Average Error: 25.0 → 10.7
Time: 7.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r683692 = x;
        double r683693 = y;
        double r683694 = r683693 - r683692;
        double r683695 = z;
        double r683696 = t;
        double r683697 = r683695 - r683696;
        double r683698 = r683694 * r683697;
        double r683699 = a;
        double r683700 = r683699 - r683696;
        double r683701 = r683698 / r683700;
        double r683702 = r683692 + r683701;
        return r683702;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r683703 = a;
        double r683704 = -1.9571495574965582e-126;
        bool r683705 = r683703 <= r683704;
        double r683706 = 4.0034989804875424e-122;
        bool r683707 = r683703 <= r683706;
        double r683708 = !r683707;
        bool r683709 = r683705 || r683708;
        double r683710 = x;
        double r683711 = y;
        double r683712 = r683711 - r683710;
        double r683713 = t;
        double r683714 = r683703 - r683713;
        double r683715 = 1.0;
        double r683716 = z;
        double r683717 = r683716 - r683713;
        double r683718 = r683715 / r683717;
        double r683719 = r683714 * r683718;
        double r683720 = r683712 / r683719;
        double r683721 = r683710 + r683720;
        double r683722 = r683710 * r683716;
        double r683723 = r683722 / r683713;
        double r683724 = r683711 + r683723;
        double r683725 = r683716 * r683711;
        double r683726 = r683725 / r683713;
        double r683727 = r683724 - r683726;
        double r683728 = r683709 ? r683721 : r683727;
        return r683728;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original25.0
Target9.5
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.9571495574965582e-126 or 4.0034989804875424e-122 < a

    1. Initial program 23.6

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

    3. Applied associate-/l*9.5

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}}\]
    4. Using strategy rm

    5. Applied div-inv9.5

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

    if -1.9571495574965582e-126 < a < 4.0034989804875424e-122

    1. Initial program 28.9

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

    2. Taylor expanded around inf 14.0

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))