Average Error: 2.1 → 0.7
Time: 18.8s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{z}{t} = -\infty:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r412576 = x;
        double r412577 = y;
        double r412578 = r412577 - r412576;
        double r412579 = z;
        double r412580 = t;
        double r412581 = r412579 / r412580;
        double r412582 = r412578 * r412581;
        double r412583 = r412576 + r412582;
        return r412583;
}
↓
double f(double x, double y, double z, double t) {
        double r412584 = z;
        double r412585 = t;
        double r412586 = r412584 / r412585;
        double r412587 = -inf.0;
        bool r412588 = r412586 <= r412587;
        double r412589 = x;
        double r412590 = y;
        double r412591 = r412590 - r412589;
        double r412592 = r412591 * r412584;
        double r412593 = 1.0;
        double r412594 = r412593 / r412585;
        double r412595 = r412592 * r412594;
        double r412596 = r412589 + r412595;
        double r412597 = -8.83466263435864e-218;
        bool r412598 = r412586 <= r412597;
        double r412599 = 0.0;
        bool r412600 = r412586 <= r412599;
        double r412601 = !r412600;
        bool r412602 = r412598 || r412601;
        double r412603 = r412591 * r412586;
        double r412604 = r412589 + r412603;
        double r412605 = r412592 / r412585;
        double r412606 = r412589 + r412605;
        double r412607 = r412602 ? r412604 : r412606;
        double r412608 = r412588 ? r412596 : r412607;
        return r412608;
}

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
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.88671875:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ z t) < -inf.0

    1. Initial program 64.0

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

    3. Applied div-inv64.0

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

    4. Applied associate-*r*0.3

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

    if -inf.0 < (/ z t) < -8.83466263435864e-218 or 0.0 < (/ z t)

    1. Initial program 0.9

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

    if -8.83466263435864e-218 < (/ z t) < 0.0

    1. Initial program 2.5

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

    3. Applied associate-*r/0.2

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} = -\infty:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \mathbf{elif}\;\frac{z}{t} \le -8.834662634358639897139141015869877498875 \cdot 10^{-218} \lor \neg \left(\frac{z}{t} \le 0.0\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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))))