Average Error: 2.1 → 2.4
Time: 5.1s
Precision: binary64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.685255496896285 \cdot 10^{-127}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \le 9.6730038929220625 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.685255496896285 \cdot 10^{-127}:\\
\;\;\;\;x + z \cdot \frac{y - x}{t}\\

\mathbf{elif}\;t \le 9.6730038929220625 \cdot 10^{-301}:\\
\;\;\;\;x + \frac{z \cdot \left(y - x\right)}{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 ((t <= -2.6852554968962853e-127)) {
		VAR = ((double) (x + ((double) (z * ((double) (((double) (y - x)) / t))))));
	} else {
		double VAR_1;
		if ((t <= 9.673003892922062e-301)) {
			VAR_1 = ((double) (x + ((double) (((double) (z * ((double) (y - x)))) / t))));
		} else {
			VAR_1 = ((double) (x + ((double) (((double) (y - x)) * ((double) (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

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

Derivation

  1. Split input into 3 regimes

  2. if t < -2.685255496896285e-127

    1. Initial program 1.4

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

    3. Applied add-cube-cbrt1.8

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

    4. Applied associate-*l*1.8

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

    5. Simplified1.1

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

    6. Taylor expanded around 0 7.4

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

    7. Simplified2.7

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

    if -2.685255496896285e-127 < t < 9.6730038929220625e-301

    1. Initial program 5.4

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

    3. Applied associate-*r/2.9

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

    if 9.6730038929220625e-301 < t

    1. Initial program 2.0

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.685255496896285 \cdot 10^{-127}:\\ \;\;\;\;x + z \cdot \frac{y - x}{t}\\ \mathbf{elif}\;t \le 9.6730038929220625 \cdot 10^{-301}:\\ \;\;\;\;x + \frac{z \cdot \left(y - x\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))))