Average Error: 10.6 → 0.8
Time: 5.9s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -4.388866292847462 \cdot 10^{-64}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.409003184810671 \cdot 10^{-276}:\\ \;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -4.388866292847462 \cdot 10^{-64}:\\
\;\;\;\;x + t \cdot \frac{y - z}{a - z}\\

\mathbf{elif}\;t \leq 1.409003184810671 \cdot 10^{-276}:\\
\;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\

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

\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y z) t) (- a z))))
↓
(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.388866292847462e-64)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= t 1.409003184810671e-276)
     (+ x (* (* t (- y z)) (/ 1.0 (- a z))))
     (+ x (* t (/ (- y z) (- a z)))))))
double code(double x, double y, double z, double t, double a) {
	return x + (((y - z) * t) / (a - z));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.388866292847462e-64) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (t <= 1.409003184810671e-276) {
		tmp = x + ((t * (y - z)) * (1.0 / (a - z)));
	} else {
		tmp = x + (t * ((y - z) / (a - z)));
	}
	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
Target0.6
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.38886629284746189e-64 or 1.40900318481067098e-276 < t

    1. Initial program 13.9

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

    3. Applied add-cube-cbrt_binary6414.3

      \[\leadsto x + \frac{\left(y - z\right) \cdot t}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]

    4. Applied times-frac_binary641.4

      \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}}\]
    5. Using strategy rm

    6. Applied pow1_binary641.4

      \[\leadsto x + \frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \color{blue}{{\left(\frac{t}{\sqrt[3]{a - z}}\right)}^{1}}\]

    7. Applied pow1_binary641.4

      \[\leadsto x + \color{blue}{{\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right)}^{1}} \cdot {\left(\frac{t}{\sqrt[3]{a - z}}\right)}^{1}\]

    8. Applied pow-prod-down_binary641.4

      \[\leadsto x + \color{blue}{{\left(\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t}{\sqrt[3]{a - z}}\right)}^{1}}\]

    9. Simplified0.9

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

    if -4.38886629284746189e-64 < t < 1.40900318481067098e-276

    1. Initial program 0.4

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

    3. Applied div-inv_binary640.4

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.388866292847462 \cdot 10^{-64}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.409003184810671 \cdot 10^{-276}:\\ \;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020273 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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