Average Error: 9.6 → 0.1
Time: 16.9s
Precision: 64
\[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\]
↓
\[\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)\]
\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}
↓
\frac{x}{y} + \left(\left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) - 2\right)
double f(double x, double y, double z, double t) {
        double r593802 = x;
        double r593803 = y;
        double r593804 = r593802 / r593803;
        double r593805 = 2.0;
        double r593806 = z;
        double r593807 = r593806 * r593805;
        double r593808 = 1.0;
        double r593809 = t;
        double r593810 = r593808 - r593809;
        double r593811 = r593807 * r593810;
        double r593812 = r593805 + r593811;
        double r593813 = r593809 * r593806;
        double r593814 = r593812 / r593813;
        double r593815 = r593804 + r593814;
        return r593815;
}
↓
double f(double x, double y, double z, double t) {
        double r593816 = x;
        double r593817 = y;
        double r593818 = r593816 / r593817;
        double r593819 = 2.0;
        double r593820 = t;
        double r593821 = r593819 / r593820;
        double r593822 = z;
        double r593823 = r593821 / r593822;
        double r593824 = r593821 + r593823;
        double r593825 = r593824 - r593819;
        double r593826 = r593818 + r593825;
        return r593826;
}

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

Original9.6
Target0.1
Herbie0.1
\[\frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right)\]

Derivation

  1. Initial program 9.6

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

  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

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

  5. Applied associate-/r*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))