Average Error: 6.6 → 2.0
Time: 3.1s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[x + \frac{\frac{y}{t}}{\frac{1}{z - x}}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
x + \frac{\frac{y}{t}}{\frac{1}{z - x}}
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) (y / t)) / ((double) (1.0 / ((double) (z - x))))))));
}

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

Original6.6
Target1.9
Herbie2.0
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Initial program 6.6

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

  3. Applied associate-/l*5.8

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

  5. Applied div-inv5.8

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

  6. Applied associate-/r*2.0

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

  7. Final simplification2.0

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

Reproduce

herbie shell --seed 2020161 
(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)) (* (neg z) (/ y t))))

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