Average Error: 6.3 → 1.8
Time: 3.1s
Precision: 64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.242968405003153 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 4.01571900785735227 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.242968405003153 \cdot 10^{-105}:\\
\;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\

\mathbf{elif}\;t \le 4.01571900785735227 \cdot 10^{-64}:\\
\;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return (x + ((y * (z - x)) / t));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((t <= -1.242968405003153e-105)) {
		VAR = (x + (y / (t / (z - x))));
	} else {
		double VAR_1;
		if ((t <= 4.015719007857352e-64)) {
			VAR_1 = (x + (1.0 / (t / (y * (z - x)))));
		} else {
			VAR_1 = (x + (y * ((z - x) / t)));
		}
		VAR = VAR_1;
	}
	return VAR;
}

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

Original6.3
Target2.1
Herbie1.8
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.242968405003153e-105

    1. Initial program 7.6

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

    3. Applied associate-/l*1.8

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

    if -1.242968405003153e-105 < t < 4.015719007857352e-64

    1. Initial program 2.5

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

    3. Applied clear-num2.6

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

    if 4.015719007857352e-64 < t

    1. Initial program 7.4

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

    3. Applied *-un-lft-identity7.4

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

    4. Applied times-frac1.3

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

    5. Simplified1.3

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.242968405003153 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{elif}\;t \le 4.01571900785735227 \cdot 10^{-64}:\\ \;\;\;\;x + \frac{1}{\frac{t}{y \cdot \left(z - x\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - x}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020079 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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