Average Error: 10.6 → 0.7
Time: 6.0s
Precision: binary64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -3.448631571517119 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 1.4127159396366662 \cdot 10^{-101}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -3.448631571517119 \cdot 10^{-115}:\\
\;\;\;\;x + y \cdot \frac{z - t}{z - a}\\

\mathbf{elif}\;y \leq 1.4127159396366662 \cdot 10^{-101}:\\
\;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\

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

\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 -3.448631571517119e-115)
   (+ x (* y (/ (- z t) (- z a))))
   (if (<= y 1.4127159396366662e-101)
     (+ x (* (* y (- z t)) (/ 1.0 (- z a))))
     (+ x (/ y (/ (- z a) (- z t)))))))
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 <= -3.448631571517119e-115) {
		tmp = x + (y * ((z - t) / (z - a)));
	} else if (y <= 1.4127159396366662e-101) {
		tmp = x + ((y * (z - t)) * (1.0 / (z - a)));
	} else {
		tmp = x + (y / ((z - a) / (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

Original10.6
Target1.4
Herbie0.7
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Split input into 3 regimes

  2. if y < -3.4486315715171189e-115

    1. Initial program 16.8

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

    3. Applied *-un-lft-identity_binary64_1693516.8

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

    4. Applied times-frac_binary64_169410.8

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

    5. Simplified0.8

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

    if -3.4486315715171189e-115 < y < 1.41271593963666615e-101

    1. Initial program 0.3

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

    3. Applied div-inv_binary64_169320.3

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

    if 1.41271593963666615e-101 < y

    1. Initial program 16.0

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

    3. Applied associate-/l*_binary64_168800.9

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.448631571517119 \cdot 10^{-115}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z - a}\\ \mathbf{elif}\;y \leq 1.4127159396366662 \cdot 10^{-101}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{z - a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z - a}{z - t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020277 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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