Average Error: 24.1 → 8.8
Time: 20.4s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -1.403564582318585211719020373880695846914 \cdot 10^{-264}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -1.403564582318585211719020373880695846914 \cdot 10^{-264}:\\
\;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\

\mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\
\;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r33053321 = x;
        double r33053322 = y;
        double r33053323 = r33053322 - r33053321;
        double r33053324 = z;
        double r33053325 = t;
        double r33053326 = r33053324 - r33053325;
        double r33053327 = r33053323 * r33053326;
        double r33053328 = a;
        double r33053329 = r33053328 - r33053325;
        double r33053330 = r33053327 / r33053329;
        double r33053331 = r33053321 + r33053330;
        return r33053331;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r33053332 = x;
        double r33053333 = y;
        double r33053334 = r33053333 - r33053332;
        double r33053335 = z;
        double r33053336 = t;
        double r33053337 = r33053335 - r33053336;
        double r33053338 = r33053334 * r33053337;
        double r33053339 = a;
        double r33053340 = r33053339 - r33053336;
        double r33053341 = r33053338 / r33053340;
        double r33053342 = r33053332 + r33053341;
        double r33053343 = -1.4035645823185852e-264;
        bool r33053344 = r33053342 <= r33053343;
        double r33053345 = r33053337 / r33053340;
        double r33053346 = r33053334 * r33053345;
        double r33053347 = r33053346 + r33053332;
        double r33053348 = 0.0;
        bool r33053349 = r33053342 <= r33053348;
        double r33053350 = r33053335 * r33053332;
        double r33053351 = r33053350 / r33053336;
        double r33053352 = r33053351 + r33053333;
        double r33053353 = r33053335 * r33053333;
        double r33053354 = r33053353 / r33053336;
        double r33053355 = r33053352 - r33053354;
        double r33053356 = r33053349 ? r33053355 : r33053347;
        double r33053357 = r33053344 ? r33053347 : r33053356;
        return r33053357;
}

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

Original24.1
Target9.5
Herbie8.8
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) (- z t)) (- a t))) < -1.4035645823185852e-264 or 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

    1. Initial program 21.1

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

    3. Applied associate-/l*7.7

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

    5. Applied div-inv7.9

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

    6. Simplified7.8

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

    if -1.4035645823185852e-264 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

    1. Initial program 57.6

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

    2. Taylor expanded around inf 19.6

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

  4. Final simplification8.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -1.403564582318585211719020373880695846914 \cdot 10^{-264}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;\left(\frac{z \cdot x}{t} + y\right) - \frac{z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{z - t}{a - t} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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