Average Error: 2.3 → 2.1
Time: 2.4s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le 3.6000243022547191 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;z \le 3.3315843616580257 \cdot 10^{269}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;z \le 3.6000243022547191 \cdot 10^{-81}:\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{elif}\;z \le 3.3315843616580257 \cdot 10^{269}:\\
\;\;\;\;x + \frac{y - x}{t} \cdot z\\

\mathbf{else}:\\
\;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{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 ((z <= 3.600024302254719e-81)) {
		VAR = ((double) (x + ((double) (((double) (y - x)) / ((double) (t / z))))));
	} else {
		double VAR_1;
		if ((z <= 3.331584361658026e+269)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - x)) / t)) * z))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (((double) sqrt(z)) * ((double) (y - x)))) * ((double) (((double) sqrt(z)) / t))))));
		}
		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

Original2.3
Target2.4
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < 3.600024302254719e-81

    1. Initial program 1.9

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

    3. Applied associate-*r/5.0

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

    5. Applied associate-/l*1.9

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

    if 3.600024302254719e-81 < z < 3.331584361658026e+269

    1. Initial program 2.9

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

    3. Applied associate-*r/9.5

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

    5. Applied associate-/l*2.6

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

    7. Applied associate-/r/2.0

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

    if 3.331584361658026e+269 < z

    1. Initial program 6.5

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

    3. Applied *-un-lft-identity6.5

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

    4. Applied add-sqr-sqrt6.8

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

    5. Applied times-frac6.8

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

    6. Applied associate-*r*14.1

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

    7. Simplified14.1

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le 3.6000243022547191 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;z \le 3.3315843616580257 \cdot 10^{269}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \left(\sqrt{z} \cdot \left(y - x\right)\right) \cdot \frac{\sqrt{z}}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020123 
(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)) -1013646692435.887) (+ 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))))