Average Error: 9.3 → 0.1
Time: 21.0s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} - 2\right)
double f(double x, double y, double z, double t) {
        double r464116 = x;
        double r464117 = y;
        double r464118 = r464116 / r464117;
        double r464119 = 2.0;
        double r464120 = z;
        double r464121 = r464120 * r464119;
        double r464122 = 1.0;
        double r464123 = t;
        double r464124 = r464122 - r464123;
        double r464125 = r464121 * r464124;
        double r464126 = r464119 + r464125;
        double r464127 = r464123 * r464120;
        double r464128 = r464126 / r464127;
        double r464129 = r464118 + r464128;
        return r464129;
}
↓
double f(double x, double y, double z, double t) {
        double r464130 = 2.0;
        double r464131 = t;
        double r464132 = r464130 / r464131;
        double r464133 = z;
        double r464134 = r464132 / r464133;
        double r464135 = r464132 + r464134;
        double r464136 = x;
        double r464137 = y;
        double r464138 = r464136 / r464137;
        double r464139 = r464138 - r464130;
        double r464140 = r464135 + r464139;
        return r464140;
}

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

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

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))))