Average Error: 1.9 → 1.8
Time: 4.3s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.15015923526592009 \cdot 10^{-238} \lor \neg \left(x \le 7.2583671978475645 \cdot 10^{-60}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \frac{\sqrt[3]{z}}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.15015923526592009 \cdot 10^{-238} \lor \neg \left(x \le 7.2583671978475645 \cdot 10^{-60}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \frac{\sqrt[3]{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 (((x <= -3.15015923526592e-238) || !(x <= 7.258367197847565e-60))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (((double) cbrt(z)) * ((double) cbrt(z)))))) * ((double) (((double) cbrt(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

Original1.9
Target2.0
Herbie1.8
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.15015923526592009e-238 or 7.2583671978475645e-60 < x

    1. Initial program 0.9

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

    if -3.15015923526592009e-238 < x < 7.2583671978475645e-60

    1. Initial program 4.4

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

    3. Applied *-un-lft-identity4.4

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

    4. Applied add-cube-cbrt5.1

      \[\leadsto x + \left(y - x\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}}}{1 \cdot t}\]

    5. Applied times-frac5.1

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1} \cdot \frac{\sqrt[3]{z}}{t}\right)}\]

    6. Applied associate-*r*4.2

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \frac{\sqrt[3]{z} \cdot \sqrt[3]{z}}{1}\right) \cdot \frac{\sqrt[3]{z}}{t}}\]

    7. Simplified4.2

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.15015923526592009 \cdot 10^{-238} \lor \neg \left(x \le 7.2583671978475645 \cdot 10^{-60}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) \cdot \frac{\sqrt[3]{z}}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020185 
(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))))