Average Error: 10.7 → 0.4
Time: 4.6s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 4.01350158765124 \cdot 10^{+221}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - y \cdot t}{z - a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 4.01350158765124 \cdot 10^{+221}\right):\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- z a))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (/ (* y (- z t)) (- z a)) (- INFINITY))
         (not (<= (/ (* y (- z t)) (- z a)) 4.01350158765124e+221)))
   (+ x (/ y (/ (- z a) (- z t))))
   (+ x (/ (- (* y z) (* y t)) (- z a)))))
double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (z - a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((y * (z - t)) / (z - a)) <= -((double) INFINITY)) || !(((y * (z - t)) / (z - a)) <= 4.01350158765124e+221)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = x + (((y * z) - (y * t)) / (z - 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

Original10.7
Target1.2
Herbie0.4
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -inf.0 or 4.01350158765124013e221 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

    1. Initial program 56.0

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

    3. Applied associate-/l*_binary64_143451.3

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

    if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 4.01350158765124013e221

    1. Initial program 0.2

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

    3. Applied sub-neg_binary64_143930.2

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

    4. Applied distribute-rgt-in_binary64_143500.2

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

    5. Simplified0.2

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

    6. Simplified0.2

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 4.01350158765124 \cdot 10^{+221}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z - y \cdot t}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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