Average Error: 10.8 → 0.8
Time: 2.9s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.6227658927523768 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \le 3.98166421751174675 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.6227658927523768 \cdot 10^{-15}:\\
\;\;\;\;x + \frac{y - z}{a - z} \cdot t\\

\mathbf{elif}\;t \le 3.98166421751174675 \cdot 10^{-34}:\\
\;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + (((y - z) * t) / (a - z)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((t <= -1.6227658927523768e-15)) {
		VAR = (x + (((y - z) / (a - z)) * t));
	} else {
		double VAR_1;
		if ((t <= 3.981664217511747e-34)) {
			VAR_1 = (x + (((y - z) * t) / (a - z)));
		} else {
			VAR_1 = (x + ((y - z) * (t / (a - z))));
		}
		VAR = VAR_1;
	}
	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
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -1.6227658927523768e-15

    1. Initial program 21.9

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

    3. Applied associate-/l*2.4

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

    5. Applied associate-/r/0.3

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

    if -1.6227658927523768e-15 < t < 3.981664217511747e-34

    1. Initial program 0.3

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

    if 3.981664217511747e-34 < t

    1. Initial program 20.4

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

    3. Applied *-un-lft-identity20.4

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

    4. Applied times-frac2.3

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

    5. Simplified2.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.6227658927523768 \cdot 10^{-15}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \le 3.98166421751174675 \cdot 10^{-34}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 
(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))))