Average Error: 24.2 → 10.8
Time: 14.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -2.8458411894470345 \cdot 10^{-92} \lor \neg \left(a \le 1.3782715591853007 \cdot 10^{-120}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -2.8458411894470345 \cdot 10^{-92} \lor \neg \left(a \le 1.3782715591853007 \cdot 10^{-120}\right):\\
\;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}\\

\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 r688691 = x;
        double r688692 = y;
        double r688693 = r688692 - r688691;
        double r688694 = z;
        double r688695 = t;
        double r688696 = r688694 - r688695;
        double r688697 = r688693 * r688696;
        double r688698 = a;
        double r688699 = r688698 - r688695;
        double r688700 = r688697 / r688699;
        double r688701 = r688691 + r688700;
        return r688701;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r688702 = a;
        double r688703 = -2.8458411894470345e-92;
        bool r688704 = r688702 <= r688703;
        double r688705 = 1.3782715591853007e-120;
        bool r688706 = r688702 <= r688705;
        double r688707 = !r688706;
        bool r688708 = r688704 || r688707;
        double r688709 = x;
        double r688710 = 1.0;
        double r688711 = t;
        double r688712 = r688702 - r688711;
        double r688713 = z;
        double r688714 = r688713 - r688711;
        double r688715 = r688712 / r688714;
        double r688716 = y;
        double r688717 = r688716 - r688709;
        double r688718 = r688715 / r688717;
        double r688719 = r688710 / r688718;
        double r688720 = r688709 + r688719;
        double r688721 = r688709 * r688713;
        double r688722 = r688721 / r688711;
        double r688723 = r688716 + r688722;
        double r688724 = r688713 * r688716;
        double r688725 = r688724 / r688711;
        double r688726 = r688723 - r688725;
        double r688727 = r688708 ? r688720 : r688726;
        return r688727;
}

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

Original24.2
Target9.5
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -2.8458411894470345e-92 or 1.3782715591853007e-120 < a

    1. Initial program 22.5

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

    3. Applied associate-/l*8.8

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

    5. Applied clear-num8.8

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}}\]

    if -2.8458411894470345e-92 < a < 1.3782715591853007e-120

    1. Initial program 28.3

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

    2. Taylor expanded around inf 15.7

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

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -2.8458411894470345 \cdot 10^{-92} \lor \neg \left(a \le 1.3782715591853007 \cdot 10^{-120}\right):\\ \;\;\;\;x + \frac{1}{\frac{\frac{a - t}{z - t}}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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))))