Average Error: 2.1 → 1.0
Time: 3.4s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -inf.0 \lor \neg \left(x + \left(y - x\right) \cdot \frac{z}{t} \le 8.9540197402834252 \cdot 10^{284}\right):\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -inf.0 \lor \neg \left(x + \left(y - x\right) \cdot \frac{z}{t} \le 8.9540197402834252 \cdot 10^{284}\right):\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

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

\end{array}
double code(double x, double y, double z, double t) {
	return ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
}
↓
double code(double x, double y, double z, double t) {
	double VAR;
	if (((((double) (x + ((double) (((double) (y - x)) * ((double) (z / t)))))) <= -inf.0) || !(((double) (x + ((double) (((double) (y - x)) * ((double) (z / t)))))) <= 8.954019740283425e+284))) {
		VAR = ((double) (x + ((double) (((double) (((double) (y - x)) * z)) * ((double) (1.0 / t))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
	}
	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

Original2.1
Target2.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (* (- y x) (/ z t))) < -inf.0 or 8.9540197402834252e284 < (+ x (* (- y x) (/ z t)))

    1. Initial program 29.4

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

    3. Applied div-inv29.4

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

    4. Applied associate-*r*8.1

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

    if -inf.0 < (+ x (* (- y x) (/ z t))) < 8.9540197402834252e284

    1. Initial program 0.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -inf.0 \lor \neg \left(x + \left(y - x\right) \cdot \frac{z}{t} \le 8.9540197402834252 \cdot 10^{284}\right):\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(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))))