Average Error: 2.2 → 1.7
Time: 6.0s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.1758493966687633 \cdot 10^{-82} \lor \neg \left(t \le 2.4845345789677921 \cdot 10^{-165}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -4.1758493966687633 \cdot 10^{-82} \lor \neg \left(t \le 2.4845345789677921 \cdot 10^{-165}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(y - x\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 (((t <= -4.1758493966687633e-82) || !(t <= 2.484534578967792e-165))) {
		VAR = ((double) (x + ((double) (((double) (y - x)) * ((double) (z / t))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (((double) (((double) cbrt(z)) * ((double) cbrt(z)))) * ((double) (y - x)))) * ((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

Original2.2
Target2.3
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -4.1758493966687633e-82 or 2.4845345789677921e-165 < t

    1. Initial program 1.5

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

    if -4.1758493966687633e-82 < t < 2.4845345789677921e-165

    1. Initial program 5.4

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

    3. Applied *-un-lft-identity5.4

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

    4. Applied add-cube-cbrt6.3

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

    5. Applied times-frac6.3

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

    6. Applied associate-*r*3.0

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

    7. Simplified3.0

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.1758493966687633 \cdot 10^{-82} \lor \neg \left(t \le 2.4845345789677921 \cdot 10^{-165}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(y - x\right)\right) \cdot \frac{\sqrt[3]{z}}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020171 
(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))))