Average Error: 6.8 → 0.7
Time: 6.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - x\right)}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3399597152785924 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{t} \cdot \left(x - z\right)}{-1}\\ \end{array}\]
x + \frac{y \cdot \left(z - x\right)}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\
\;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\

\mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3399597152785924 \cdot 10^{+306}:\\
\;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\frac{y}{t} \cdot \left(x - z\right)}{-1}\\

\end{array}
(FPCore (x y z t) :precision binary64 (+ x (/ (* y (- z x)) t)))
↓
(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x (/ (* y (- z x)) t)) (- INFINITY))
   (+ x (* y (* (- z x) (/ 1.0 t))))
   (if (<= (+ x (/ (* y (- z x)) t)) 2.3399597152785924e+306)
     (+ x (/ (* y (- z x)) t))
     (+ x (/ (* (/ y t) (- x z)) -1.0)))))
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 tmp;
	if ((x + ((y * (z - x)) / t)) <= -((double) INFINITY)) {
		tmp = x + (y * ((z - x) * (1.0 / t)));
	} else if ((x + ((y * (z - x)) / t)) <= 2.3399597152785924e+306) {
		tmp = x + ((y * (z - x)) / t);
	} else {
		tmp = x + (((y / t) * (x - z)) / -1.0);
	}
	return tmp;
}

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

Original6.8
Target2.1
Herbie0.7
\[x - \left(x \cdot \frac{y}{t} + \left(-z\right) \cdot \frac{y}{t}\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity_binary64_1167264.0

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

    4. Applied times-frac_binary64_116780.2

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

    5. Simplified0.2

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

    7. Applied div-inv_binary64_116690.2

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

    if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 2.33995971527859238e306

    1. Initial program 0.7

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

    if 2.33995971527859238e306 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

    1. Initial program 61.9

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

    3. Applied add-cube-cbrt_binary64_1170761.9

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

    4. Applied times-frac_binary64_116781.2

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

    5. Taylor expanded around -inf 61.9

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

    6. Simplified0.3

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

    8. Applied sub-div_binary64_116790.3

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

    9. Applied associate-*r/_binary64_116140.3

      \[\leadsto x + \color{blue}{\frac{\frac{y}{t} \cdot \left(x - z\right)}{-1}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty:\\ \;\;\;\;x + y \cdot \left(\left(z - x\right) \cdot \frac{1}{t}\right)\\ \mathbf{elif}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq 2.3399597152785924 \cdot 10^{+306}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{t} \cdot \left(x - z\right)}{-1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020342 
(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)))