Average Error: 6.0 → 1.1
Time: 2.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.49706583532450338 \cdot 10^{32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 6.520793096727247 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(\left(z - t\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot y\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.49706583532450338 \cdot 10^{32}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \le 6.520793096727247 \cdot 10^{-105}:\\
\;\;\;\;x + \frac{1}{a} \cdot \left(\left(z - t\right) \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{z - t}{a} \cdot y\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (y * ((double) (z - t)))) / a))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= -2.4970658353245034e+32)) {
		VAR = ((double) (x + ((double) (y / ((double) (a / ((double) (z - t))))))));
	} else {
		double VAR_1;
		if ((y <= 6.520793096727247e-105)) {
			VAR_1 = ((double) (x + ((double) (((double) (1.0 / a)) * ((double) (((double) (z - t)) * y))))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (z - t)) / a)) * y))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original6.0
Target0.7
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.4970658353245034e+32

    1. Initial program 17.1

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

    3. Applied *-commutative17.1

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

    4. Applied associate-/l*3.9

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

    6. Applied associate-/r/1.0

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

    8. Applied clear-num1.2

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

    9. Applied associate-*l/1.1

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

    10. Simplified1.1

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

    if -2.4970658353245034e+32 < y < 6.520793096727247e-105

    1. Initial program 0.5

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

    3. Applied *-commutative0.5

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

    4. Applied associate-/l*2.0

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

    6. Applied div-inv2.1

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

    7. Applied *-un-lft-identity2.1

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

    8. Applied times-frac0.6

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

    9. Simplified0.6

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

    if 6.520793096727247e-105 < y

    1. Initial program 9.8

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

    3. Applied *-commutative9.8

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

    4. Applied associate-/l*2.6

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

    6. Applied associate-/r/1.9

      \[\leadsto x + \color{blue}{\frac{z - t}{a} \cdot y}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.49706583532450338 \cdot 10^{32}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 6.520793096727247 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{1}{a} \cdot \left(\left(z - t\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{a} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2020114 
(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 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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