Average Error: 2.2 → 1.6
Time: 7.6s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -1.48115679118647278 \cdot 10^{-195} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{1}{\frac{t}{x \cdot z}}\right)\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} \le -1.48115679118647278 \cdot 10^{-195} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{1}{\frac{t}{x \cdot z}}\right)\\

\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 ((((z / t) <= -1.4811567911864728e-195) || !((z / t) <= -0.0))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * (z / t)))));
	} else {
		VAR = ((double) (x + ((double) ((((double) (z * y)) / t) - (1.0 / (t / ((double) (x * z))))))));
	}
	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

Original2.2
Target2.4
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ z t) < -1.48115679118647278e-195 or -0.0 < (/ z t)

    1. Initial program 2.0

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

    if -1.48115679118647278e-195 < (/ z t) < -0.0

    1. Initial program 2.7

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

    2. Taylor expanded around 0 0.3

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

    4. Applied clear-num0.3

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \le -1.48115679118647278 \cdot 10^{-195} \lor \neg \left(\frac{z}{t} \le -0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{z \cdot y}{t} - \frac{1}{\frac{t}{x \cdot z}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))))