Average Error: 2.2 → 2.3
Time: 3.0s
Precision: 64
\[\frac{x}{y} \cdot \left(z - t\right) + t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.49327115381347073 \cdot 10^{-30} \lor \neg \left(t \le 1.97952534099318673 \cdot 10^{-91}\right):\\ \;\;\;\;{\left(\frac{x}{y} \cdot \left(z - t\right) + t\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]
\frac{x}{y} \cdot \left(z - t\right) + t
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.49327115381347073 \cdot 10^{-30} \lor \neg \left(t \le 1.97952534099318673 \cdot 10^{-91}\right):\\
\;\;\;\;{\left(\frac{x}{y} \cdot \left(z - t\right) + t\right)}^{1}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{z - t}{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 (((t <= -2.4932711538134707e-30) || !(t <= 1.9795253409931867e-91))) {
		temp = pow((((x / y) * (z - t)) + t), 1.0);
	} 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

Original2.2
Target2.4
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.4932711538134707e-30 or 1.9795253409931867e-91 < t

    1. Initial program 0.3

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

    3. Applied pow10.3

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

    if -2.4932711538134707e-30 < t < 1.9795253409931867e-91

    1. Initial program 4.7

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

    3. Applied div-inv4.7

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

    4. Applied associate-*l*5.0

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

    5. Simplified4.9

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.49327115381347073 \cdot 10^{-30} \lor \neg \left(t \le 1.97952534099318673 \cdot 10^{-91}\right):\\ \;\;\;\;{\left(\frac{x}{y} \cdot \left(z - t\right) + t\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020058 
(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))