Average Error: 6.3 → 0.9
Time: 5.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.692802743980515 \cdot 10^{+154} \lor \neg \left(y \cdot \left(z - t\right) \leq 1.643207220262327 \cdot 10^{+82}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \leq -2.692802743980515 \cdot 10^{+154} \lor \neg \left(y \cdot \left(z - t\right) \leq 1.643207220262327 \cdot 10^{+82}\right):\\
\;\;\;\;\left(z - t\right) \cdot \frac{y}{a} + x\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{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 (or (<= (* y (- z t)) -2.692802743980515e+154)
         (not (<= (* y (- z t)) 1.643207220262327e+82)))
   (+ (* (- z t) (/ y a)) x)
   (+ 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)) <= -2.692802743980515e+154) || !((y * (z - t)) <= 1.643207220262327e+82)) {
		tmp = ((z - t) * (y / a)) + x;
	} 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

Original6.3
Target0.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 y (-.f64 z t)) < -2.69280274398051471e154 or 1.64320722026232701e82 < (*.f64 y (-.f64 z t))

    1. Initial program 18.1

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

    3. Applied add-cube-cbrt_binary64_1123018.6

      \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

    4. Applied times-frac_binary64_112042.4

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

    6. Applied pow1_binary64_112562.4

      \[\leadsto x + \frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \color{blue}{{\left(\frac{z - t}{\sqrt[3]{a}}\right)}^{1}}\]

    7. Applied pow1_binary64_112562.4

      \[\leadsto x + \color{blue}{{\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}}\right)}^{1}} \cdot {\left(\frac{z - t}{\sqrt[3]{a}}\right)}^{1}\]

    8. Applied pow-prod-down_binary64_112662.4

      \[\leadsto x + \color{blue}{{\left(\frac{y}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{z - t}{\sqrt[3]{a}}\right)}^{1}}\]

    9. Simplified1.7

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

    10. Taylor expanded around 0 18.1

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

    11. Simplified1.7

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

    if -2.69280274398051471e154 < (*.f64 y (-.f64 z t)) < 1.64320722026232701e82

    1. Initial program 0.5

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2.692802743980515 \cdot 10^{+154} \lor \neg \left(y \cdot \left(z - t\right) \leq 1.643207220262327 \cdot 10^{+82}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(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)))