Average Error: 3.7 → 2.6
Time: 28.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{\left(\frac{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}\]
\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{\sqrt{a + t}}{\sqrt[3]{t}} \cdot \frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1572626 = x;
        double r1572627 = y;
        double r1572628 = 2.0;
        double r1572629 = z;
        double r1572630 = t;
        double r1572631 = a;
        double r1572632 = r1572630 + r1572631;
        double r1572633 = sqrt(r1572632);
        double r1572634 = r1572629 * r1572633;
        double r1572635 = r1572634 / r1572630;
        double r1572636 = b;
        double r1572637 = c;
        double r1572638 = r1572636 - r1572637;
        double r1572639 = 5.0;
        double r1572640 = 6.0;
        double r1572641 = r1572639 / r1572640;
        double r1572642 = r1572631 + r1572641;
        double r1572643 = 3.0;
        double r1572644 = r1572630 * r1572643;
        double r1572645 = r1572628 / r1572644;
        double r1572646 = r1572642 - r1572645;
        double r1572647 = r1572638 * r1572646;
        double r1572648 = r1572635 - r1572647;
        double r1572649 = r1572628 * r1572648;
        double r1572650 = exp(r1572649);
        double r1572651 = r1572627 * r1572650;
        double r1572652 = r1572626 + r1572651;
        double r1572653 = r1572626 / r1572652;
        return r1572653;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1572654 = x;
        double r1572655 = y;
        double r1572656 = a;
        double r1572657 = t;
        double r1572658 = r1572656 + r1572657;
        double r1572659 = sqrt(r1572658);
        double r1572660 = cbrt(r1572657);
        double r1572661 = r1572659 / r1572660;
        double r1572662 = z;
        double r1572663 = r1572660 * r1572660;
        double r1572664 = r1572662 / r1572663;
        double r1572665 = r1572661 * r1572664;
        double r1572666 = 5.0;
        double r1572667 = 6.0;
        double r1572668 = r1572666 / r1572667;
        double r1572669 = r1572656 + r1572668;
        double r1572670 = 2.0;
        double r1572671 = 3.0;
        double r1572672 = r1572657 * r1572671;
        double r1572673 = r1572670 / r1572672;
        double r1572674 = r1572669 - r1572673;
        double r1572675 = b;
        double r1572676 = c;
        double r1572677 = r1572675 - r1572676;
        double r1572678 = r1572674 * r1572677;
        double r1572679 = r1572665 - r1572678;
        double r1572680 = r1572679 * r1572670;
        double r1572681 = exp(r1572680);
        double r1572682 = r1572655 * r1572681;
        double r1572683 = r1572654 + r1572682;
        double r1572684 = r1572654 / r1572683;
        return r1572684;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.7

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

  3. Applied add-cube-cbrt3.7

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

  4. Applied times-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2019154 
(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)))))))))))