Average Error: 24.6 → 10.3
Time: 23.1s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -9.552154943493009451397668509160896818957 \cdot 10^{-235} \lor \neg \left(a \le 1.652446675351756820364252107547174983616 \cdot 10^{-178}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -9.552154943493009451397668509160896818957 \cdot 10^{-235} \lor \neg \left(a \le 1.652446675351756820364252107547174983616 \cdot 10^{-178}\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 r737156 = x;
        double r737157 = y;
        double r737158 = r737157 - r737156;
        double r737159 = z;
        double r737160 = t;
        double r737161 = r737159 - r737160;
        double r737162 = r737158 * r737161;
        double r737163 = a;
        double r737164 = r737163 - r737160;
        double r737165 = r737162 / r737164;
        double r737166 = r737156 + r737165;
        return r737166;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r737167 = a;
        double r737168 = -9.55215494349301e-235;
        bool r737169 = r737167 <= r737168;
        double r737170 = 1.6524466753517568e-178;
        bool r737171 = r737167 <= r737170;
        double r737172 = !r737171;
        bool r737173 = r737169 || r737172;
        double r737174 = x;
        double r737175 = y;
        double r737176 = r737175 - r737174;
        double r737177 = z;
        double r737178 = t;
        double r737179 = r737177 - r737178;
        double r737180 = r737167 - r737178;
        double r737181 = r737179 / r737180;
        double r737182 = r737176 * r737181;
        double r737183 = r737174 + r737182;
        double r737184 = r737174 * r737177;
        double r737185 = r737184 / r737178;
        double r737186 = r737175 + r737185;
        double r737187 = r737177 * r737175;
        double r737188 = r737187 / r737178;
        double r737189 = r737186 - r737188;
        double r737190 = r737173 ? r737183 : r737189;
        return r737190;
}

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

Original24.6
Target9.3
Herbie10.3
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -9.55215494349301e-235 or 1.6524466753517568e-178 < a

    1. Initial program 23.7

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

    3. Applied *-un-lft-identity23.7

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

    4. Applied times-frac10.1

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

    5. Simplified10.1

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

    if -9.55215494349301e-235 < a < 1.6524466753517568e-178

    1. Initial program 29.6

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

    2. Taylor expanded around inf 11.4

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

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -9.552154943493009451397668509160896818957 \cdot 10^{-235} \lor \neg \left(a \le 1.652446675351756820364252107547174983616 \cdot 10^{-178}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 
(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))))