Average Error: 9.5 → 0.1
Time: 4.0min
Precision: binary64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{\frac{2}{z} + 2 \cdot 1}{t} - \left(2 - \frac{x}{y}\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{\frac{2}{z} + 2 \cdot 1}{t} - \left(2 - \frac{x}{y}\right)
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 / z) + ((double) (2.0 * 1.0)))) / t) - ((double) (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

Original9.5
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.5

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020181 
(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))))