Average Error: 3.8 → 1.8
Time: 1.4m
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{(\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \left(\frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) + \left(\left(-\left(b - c\right)\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right)\right))_* \cdot 2.0}}\]
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r8168554 = x;
        double r8168555 = y;
        double r8168556 = 2.0;
        double r8168557 = z;
        double r8168558 = t;
        double r8168559 = a;
        double r8168560 = r8168558 + r8168559;
        double r8168561 = sqrt(r8168560);
        double r8168562 = r8168557 * r8168561;
        double r8168563 = r8168562 / r8168558;
        double r8168564 = b;
        double r8168565 = c;
        double r8168566 = r8168564 - r8168565;
        double r8168567 = 5.0;
        double r8168568 = 6.0;
        double r8168569 = r8168567 / r8168568;
        double r8168570 = r8168559 + r8168569;
        double r8168571 = 3.0;
        double r8168572 = r8168558 * r8168571;
        double r8168573 = r8168556 / r8168572;
        double r8168574 = r8168570 - r8168573;
        double r8168575 = r8168566 * r8168574;
        double r8168576 = r8168563 - r8168575;
        double r8168577 = r8168556 * r8168576;
        double r8168578 = exp(r8168577);
        double r8168579 = r8168555 * r8168578;
        double r8168580 = r8168554 + r8168579;
        double r8168581 = r8168554 / r8168580;
        return r8168581;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r8168582 = x;
        double r8168583 = y;
        double r8168584 = z;
        double r8168585 = t;
        double r8168586 = cbrt(r8168585);
        double r8168587 = r8168586 * r8168586;
        double r8168588 = r8168584 / r8168587;
        double r8168589 = a;
        double r8168590 = r8168589 + r8168585;
        double r8168591 = sqrt(r8168590);
        double r8168592 = r8168591 / r8168586;
        double r8168593 = b;
        double r8168594 = c;
        double r8168595 = r8168593 - r8168594;
        double r8168596 = -r8168595;
        double r8168597 = 5.0;
        double r8168598 = 6.0;
        double r8168599 = r8168597 / r8168598;
        double r8168600 = r8168599 + r8168589;
        double r8168601 = 2.0;
        double r8168602 = 3.0;
        double r8168603 = r8168585 * r8168602;
        double r8168604 = r8168601 / r8168603;
        double r8168605 = r8168600 - r8168604;
        double r8168606 = r8168596 * r8168605;
        double r8168607 = fma(r8168588, r8168592, r8168606);
        double r8168608 = r8168607 * r8168601;
        double r8168609 = exp(r8168608);
        double r8168610 = r8168583 * r8168609;
        double r8168611 = r8168582 + r8168610;
        double r8168612 = r8168582 / r8168611;
        return r8168612;
}


\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}{x + y \cdot e^{(\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \left(\frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) + \left(\left(-\left(b - c\right)\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right)\right))_* \cdot 2.0}}

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 3.8

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

  3. Applied add-cube-cbrt3.8

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  4. Applied times-frac2.7

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

  5. Applied fma-neg1.8

    \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{(\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \left(\frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) + \left(-\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right))_*}}}\]

  6. Final simplification1.8

    \[\leadsto \frac{x}{x + y \cdot e^{(\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right) \cdot \left(\frac{\sqrt{a + t}}{\sqrt[3]{t}}\right) + \left(\left(-\left(b - c\right)\right) \cdot \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right)\right))_* \cdot 2.0}}\]

Reproduce

herbie shell --seed 2019101 +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)))))))))))