Average Error: 6.0 → 0.7
Time: 2.5s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.5913530452109281 \cdot 10^{32} \lor \neg \left(y \le 3.7470210040198909 \cdot 10^{-26}\right):\\ \;\;\;\;x - \frac{-y}{\frac{-a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.5913530452109281 \cdot 10^{32} \lor \neg \left(y \le 3.7470210040198909 \cdot 10^{-26}\right):\\
\;\;\;\;x - \frac{-y}{\frac{-a}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\

\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 <= -3.591353045210928e+32) || !(y <= 3.747021004019891e-26))) {
		VAR = ((double) (x - ((double) (((double) -(y)) / ((double) (((double) -(a)) / ((double) (z - t))))))));
	} else {
		VAR = ((double) (x - ((double) (((double) (((double) (z * y)) / a)) - ((double) (((double) (t * y)) / a))))));
	}
	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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.591353045210928e+32 or 3.747021004019891e-26 < y

    1. Initial program 15.1

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

    3. Applied *-commutative15.1

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

    4. Applied associate-/l*3.4

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

    6. Applied frac-2neg3.4

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

    7. Applied associate-/r/1.0

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

    9. Applied clear-num1.1

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

    10. Applied associate-*l/0.9

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

    11. Simplified0.9

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

    if -3.591353045210928e+32 < y < 3.747021004019891e-26

    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*1.9

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

    6. Applied frac-2neg1.9

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

    7. Applied associate-/r/9.0

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

    8. Taylor expanded around 0 0.5

      \[\leadsto x - \color{blue}{\left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.5913530452109281 \cdot 10^{32} \lor \neg \left(y \le 3.7470210040198909 \cdot 10^{-26}\right):\\ \;\;\;\;x - \frac{-y}{\frac{-a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(\frac{z \cdot y}{a} - \frac{t \cdot y}{a}\right)\\ \end{array}\]

Reproduce

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

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