Average Error: 1.5 → 0.9
Time: 6.3s
Precision: binary64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 8.885169190430442 \cdot 10^{+127}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \frac{1}{\frac{1}{z - t}}\\ \end{array}\]
x + y \cdot \frac{z - t}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z - t}{a - t} \leq 8.885169190430442 \cdot 10^{+127}:\\
\;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{a - t} \cdot \frac{1}{\frac{1}{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 (<= (/ (- z t) (- a t)) 8.885169190430442e+127)
   (+ x (/ y (/ (- a t) (- z t))))
   (+ x (* (/ y (- a t)) (/ 1.0 (/ 1.0 (- z t)))))))
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 tmp;
	if (((z - t) / (a - t)) <= 8.885169190430442e+127) {
		tmp = x + (y / ((a - t) / (z - t)));
	} else {
		tmp = x + ((y / (a - t)) * (1.0 / (1.0 / (z - t))));
	}
	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

Original1.5
Target0.5
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y < -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 8.885169190430442e127

    1. Initial program 0.8

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

    3. Applied clear-num_binary640.9

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied un-div-inv_binary640.8

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]

    if 8.885169190430442e127 < (/.f64 (-.f64 z t) (-.f64 a t))

    1. Initial program 12.6

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

    3. Applied clear-num_binary6412.7

      \[\leadsto x + y \cdot \color{blue}{\frac{1}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv_binary6412.7

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

    6. Applied *-un-lft-identity_binary6412.7

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

    7. Applied times-frac_binary6412.7

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

    8. Applied associate-*r*_binary641.3

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

    9. Simplified1.3

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z - t}{a - t} \leq 8.885169190430442 \cdot 10^{+127}:\\ \;\;\;\;x + \frac{y}{\frac{a - t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a - t} \cdot \frac{1}{\frac{1}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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)))))