Average Error: 10.7 → 0.7
Time: 6.1s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -3.9268247044397842 \cdot 10^{-161} \lor \neg \left(t \le 3.56104037216443586 \cdot 10^{-149}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot t}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \le -3.9268247044397842 \cdot 10^{-161} \lor \neg \left(t \le 3.56104037216443586 \cdot 10^{-149}\right):\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot t\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((t <= -3.926824704439784e-161) || !(t <= 3.561040372164436e-149))) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) / ((double) (a - z)))) * t))));
	} else {
		VAR = ((double) (x + ((double) (1.0 / ((double) (((double) (a - z)) / ((double) (((double) (y - z)) * t))))))));
	}
	return VAR;
}

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
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -3.9268247044397842e-161 or 3.56104037216443586e-149 < t

    1. Initial program 14.7

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

    3. Applied associate-/l*2.7

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

    5. Applied associate-/r/0.8

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

    if -3.9268247044397842e-161 < t < 3.56104037216443586e-149

    1. Initial program 0.4

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

    3. Applied clear-num0.4

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -3.9268247044397842 \cdot 10^{-161} \lor \neg \left(t \le 3.56104037216443586 \cdot 10^{-149}\right):\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a - z}{\left(y - z\right) \cdot t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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