Average Error: 9.4 → 0.1
Time: 2.5s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\frac{\frac{2}{z} + 2}{t} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\frac{\frac{2}{z} + 2}{t} - 2\right)
double f(double x, double y, double z, double t) {
        double r821199 = x;
        double r821200 = y;
        double r821201 = r821199 / r821200;
        double r821202 = 2.0;
        double r821203 = z;
        double r821204 = r821203 * r821202;
        double r821205 = 1.0;
        double r821206 = t;
        double r821207 = r821205 - r821206;
        double r821208 = r821204 * r821207;
        double r821209 = r821202 + r821208;
        double r821210 = r821206 * r821203;
        double r821211 = r821209 / r821210;
        double r821212 = r821201 + r821211;
        return r821212;
}
↓
double f(double x, double y, double z, double t) {
        double r821213 = x;
        double r821214 = y;
        double r821215 = r821213 / r821214;
        double r821216 = 2.0;
        double r821217 = z;
        double r821218 = r821216 / r821217;
        double r821219 = r821218 + r821216;
        double r821220 = t;
        double r821221 = r821219 / r821220;
        double r821222 = r821221 - r821216;
        double r821223 = r821215 + r821222;
        return r821223;
}

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

Original9.4
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.4

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

  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. Using strategy rm

  5. Applied associate-*l/0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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))))