Average Error: 2.0 → 1.5
Time: 4.6s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\
\;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (((x / y) * (z - t)) + t);
}
↓
double code(double x, double y, double z, double t) {
	double temp;
	if (((y <= -5.910237375042319e+67) || !(y <= 4.006446543357022e-49))) {
		temp = (((x / y) * (z - t)) + t);
	} else {
		temp = (((x * (z - t)) / y) + t);
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.1
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.910237375042319e+67 or 4.006446543357022e-49 < y

    1. Initial program 0.9

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

    if -5.910237375042319e+67 < y < 4.006446543357022e-49

    1. Initial program 3.6

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

    3. Applied add-cube-cbrt4.3

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

    4. Applied *-un-lft-identity4.3

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

    5. Applied times-frac4.3

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

    6. Applied associate-*l*2.3

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]
    7. Using strategy rm

    8. Applied associate-*l/3.1

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

    9. Applied frac-times3.1

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

    10. Simplified3.1

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

    11. Simplified2.3

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.910237375042319 \cdot 10^{67} \lor \neg \left(y \le 4.0064465433570219 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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