Average Error: 9.3 → 0.1
Time: 6.6s
Precision: binary64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \left(\frac{2}{z \cdot t} - 2\right)\right) + \frac{x}{y}\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \left(\frac{2}{z \cdot t} - 2\right)\right) + \frac{x}{y}
double code(double x, double y, double z, double t) {
	return ((double) ((x / y) + (((double) (2.0 + ((double) (((double) (z * 2.0)) * ((double) (1.0 - t)))))) / ((double) (t * z)))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) ((2.0 / t) + ((double) ((2.0 / ((double) (z * t))) - 2.0)))) + (x / y)));
}

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. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied div-inv0.1

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

  7. Applied associate-/l*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))