Average Error: 9.4 → 0.1
Time: 18.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right)
double f(double x, double y, double z, double t) {
        double r1012479 = x;
        double r1012480 = y;
        double r1012481 = r1012479 / r1012480;
        double r1012482 = 2.0;
        double r1012483 = z;
        double r1012484 = r1012483 * r1012482;
        double r1012485 = 1.0;
        double r1012486 = t;
        double r1012487 = r1012485 - r1012486;
        double r1012488 = r1012484 * r1012487;
        double r1012489 = r1012482 + r1012488;
        double r1012490 = r1012486 * r1012483;
        double r1012491 = r1012489 / r1012490;
        double r1012492 = r1012481 + r1012491;
        return r1012492;
}
↓
double f(double x, double y, double z, double t) {
        double r1012493 = x;
        double r1012494 = y;
        double r1012495 = r1012493 / r1012494;
        double r1012496 = 2.0;
        double r1012497 = t;
        double r1012498 = r1012496 / r1012497;
        double r1012499 = r1012498 - r1012496;
        double r1012500 = z;
        double r1012501 = r1012498 / r1012500;
        double r1012502 = r1012499 + r1012501;
        double r1012503 = r1012495 + r1012502;
        return r1012503;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

    \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) - 2\right)}\]

  3. Simplified0.1

    \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right)}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{y} + \left(\left(\frac{2}{t} - 2\right) + \frac{\frac{2}{t}}{z}\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y)))

  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))