Average Error: 9.5 → 0.1
Time: 11.2s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) - 2
double f(double x, double y, double z, double t) {
        double r593109 = x;
        double r593110 = y;
        double r593111 = r593109 / r593110;
        double r593112 = 2.0;
        double r593113 = z;
        double r593114 = r593113 * r593112;
        double r593115 = 1.0;
        double r593116 = t;
        double r593117 = r593115 - r593116;
        double r593118 = r593114 * r593117;
        double r593119 = r593112 + r593118;
        double r593120 = r593116 * r593113;
        double r593121 = r593119 / r593120;
        double r593122 = r593111 + r593121;
        return r593122;
}
↓
double f(double x, double y, double z, double t) {
        double r593123 = 2.0;
        double r593124 = z;
        double r593125 = r593123 / r593124;
        double r593126 = r593125 + r593123;
        double r593127 = t;
        double r593128 = r593126 / r593127;
        double r593129 = x;
        double r593130 = y;
        double r593131 = r593129 / r593130;
        double r593132 = r593128 + r593131;
        double r593133 = r593132 - r593123;
        return r593133;
}

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. 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 sub-neg0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019297 
(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))))