Average Error: 10.8 → 0.9
Time: 5.9s
Precision: binary64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -8.723683931925445 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.011765985381093 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{z}{t}}\\ \end{array}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -8.723683931925445 \cdot 10^{-11}:\\
\;\;\;\;x + t \cdot \frac{y - z}{a - z}\\

\mathbf{elif}\;t \leq 1.011765985381093 \cdot 10^{-68}:\\
\;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{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 -8.723683931925445e-11)
   (+ x (* t (/ (- y z) (- a z))))
   (if (<= t 1.011765985381093e-68)
     (+ x (/ (* t (- y z)) (- a z)))
     (+ x (/ (- y z) (- (/ a t) (/ z t)))))))
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 <= -8.723683931925445e-11) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else if (t <= 1.011765985381093e-68) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = x + ((y - z) / ((a / t) - (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

Original10.8
Target0.5
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;t < -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t < 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.72368393192544464e-11

    1. Initial program 23.6

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

    3. Applied associate-/l*_binary64_129812.4

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

    5. Applied associate-/r/_binary64_129820.4

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

    if -8.72368393192544464e-11 < t < 1.01176598538109304e-68

    1. Initial program 0.2

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

    if 1.01176598538109304e-68 < t

    1. Initial program 17.8

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

    3. Applied associate-/l*_binary64_129812.5

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

    5. Applied div-sub_binary64_130412.6

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.723683931925445 \cdot 10^{-11}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq 1.011765985381093 \cdot 10^{-68}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a}{t} - \frac{z}{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020344 
(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))))