Average Error: 9.8 → 0.1
Time: 57.8s
Precision: binary64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{t}}{z} + \frac{x}{y}\right) + \left(\frac{2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{t}}{z} + \frac{x}{y}\right) + \left(\frac{2}{t} - 2\right)
(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
↓
(FPCore (x y z t)
 :precision binary64
 (+ (+ (/ (/ 2.0 t) z) (/ x y)) (- (/ 2.0 t) 2.0)))
double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}
↓
double code(double x, double y, double z, double t) {
	return (((2.0 / t) / z) + (x / y)) + ((2.0 / t) - 2.0);
}

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

Original9.8
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.8

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

  2. Simplified0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2021176 
(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))))