Average Error: 25.2 → 12.1
Time: 6.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.50374357984312286 \cdot 10^{-108} \lor \neg \left(a \le -9.9251003126439114 \cdot 10^{-170}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.50374357984312286 \cdot 10^{-108} \lor \neg \left(a \le -9.9251003126439114 \cdot 10^{-170}\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 r570498 = x;
        double r570499 = y;
        double r570500 = r570499 - r570498;
        double r570501 = z;
        double r570502 = t;
        double r570503 = r570501 - r570502;
        double r570504 = r570500 * r570503;
        double r570505 = a;
        double r570506 = r570505 - r570502;
        double r570507 = r570504 / r570506;
        double r570508 = r570498 + r570507;
        return r570508;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r570509 = a;
        double r570510 = -1.5037435798431229e-108;
        bool r570511 = r570509 <= r570510;
        double r570512 = -9.925100312643911e-170;
        bool r570513 = r570509 <= r570512;
        double r570514 = !r570513;
        bool r570515 = r570511 || r570514;
        double r570516 = x;
        double r570517 = y;
        double r570518 = r570517 - r570516;
        double r570519 = z;
        double r570520 = t;
        double r570521 = r570519 - r570520;
        double r570522 = r570509 - r570520;
        double r570523 = r570521 / r570522;
        double r570524 = r570518 * r570523;
        double r570525 = r570516 + r570524;
        double r570526 = r570516 * r570519;
        double r570527 = r570526 / r570520;
        double r570528 = r570517 + r570527;
        double r570529 = r570519 * r570517;
        double r570530 = r570529 / r570520;
        double r570531 = r570528 - r570530;
        double r570532 = r570515 ? r570525 : r570531;
        return r570532;
}

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

Original25.2
Target9.3
Herbie12.1
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.5037435798431229e-108 or -9.925100312643911e-170 < a

    1. Initial program 25.1

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

    3. Applied *-un-lft-identity25.1

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

    4. Applied times-frac11.5

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

    5. Simplified11.5

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

    if -1.5037435798431229e-108 < a < -9.925100312643911e-170

    1. Initial program 28.1

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

    2. Taylor expanded around inf 22.9

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.50374357984312286 \cdot 10^{-108} \lor \neg \left(a \le -9.9251003126439114 \cdot 10^{-170}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 
(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))))