Average Error: 10.8 → 1.2
Time: 4.3s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -5.212099959314552 \cdot 10^{-302}:\\ \;\;\;\;x + t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{elif}\;t \leq 128923762327.44762:\\ \;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -5.212099959314552 \cdot 10^{-302}:\\
\;\;\;\;x + t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\

\mathbf{elif}\;t \leq 128923762327.44762:\\
\;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\

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

\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 -5.212099959314552e-302)
   (+ x (* t (- (/ y (- a z)) (/ z (- a z)))))
   (if (<= t 128923762327.44762)
     (+ x (* (* t (- y z)) (/ 1.0 (- a z))))
     (+ x (/ (- y z) (/ (- a z) t))))))
double code(double x, double y, double z, double t, double a) {
	return ((double) (x + (((double) (((double) (y - z)) * t)) / ((double) (a - z)))));
}
↓
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.212099959314552e-302)) {
		tmp = ((double) (x + ((double) (t * ((double) ((y / ((double) (a - z))) - (z / ((double) (a - z)))))))));
	} else {
		double tmp_1;
		if ((t <= 128923762327.44762)) {
			tmp_1 = ((double) (x + ((double) (((double) (t * ((double) (y - z)))) * (1.0 / ((double) (a - z)))))));
		} else {
			tmp_1 = ((double) (x + (((double) (y - z)) / (((double) (a - 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

Original10.8
Target0.6
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -5.2120999593145522e-302

    1. Initial program 10.9

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

    3. Applied add-cube-cbrt_binary6411.2

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

    4. Applied times-frac_binary641.8

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

    6. Applied pow1_binary641.8

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

    7. Applied pow1_binary641.8

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

    8. Applied pow-prod-down_binary641.8

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

    9. Simplified1.3

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

    11. Applied div-sub_binary641.3

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

    if -5.2120999593145522e-302 < t < 128923762327.447617

    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

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

    if 128923762327.447617 < t

    1. Initial program 24.1

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

    3. Applied associate-/l*_binary642.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.212099959314552 \cdot 10^{-302}:\\ \;\;\;\;x + t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{elif}\;t \leq 128923762327.44762:\\ \;\;\;\;x + \left(t \cdot \left(y - z\right)\right) \cdot \frac{1}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))))