Average Error: 10.8 → 0.8
Time: 8.2s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -3218.6894946389293 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 3.734976718309057 \cdot 10^{+283}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -3218.6894946389293 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 3.734976718309057 \cdot 10^{+283}\right):\\
\;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\

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

\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 (or (<= (/ (* (- y z) t) (- a z)) -3218.6894946389293)
         (not (<= (/ (* (- y z) t) (- a z)) 3.734976718309057e+283)))
   (+ x (* (- y z) (/ t (- a z))))
   (+ (/ (* (- y z) t) (- a z)) x)))
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 (((((y - z) * t) / (a - z)) <= -3218.6894946389293) || !((((y - z) * t) / (a - z)) <= 3.734976718309057e+283)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = (((y - z) * t) / (a - z)) + x;
	}
	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
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 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -3218.6894946389293 or 3.73497671830905731e283 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

    1. Initial program 33.9

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

    3. Applied *-un-lft-identity_binary64_1557933.9

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

    4. Applied times-frac_binary64_155851.9

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

    5. Simplified1.9

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

    if -3218.6894946389293 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 3.73497671830905731e283

    1. Initial program 0.3

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} \leq -3218.6894946389293 \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \leq 3.734976718309057 \cdot 10^{+283}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot t}{a - z} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020292 
(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))))