Average Error: 1.3 → 1.1
Time: 5.9s
Precision: binary64
\[x + y \cdot \frac{z - t}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -6.850122719949887 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 1.3883953432163486 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array}\]
x + y \cdot \frac{z - t}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -6.850122719949887 \cdot 10^{-23}:\\
\;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\

\mathbf{elif}\;y \leq 1.3883953432163486 \cdot 10^{-108}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- z a)))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.850122719949887e-23)
   (+ x (* y (- (/ z (- z a)) (/ t (- z a)))))
   (if (<= y 1.3883953432163486e-108)
     (+ x (/ (* y (- z t)) (- z a)))
     (+ x (* (- z t) (/ y (- z a)))))))
double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (z - a)));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.850122719949887e-23) {
		tmp = x + (y * ((z / (z - a)) - (t / (z - a))));
	} else if (y <= 1.3883953432163486e-108) {
		tmp = x + ((y * (z - t)) / (z - a));
	} else {
		tmp = x + ((z - t) * (y / (z - a)));
	}
	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

Original1.3
Target1.2
Herbie1.1
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -6.85012271994988688e-23

    1. Initial program 0.6

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

    3. Applied div-sub_binary64_176060.6

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

    if -6.85012271994988688e-23 < y < 1.3883953432163486e-108

    1. Initial program 2.2

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

    3. Applied associate-*r/_binary64_175450.3

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

    if 1.3883953432163486e-108 < y

    1. Initial program 0.7

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

    3. Applied div-sub_binary64_176060.7

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

    5. Applied div-inv_binary64_175980.7

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

    6. Applied div-inv_binary64_175980.7

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

    7. Applied distribute-rgt-out--_binary64_175570.7

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

    8. Applied associate-*r*_binary64_175432.6

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

    9. Simplified2.5

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.850122719949887 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \left(\frac{z}{z - a} - \frac{t}{z - a}\right)\\ \mathbf{elif}\;y \leq 1.3883953432163486 \cdot 10^{-108}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{z - a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020281 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64

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

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