Average Error: 10.8 → 0.5
Time: 5.3s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -inf.0 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 4.30825504485863338 \cdot 10^{254}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot t\right) \cdot \frac{1}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -inf.0 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 4.30825504485863338 \cdot 10^{254}\right):\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\

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

\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 (((((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z)))) <= -inf.0) || !(((double) (((double) (((double) (y - z)) * t)) / ((double) (a - z)))) <= 4.3082550448586334e+254))) {
		VAR = ((double) (x + ((double) (((double) (y - z)) * ((double) (t / ((double) (a - z))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (y - z)) * t)) * ((double) (1.0 / ((double) (a - z))))))));
	}
	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

Original10.8
Target0.5
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 4.30825504485863338e254 < (/ (* (- y z) t) (- a z))

    1. Initial program 59.5

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

    3. Applied *-un-lft-identity59.5

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

    4. Applied times-frac1.5

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

    5. Simplified1.5

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

    if -inf.0 < (/ (* (- y z) t) (- a z)) < 4.30825504485863338e254

    1. Initial program 0.3

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

    3. Applied div-inv0.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -inf.0 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 4.30825504485863338 \cdot 10^{254}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - z\right) \cdot t\right) \cdot \frac{1}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020173 
(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))))