Average Error: 0.4 → 0.3
Time: 1.1m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]
\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}{1 - v \cdot v}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}
double f(double v, double t) {
        double r7808088 = 1.0;
        double r7808089 = 5.0;
        double r7808090 = v;
        double r7808091 = r7808090 * r7808090;
        double r7808092 = r7808089 * r7808091;
        double r7808093 = r7808088 - r7808092;
        double r7808094 = atan2(1.0, 0.0);
        double r7808095 = t;
        double r7808096 = r7808094 * r7808095;
        double r7808097 = 2.0;
        double r7808098 = 3.0;
        double r7808099 = r7808098 * r7808091;
        double r7808100 = r7808088 - r7808099;
        double r7808101 = r7808097 * r7808100;
        double r7808102 = sqrt(r7808101);
        double r7808103 = r7808096 * r7808102;
        double r7808104 = r7808088 - r7808091;
        double r7808105 = r7808103 * r7808104;
        double r7808106 = r7808093 / r7808105;
        return r7808106;
}
↓
double f(double v, double t) {
        double r7808107 = 1.0;
        double r7808108 = v;
        double r7808109 = r7808108 * r7808108;
        double r7808110 = 5.0;
        double r7808111 = r7808109 * r7808110;
        double r7808112 = r7808107 - r7808111;
        double r7808113 = r7808107 - r7808109;
        double r7808114 = r7808112 / r7808113;
        double r7808115 = atan2(1.0, 0.0);
        double r7808116 = r7808114 / r7808115;
        double r7808117 = t;
        double r7808118 = r7808116 / r7808117;
        double r7808119 = -6.0;
        double r7808120 = r7808109 * r7808119;
        double r7808121 = 2.0;
        double r7808122 = r7808120 + r7808121;
        double r7808123 = sqrt(r7808122);
        double r7808124 = r7808118 / r7808123;
        return r7808124;
}

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

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019143 
(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)))))