Average Error: 1.4 → 0.7
Time: 5.1s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -6.583074756991604 \cdot 10^{-103}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 2.408267500581704 \cdot 10^{-224}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -6.583074756991604 \cdot 10^{-103}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;y \leq 2.408267500581704 \cdot 10^{-224}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.583074756991604e-103)
   (+ x (* y (/ (- z t) (- a t))))
   (if (<= y 2.408267500581704e-224)
     (+ x (* (* y (- z t)) (/ 1.0 (- a t))))
     (+ x (/ y (/ (- a t) (- z t)))))))
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 tmp;
	if ((y <= -6.583074756991604e-103)) {
		tmp = ((double) (x + ((double) (y * (((double) (z - t)) / ((double) (a - t)))))));
	} else {
		double tmp_1;
		if ((y <= 2.408267500581704e-224)) {
			tmp_1 = ((double) (x + ((double) (((double) (y * ((double) (z - t)))) * (1.0 / ((double) (a - t)))))));
		} else {
			tmp_1 = ((double) (x + (y / (((double) (a - t)) / ((double) (z - t))))));
		}
		tmp = tmp_1;
	}
	return tmp;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -6.583074756991604e-103

    1. Initial program 0.6

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

    if -6.583074756991604e-103 < y < 2.40826750058170389e-224

    1. Initial program 3.1

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

    3. Applied div-inv_binary643.1

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

    4. Applied associate-*r*_binary640.4

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

    if 2.40826750058170389e-224 < y

    1. Initial program 0.9

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

    3. Applied associate-*r/_binary6412.0

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

    5. Applied associate-/l*_binary640.9

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.583074756991604 \cdot 10^{-103}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \leq 2.408267500581704 \cdot 10^{-224}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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)))))