0;
        double r41824132 = 3.0;
        double r41824133 = r41824123 * r41824132;
        double r41824134 = r41824121 - r41824133;
        double r41824135 = r41824131 * r41824134;
        double r41824136 = sqrt(r41824135);
        double r41824137 = r41824130 / r41824136;
        double r41824138 = r41824121 - r41824123;
        double r41824139 = r41824137 / r41824138;
        return r41824139;
}

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-/r*0.5

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

  5. Applied associate-/r*0.4

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

  7. Applied associate-/r*0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019121 
(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)))))