Average Error: 9.7 → 0.1
Time: 2.8s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\left(\frac{\frac{2}{z} + 2}{t} + \frac{x}{y}\right) + \left(-2\right)\]
\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) + \left(-2\right)
double f(double x, double y, double z, double t) {
        double r899405 = x;
        double r899406 = y;
        double r899407 = r899405 / r899406;
        double r899408 = 2.0;
        double r899409 = z;
        double r899410 = r899409 * r899408;
        double r899411 = 1.0;
        double r899412 = t;
        double r899413 = r899411 - r899412;
        double r899414 = r899410 * r899413;
        double r899415 = r899408 + r899414;
        double r899416 = r899412 * r899409;
        double r899417 = r899415 / r899416;
        double r899418 = r899407 + r899417;
        return r899418;
}
↓
double f(double x, double y, double z, double t) {
        double r899419 = 2.0;
        double r899420 = z;
        double r899421 = r899419 / r899420;
        double r899422 = r899421 + r899419;
        double r899423 = t;
        double r899424 = r899422 / r899423;
        double r899425 = x;
        double r899426 = y;
        double r899427 = r899425 / r899426;
        double r899428 = r899424 + r899427;
        double r899429 = -r899419;
        double r899430 = r899428 + r899429;
        return r899430;
}

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

Original9.7
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.7

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

  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

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

Reproduce

herbie shell --seed 2020025 
(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))))