Average Error: 6.0 → 0.8
Time: 4.1s
Precision: binary64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.7144402286755834 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.2509373205922187 \cdot 10^{+181}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -2.7144402286755834 \cdot 10^{+130}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\

\mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.2509373205922187 \cdot 10^{+181}:\\
\;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (- x (/ (* y (- z t)) a)))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (- z t)) -2.7144402286755834e+130)
   (+ x (* (/ y a) (- t z)))
   (if (<= (* y (- z t)) 2.2509373205922187e+181)
     (- x (/ 1.0 (/ a (* y (- z t)))))
     (- x (* y (/ (- z t) a))))))
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) {
	double tmp;
	if ((y * (z - t)) <= -2.7144402286755834e+130) {
		tmp = x + ((y / a) * (t - z));
	} else if ((y * (z - t)) <= 2.2509373205922187e+181) {
		tmp = x - (1.0 / (a / (y * (z - t))));
	} else {
		tmp = x - (y * ((z - t) / a));
	}
	return tmp;
}

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
Target0.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 y (-.f64 z t)) < -2.71444022867558344e130

    1. Initial program 20.2

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

    3. Applied sub-neg_binary64_984320.2

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

    4. Simplified1.5

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

    if -2.71444022867558344e130 < (*.f64 y (-.f64 z t)) < 2.250937320592219e181

    1. Initial program 0.5

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

    3. Applied clear-num_binary64_98490.5

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

    if 2.250937320592219e181 < (*.f64 y (-.f64 z t))

    1. Initial program 23.2

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

    3. Applied *-un-lft-identity_binary64_985023.2

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

    4. Applied times-frac_binary64_98561.7

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

    5. Simplified1.7

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.7144402286755834 \cdot 10^{+130}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2.2509373205922187 \cdot 10^{+181}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020281 
(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)))