Average Error: 6.6 → 2.5
Time: 4.5s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x + \frac{y}{a} \cdot \left(z - t\right)\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
x + \frac{y}{a} \cdot \left(z - t\right)
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (y * ((double) (z - t)))) / a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) ((y / a) * ((double) (z - t))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.6
Target0.7
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 6.6

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

  2. Simplified6.0

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

  4. Applied clear-num6.1

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

  6. Applied associate-/r/6.1

    \[\leadsto x + y \cdot \color{blue}{\left(\frac{1}{a} \cdot \left(z - t\right)\right)}\]

  7. Applied associate-*r*2.5

    \[\leadsto x + \color{blue}{\left(y \cdot \frac{1}{a}\right) \cdot \left(z - t\right)}\]

  8. Simplified2.5

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

  9. Final simplification2.5

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

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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