Average Error: 4.0 → 2.7
Time: 44.0s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\frac{x}{x + y \cdot e^{2 \cdot \left(\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}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r124537 = x;
        double r124538 = y;
        double r124539 = 2.0;
        double r124540 = z;
        double r124541 = t;
        double r124542 = a;
        double r124543 = r124541 + r124542;
        double r124544 = sqrt(r124543);
        double r124545 = r124540 * r124544;
        double r124546 = r124545 / r124541;
        double r124547 = b;
        double r124548 = c;
        double r124549 = r124547 - r124548;
        double r124550 = 5.0;
        double r124551 = 6.0;
        double r124552 = r124550 / r124551;
        double r124553 = r124542 + r124552;
        double r124554 = 3.0;
        double r124555 = r124541 * r124554;
        double r124556 = r124539 / r124555;
        double r124557 = r124553 - r124556;
        double r124558 = r124549 * r124557;
        double r124559 = r124546 - r124558;
        double r124560 = r124539 * r124559;
        double r124561 = exp(r124560);
        double r124562 = r124538 * r124561;
        double r124563 = r124537 + r124562;
        double r124564 = r124537 / r124563;
        return r124564;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r124565 = x;
        double r124566 = y;
        double r124567 = 2.0;
        double r124568 = z;
        double r124569 = t;
        double r124570 = cbrt(r124569);
        double r124571 = r124570 * r124570;
        double r124572 = r124568 / r124571;
        double r124573 = a;
        double r124574 = r124569 + r124573;
        double r124575 = sqrt(r124574);
        double r124576 = r124575 / r124570;
        double r124577 = r124572 * r124576;
        double r124578 = b;
        double r124579 = c;
        double r124580 = r124578 - r124579;
        double r124581 = 5.0;
        double r124582 = 6.0;
        double r124583 = r124581 / r124582;
        double r124584 = r124573 + r124583;
        double r124585 = 3.0;
        double r124586 = r124569 * r124585;
        double r124587 = r124567 / r124586;
        double r124588 = r124584 - r124587;
        double r124589 = r124580 * r124588;
        double r124590 = r124577 - r124589;
        double r124591 = r124567 * r124590;
        double r124592 = exp(r124591);
        double r124593 = r124566 * r124592;
        double r124594 = r124565 + r124593;
        double r124595 = r124565 / r124594;
        return r124595;
}

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 4.0

    \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt4.0

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  4. Applied times-frac2.7

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

  5. Final simplification2.7

    \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))