Average Error: 1.9 → 1.5
Time: 12.2s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -2.00668391931767575 \cdot 10^{34} \lor \neg \left(t \le 3.16207688033320828 \cdot 10^{29}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;t \le -2.00668391931767575 \cdot 10^{34} \lor \neg \left(t \le 3.16207688033320828 \cdot 10^{29}\right):\\
\;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r680193 = x;
        double r680194 = y;
        double r680195 = r680194 - r680193;
        double r680196 = z;
        double r680197 = t;
        double r680198 = r680196 / r680197;
        double r680199 = r680195 * r680198;
        double r680200 = r680193 + r680199;
        return r680200;
}
↓
double f(double x, double y, double z, double t) {
        double r680201 = t;
        double r680202 = -2.0066839193176758e+34;
        bool r680203 = r680201 <= r680202;
        double r680204 = 3.1620768803332083e+29;
        bool r680205 = r680201 <= r680204;
        double r680206 = !r680205;
        bool r680207 = r680203 || r680206;
        double r680208 = x;
        double r680209 = z;
        double r680210 = y;
        double r680211 = r680210 - r680208;
        double r680212 = r680201 / r680211;
        double r680213 = r680209 / r680212;
        double r680214 = r680208 + r680213;
        double r680215 = r680211 * r680209;
        double r680216 = r680215 / r680201;
        double r680217 = r680208 + r680216;
        double r680218 = r680207 ? r680214 : r680217;
        return r680218;
}

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
Target2.1
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -2.0066839193176758e+34 or 3.1620768803332083e+29 < t

    1. Initial program 1.1

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

    2. Taylor expanded around 0 10.3

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

    3. Simplified1.2

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

    if -2.0066839193176758e+34 < t < 3.1620768803332083e+29

    1. Initial program 3.0

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

    3. Applied associate-*r/1.8

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -2.00668391931767575 \cdot 10^{34} \lor \neg \left(t \le 3.16207688033320828 \cdot 10^{29}\right):\\ \;\;\;\;x + \frac{z}{\frac{t}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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))))