Average Error: 10.9 → 0.9
Time: 5.4s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -7556432.438506252 \lor \neg \left(y \leq -9.698192082570641 \cdot 10^{-239}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -7556432.438506252 \lor \neg \left(y \leq -9.698192082570641 \cdot 10^{-239}\right):\\
\;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\

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

\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 -7556432.438506252) (not (<= y -9.698192082570641e-239)))
   (+ x (/ y (/ (- z a) (- z t))))
   (+ x (/ 1.0 (/ (- z a) (* y (- z t)))))))
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 <= -7556432.438506252) || !(y <= -9.698192082570641e-239)) {
		tmp = x + (y / ((z - a) / (z - t)));
	} else {
		tmp = x + (1.0 / ((z - a) / (y * (z - t))));
	}
	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

Original10.9
Target1.2
Herbie0.9
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -7556432.43850625213 or -9.698192082570641e-239 < y

    1. Initial program 13.8

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

    3. Applied associate-/l*_binary64_153681.1

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

    if -7556432.43850625213 < y < -9.698192082570641e-239

    1. Initial program 0.2

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

    3. Applied clear-num_binary64_154220.2

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7556432.438506252 \lor \neg \left(y \leq -9.698192082570641 \cdot 10^{-239}\right):\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{z - a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020342 
(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))))