Average Error: 9.3 → 0.1
Time: 3.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{1}{t} \cdot \left(\frac{2}{z} + 2\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r755476 = x;
        double r755477 = y;
        double r755478 = r755476 / r755477;
        double r755479 = 2.0;
        double r755480 = z;
        double r755481 = r755480 * r755479;
        double r755482 = 1.0;
        double r755483 = t;
        double r755484 = r755482 - r755483;
        double r755485 = r755481 * r755484;
        double r755486 = r755479 + r755485;
        double r755487 = r755483 * r755480;
        double r755488 = r755486 / r755487;
        double r755489 = r755478 + r755488;
        return r755489;
}
↓
double f(double x, double y, double z, double t) {
        double r755490 = x;
        double r755491 = y;
        double r755492 = r755490 / r755491;
        double r755493 = 1.0;
        double r755494 = t;
        double r755495 = r755493 / r755494;
        double r755496 = 2.0;
        double r755497 = z;
        double r755498 = r755496 / r755497;
        double r755499 = r755498 + r755496;
        double r755500 = r755495 * r755499;
        double r755501 = r755500 - r755496;
        double r755502 = r755492 + r755501;
        return r755502;
}

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

Original9.3
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.3

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

  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

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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))))