Average Error: 3.8 → 2.6
Time: 8.6s
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 r57463 = x;
        double r57464 = y;
        double r57465 = 2.0;
        double r57466 = z;
        double r57467 = t;
        double r57468 = a;
        double r57469 = r57467 + r57468;
        double r57470 = sqrt(r57469);
        double r57471 = r57466 * r57470;
        double r57472 = r57471 / r57467;
        double r57473 = b;
        double r57474 = c;
        double r57475 = r57473 - r57474;
        double r57476 = 5.0;
        double r57477 = 6.0;
        double r57478 = r57476 / r57477;
        double r57479 = r57468 + r57478;
        double r57480 = 3.0;
        double r57481 = r57467 * r57480;
        double r57482 = r57465 / r57481;
        double r57483 = r57479 - r57482;
        double r57484 = r57475 * r57483;
        double r57485 = r57472 - r57484;
        double r57486 = r57465 * r57485;
        double r57487 = exp(r57486);
        double r57488 = r57464 * r57487;
        double r57489 = r57463 + r57488;
        double r57490 = r57463 / r57489;
        return r57490;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r57491 = x;
        double r57492 = y;
        double r57493 = 2.0;
        double r57494 = z;
        double r57495 = t;
        double r57496 = cbrt(r57495);
        double r57497 = r57496 * r57496;
        double r57498 = r57494 / r57497;
        double r57499 = a;
        double r57500 = r57495 + r57499;
        double r57501 = sqrt(r57500);
        double r57502 = r57501 / r57496;
        double r57503 = r57498 * r57502;
        double r57504 = b;
        double r57505 = c;
        double r57506 = r57504 - r57505;
        double r57507 = 5.0;
        double r57508 = 6.0;
        double r57509 = r57507 / r57508;
        double r57510 = r57499 + r57509;
        double r57511 = 3.0;
        double r57512 = r57495 * r57511;
        double r57513 = r57493 / r57512;
        double r57514 = r57510 - r57513;
        double r57515 = r57506 * r57514;
        double r57516 = r57503 - r57515;
        double r57517 = r57493 * r57516;
        double r57518 = exp(r57517);
        double r57519 = r57492 * r57518;
        double r57520 = r57491 + r57519;
        double r57521 = r57491 / r57520;
        return r57521;
}

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 3.8

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

  3. Applied add-cube-cbrt3.8

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

  4. Applied times-frac2.6

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

  5. Final simplification2.6

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

Reproduce

herbie shell --seed 2020100 
(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)))))))))))