Average Error: 1.4 → 0.8
Time: 8.6s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.060365571784887 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \le 6.1636889221917999 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.060365571784887 \cdot 10^{-22}:\\
\;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\

\mathbf{elif}\;y \le 6.1636889221917999 \cdot 10^{-12}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\

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

\end{array}
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (a - t)))))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((y <= -2.060365571784887e-22)) {
		VAR = ((double) (x + ((double) ((y / ((double) (a - t))) * ((double) (z - t))))));
	} else {
		double VAR_1;
		if ((y <= 6.1636889221918e-12)) {
			VAR_1 = ((double) (x + (((double) (y * ((double) (z - t)))) / ((double) (a - t)))));
		} else {
			VAR_1 = ((double) (x + ((double) (y * ((double) (((double) (z - t)) * (1.0 / ((double) (a - t)))))))));
		}
		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

Original1.4
Target0.4
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -2.060365571784887e-22

    1. Initial program 0.5

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

    3. Applied pow10.5

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

    4. Applied pow10.5

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

    5. Applied pow-prod-down0.5

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

    6. Simplified2.2

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

    if -2.060365571784887e-22 < y < 6.1636889221917999e-12

    1. Initial program 2.3

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

    3. Applied associate-*r/0.3

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

    if 6.1636889221917999e-12 < y

    1. Initial program 0.5

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

    3. Applied div-inv0.6

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.060365571784887 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \left(z - t\right)\\ \mathbf{elif}\;y \le 6.1636889221917999 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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)))))