Average Error: 6.2 → 2.1
Time: 2.9s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{y}{t} \cdot \left(z - x\right)\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{y}{t} \cdot \left(z - x\right)
double f(double x, double y, double z, double t) {
        double r343754 = x;
        double r343755 = y;
        double r343756 = z;
        double r343757 = r343756 - r343754;
        double r343758 = r343755 * r343757;
        double r343759 = t;
        double r343760 = r343758 / r343759;
        double r343761 = r343754 + r343760;
        return r343761;
}
↓
double f(double x, double y, double z, double t) {
        double r343762 = x;
        double r343763 = y;
        double r343764 = t;
        double r343765 = r343763 / r343764;
        double r343766 = z;
        double r343767 = r343766 - r343762;
        double r343768 = r343765 * r343767;
        double r343769 = r343762 + r343768;
        return r343769;
}

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

Original6.2
Target2.1
Herbie2.1
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.2

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

  3. Applied clear-num6.3

    \[\leadsto x + \color{blue}{\frac{1}{\frac{t}{y \cdot \left(z - x\right)}}}\]
  4. Using strategy rm

  5. Applied associate-/r*2.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{\frac{t}{y}}{z - x}}}\]
  6. Using strategy rm

  7. Applied div-inv2.1

    \[\leadsto x + \frac{1}{\color{blue}{\frac{t}{y} \cdot \frac{1}{z - x}}}\]

  8. Applied add-sqr-sqrt2.1

    \[\leadsto x + \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\frac{t}{y} \cdot \frac{1}{z - x}}\]

  9. Applied times-frac2.3

    \[\leadsto x + \color{blue}{\frac{\sqrt{1}}{\frac{t}{y}} \cdot \frac{\sqrt{1}}{\frac{1}{z - x}}}\]

  10. Simplified2.2

    \[\leadsto x + \color{blue}{\frac{y}{t}} \cdot \frac{\sqrt{1}}{\frac{1}{z - x}}\]

  11. Simplified2.1

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

  12. Final simplification2.1

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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