Average Error: 9.1 → 0.1
Time: 10.6s
Precision: binary64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
↓
\[\frac{x}{y} + \left(-2 - \left(\frac{-2}{t} + \frac{-2}{t \cdot z}\right)\right) \]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(-2 - \left(\frac{-2}{t} + \frac{-2}{t \cdot z}\right)\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
 (+ (/ x y) (- -2.0 (+ (/ -2.0 t) (/ -2.0 (* t z))))))
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 (x / y) + (-2.0 - ((-2.0 / t) + (-2.0 / (t * z))));
}

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

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

Derivation

  1. Initial program 9.1

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

  2. Simplified0.1

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

  3. Applied add-cube-cbrt_binary640.6

    \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\left(\sqrt[3]{\frac{-2 + \frac{-2}{z}}{t}} \cdot \sqrt[3]{\frac{-2 + \frac{-2}{z}}{t}}\right) \cdot \sqrt[3]{\frac{-2 + \frac{-2}{z}}{t}}}\right) \]

  4. Taylor expanded in z around 0 0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021280 
(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))))