Average Error: 6.5 → 1.9
Time: 2.7s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{z - x}{\frac{t}{y}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{z - x}{\frac{t}{y}}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - x)))) / t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (z - x)) / ((double) (t / y))))));
}

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

Original6.5
Target2.0
Herbie1.9
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied clear-num6.6

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

  5. Applied associate-/r*2.0

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

  6. Taylor expanded around 0 6.5

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

  7. Simplified1.9

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

  8. Final simplification1.9

    \[\leadsto x + \frac{z - x}{\frac{t}{y}}\]

Reproduce

herbie shell --seed 2020126 
(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)))