Average Error: 1.4 → 1.5
Time: 38.4s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.4811076684293724 \cdot 10^{-46} \lor \neg \left(t \le 6.14088417278226504 \cdot 10^{-47}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -1.4811076684293724 \cdot 10^{-46} \lor \neg \left(t \le 6.14088417278226504 \cdot 10^{-47}\right):\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (a - t))))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if (((t <= -1.4811076684293724e-46) || !(t <= 6.140884172782265e-47))) {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (z - t)) / ((double) (a - t))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) * ((double) (1.0 / ((double) (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

Original1.4
Target0.5
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -1.4811076684293724e-46 or 6.14088417278226504e-47 < t

    1. Initial program 0.2

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

    if -1.4811076684293724e-46 < t < 6.14088417278226504e-47

    1. Initial program 3.4

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

    3. Applied div-inv3.5

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

    4. Applied associate-*r*3.5

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.4811076684293724 \cdot 10^{-46} \lor \neg \left(t \le 6.14088417278226504 \cdot 10^{-47}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1.0 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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