Average Error: 24.0 → 10.5
Time: 23.2s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -9.750789174983166 \cdot 10^{-119}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 6.1598368637294395 \cdot 10^{-208}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -9.750789174983166 \cdot 10^{-119}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\

\mathbf{elif}\;a \le 6.1598368637294395 \cdot 10^{-208}:\\
\;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r31636242 = x;
        double r31636243 = y;
        double r31636244 = r31636243 - r31636242;
        double r31636245 = z;
        double r31636246 = t;
        double r31636247 = r31636245 - r31636246;
        double r31636248 = r31636244 * r31636247;
        double r31636249 = a;
        double r31636250 = r31636249 - r31636246;
        double r31636251 = r31636248 / r31636250;
        double r31636252 = r31636242 + r31636251;
        return r31636252;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r31636253 = a;
        double r31636254 = -9.750789174983166e-119;
        bool r31636255 = r31636253 <= r31636254;
        double r31636256 = x;
        double r31636257 = y;
        double r31636258 = r31636257 - r31636256;
        double r31636259 = z;
        double r31636260 = t;
        double r31636261 = r31636259 - r31636260;
        double r31636262 = r31636253 - r31636260;
        double r31636263 = r31636261 / r31636262;
        double r31636264 = r31636258 * r31636263;
        double r31636265 = r31636256 + r31636264;
        double r31636266 = 6.1598368637294395e-208;
        bool r31636267 = r31636253 <= r31636266;
        double r31636268 = r31636256 * r31636259;
        double r31636269 = r31636268 / r31636260;
        double r31636270 = r31636257 + r31636269;
        double r31636271 = r31636259 * r31636257;
        double r31636272 = r31636271 / r31636260;
        double r31636273 = r31636270 - r31636272;
        double r31636274 = r31636267 ? r31636273 : r31636265;
        double r31636275 = r31636255 ? r31636265 : r31636274;
        return r31636275;
}

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

Original24.0
Target9.5
Herbie10.5
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -9.750789174983166e-119 or 6.1598368637294395e-208 < a

    1. Initial program 22.7

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

    3. Applied *-un-lft-identity22.7

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

    4. Applied times-frac10.0

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

    5. Simplified10.0

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

    if -9.750789174983166e-119 < a < 6.1598368637294395e-208

    1. Initial program 28.9

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

    2. Taylor expanded around inf 12.3

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

  4. Final simplification10.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -9.750789174983166 \cdot 10^{-119}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \le 6.1598368637294395 \cdot 10^{-208}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"

  :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))))