Average Error: 5.9 → 2.6
Time: 7.5s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[x - \frac{\frac{1}{a} \cdot y}{\frac{1}{z - t}}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
x - \frac{\frac{1}{a} \cdot y}{\frac{1}{z - t}}
(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a)
 :precision binary64
 (- x (/ (* (/ 1.0 a) y) (/ 1.0 (- z t)))))
double code(double x, double y, double z, double t, double a) {
	return x - ((y * (z - t)) / a);
}
↓
double code(double x, double y, double z, double t, double a) {
	return x - (((1.0 / a) * y) / (1.0 / (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

Original5.9
Target0.6
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Initial program 5.9

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

  3. Applied clear-num_binary64_96256.0

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

  5. Applied associate-/r*_binary64_95702.5

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

  7. Applied div-inv_binary64_96232.5

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

  8. Applied associate-/r*_binary64_95702.7

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

  9. Simplified2.6

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

  10. Final simplification2.6

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

Reproduce

herbie shell --seed 2020352 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))