Average Error: 10.4 → 0.7
Time: 5.2s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -2.98575735952740302 \cdot 10^{225} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.5239238908574738 \cdot 10^{258}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -2.98575735952740302 \cdot 10^{225} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.5239238908574738 \cdot 10^{258}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / (a - t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((((y * (z - t)) / (a - t)) <= -2.985757359527403e+225) || !(((y * (z - t)) / (a - t)) <= 3.523923890857474e+258))) {
		VAR = fma((y / (a - t)), (z - t), x);
	} else {
		VAR = (x + ((y * (z - t)) / (a - 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

Original10.4
Target1.3
Herbie0.7
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* y (- z t)) (- a t)) < -2.985757359527403e+225 or 3.523923890857474e+258 < (/ (* y (- z t)) (- a t))

    1. Initial program 53.1

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

    2. Simplified2.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]

    if -2.985757359527403e+225 < (/ (* y (- z t)) (- a t)) < 3.523923890857474e+258

    1. Initial program 0.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \le -2.98575735952740302 \cdot 10^{225} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \le 3.5239238908574738 \cdot 10^{258}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020092 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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