Average Error: 24.8 → 10.7
Time: 6.9s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.71252033879547009 \cdot 10^{-209} \lor \neg \left(a \le 2.699618550558612 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -3.71252033879547009 \cdot 10^{-209} \lor \neg \left(a \le 2.699618550558612 \cdot 10^{-210}\right):\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - 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 r681639 = x;
        double r681640 = y;
        double r681641 = r681640 - r681639;
        double r681642 = z;
        double r681643 = t;
        double r681644 = r681642 - r681643;
        double r681645 = r681641 * r681644;
        double r681646 = a;
        double r681647 = r681646 - r681643;
        double r681648 = r681645 / r681647;
        double r681649 = r681639 + r681648;
        return r681649;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r681650 = a;
        double r681651 = -3.71252033879547e-209;
        bool r681652 = r681650 <= r681651;
        double r681653 = 2.699618550558612e-210;
        bool r681654 = r681650 <= r681653;
        double r681655 = !r681654;
        bool r681656 = r681652 || r681655;
        double r681657 = x;
        double r681658 = y;
        double r681659 = r681658 - r681657;
        double r681660 = z;
        double r681661 = t;
        double r681662 = r681660 - r681661;
        double r681663 = r681650 - r681661;
        double r681664 = r681662 / r681663;
        double r681665 = r681659 * r681664;
        double r681666 = r681657 + r681665;
        double r681667 = r681657 * r681660;
        double r681668 = r681667 / r681661;
        double r681669 = r681658 + r681668;
        double r681670 = r681660 * r681658;
        double r681671 = r681670 / r681661;
        double r681672 = r681669 - r681671;
        double r681673 = r681656 ? r681666 : r681672;
        return r681673;
}

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

Original24.8
Target9.6
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.71252033879547e-209 or 2.699618550558612e-210 < a

    1. Initial program 23.9

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

    3. Applied *-un-lft-identity23.9

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

    4. Applied times-frac10.7

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

    5. Simplified10.7

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

    if -3.71252033879547e-209 < a < 2.699618550558612e-210

    1. Initial program 30.7

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

    2. Taylor expanded around inf 10.2

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.71252033879547009 \cdot 10^{-209} \lor \neg \left(a \le 2.699618550558612 \cdot 10^{-210}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))))