Average Error: 3.6 → 1.6
Time: 19.3s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{\mathsf{fma}\left(y, e^{2.0 \cdot \mathsf{fma}\left(c - b, \frac{5.0}{6.0} - \left(\frac{\frac{2.0}{t}}{3.0} - a\right), \frac{\sqrt{a + t}}{\frac{t}{z}}\right)}, x\right)}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}
↓
\frac{x}{\mathsf{fma}\left(y, e^{2.0 \cdot \mathsf{fma}\left(c - b, \frac{5.0}{6.0} - \left(\frac{\frac{2.0}{t}}{3.0} - a\right), \frac{\sqrt{a + t}}{\frac{t}{z}}\right)}, x\right)}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2603653 = x;
        double r2603654 = y;
        double r2603655 = 2.0;
        double r2603656 = z;
        double r2603657 = t;
        double r2603658 = a;
        double r2603659 = r2603657 + r2603658;
        double r2603660 = sqrt(r2603659);
        double r2603661 = r2603656 * r2603660;
        double r2603662 = r2603661 / r2603657;
        double r2603663 = b;
        double r2603664 = c;
        double r2603665 = r2603663 - r2603664;
        double r2603666 = 5.0;
        double r2603667 = 6.0;
        double r2603668 = r2603666 / r2603667;
        double r2603669 = r2603658 + r2603668;
        double r2603670 = 3.0;
        double r2603671 = r2603657 * r2603670;
        double r2603672 = r2603655 / r2603671;
        double r2603673 = r2603669 - r2603672;
        double r2603674 = r2603665 * r2603673;
        double r2603675 = r2603662 - r2603674;
        double r2603676 = r2603655 * r2603675;
        double r2603677 = exp(r2603676);
        double r2603678 = r2603654 * r2603677;
        double r2603679 = r2603653 + r2603678;
        double r2603680 = r2603653 / r2603679;
        return r2603680;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r2603681 = x;
        double r2603682 = y;
        double r2603683 = 2.0;
        double r2603684 = c;
        double r2603685 = b;
        double r2603686 = r2603684 - r2603685;
        double r2603687 = 5.0;
        double r2603688 = 6.0;
        double r2603689 = r2603687 / r2603688;
        double r2603690 = t;
        double r2603691 = r2603683 / r2603690;
        double r2603692 = 3.0;
        double r2603693 = r2603691 / r2603692;
        double r2603694 = a;
        double r2603695 = r2603693 - r2603694;
        double r2603696 = r2603689 - r2603695;
        double r2603697 = r2603694 + r2603690;
        double r2603698 = sqrt(r2603697);
        double r2603699 = z;
        double r2603700 = r2603690 / r2603699;
        double r2603701 = r2603698 / r2603700;
        double r2603702 = fma(r2603686, r2603696, r2603701);
        double r2603703 = r2603683 * r2603702;
        double r2603704 = exp(r2603703);
        double r2603705 = fma(r2603682, r2603704, r2603681);
        double r2603706 = r2603681 / r2603705;
        return r2603706;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 3.6

    \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  2. Simplified1.6

    \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, e^{2.0 \cdot \mathsf{fma}\left(c - b, \frac{5.0}{6.0} - \left(\frac{\frac{2.0}{t}}{3.0} - a\right), \frac{\sqrt{a + t}}{\frac{t}{z}}\right)}, x\right)}}\]

  3. Final simplification1.6

    \[\leadsto \frac{x}{\mathsf{fma}\left(y, e^{2.0 \cdot \mathsf{fma}\left(c - b, \frac{5.0}{6.0} - \left(\frac{\frac{2.0}{t}}{3.0} - a\right), \frac{\sqrt{a + t}}{\frac{t}{z}}\right)}, x\right)}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))