Average Error: 1.8 → 2.0
Time: 3.2s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -1.275876279945464 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq 1.1341919036208424 \cdot 10^{-288}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -1.275876279945464 \cdot 10^{-39}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{elif}\;x \leq 1.1341919036208424 \cdot 10^{-288}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if ((x <= -1.275876279945464e-39)) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
	} else {
		double VAR_1;
		if ((x <= 1.1341919036208424e-288)) {
			VAR_1 = ((double) (x + ((double) (z * (((double) (y - x)) / t)))));
		} else {
			VAR_1 = ((double) (x + (((double) (y - x)) / (t / z))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original1.8
Target2.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} < -1013646692435.8867:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} < -0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.2758762799454639e-39

    1. Initial program 0.1

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

    if -1.2758762799454639e-39 < x < 1.13419190362084238e-288

    1. Initial program 3.6

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

    3. Applied associate-*r/4.4

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

    4. Taylor expanded around 0 4.4

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

    5. Simplified4.5

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

    if 1.13419190362084238e-288 < x

    1. Initial program 1.8

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

    3. Applied associate-*r/5.9

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

    5. Applied associate-/l*1.7

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.275876279945464 \cdot 10^{-39}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{elif}\;x \leq 1.1341919036208424 \cdot 10^{-288}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.8867) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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