Average Error: 25.0 → 10.7
Time: 7.5s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\
\;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - 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 r712033 = x;
        double r712034 = y;
        double r712035 = r712034 - r712033;
        double r712036 = z;
        double r712037 = t;
        double r712038 = r712036 - r712037;
        double r712039 = r712035 * r712038;
        double r712040 = a;
        double r712041 = r712040 - r712037;
        double r712042 = r712039 / r712041;
        double r712043 = r712033 + r712042;
        return r712043;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r712044 = a;
        double r712045 = -1.9571495574965582e-126;
        bool r712046 = r712044 <= r712045;
        double r712047 = 4.0034989804875424e-122;
        bool r712048 = r712044 <= r712047;
        double r712049 = !r712048;
        bool r712050 = r712046 || r712049;
        double r712051 = x;
        double r712052 = y;
        double r712053 = r712052 - r712051;
        double r712054 = t;
        double r712055 = r712044 - r712054;
        double r712056 = 1.0;
        double r712057 = z;
        double r712058 = r712057 - r712054;
        double r712059 = r712056 / r712058;
        double r712060 = r712055 * r712059;
        double r712061 = r712053 / r712060;
        double r712062 = r712051 + r712061;
        double r712063 = r712051 * r712057;
        double r712064 = r712063 / r712054;
        double r712065 = r712052 + r712064;
        double r712066 = r712057 * r712052;
        double r712067 = r712066 / r712054;
        double r712068 = r712065 - r712067;
        double r712069 = r712050 ? r712062 : r712068;
        return r712069;
}

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

Original25.0
Target9.5
Herbie10.7
\[\begin{array}{l} \mathbf{if}\;a \lt -1.615306284544257464183904494091872805513 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.774403170083174201868024161554637965035 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.9571495574965582e-126 or 4.0034989804875424e-122 < a

    1. Initial program 23.6

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

    3. Applied associate-/l*9.5

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

    5. Applied div-inv9.5

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

    if -1.9571495574965582e-126 < a < 4.0034989804875424e-122

    1. Initial program 28.9

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

    2. Taylor expanded around inf 14.0

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

  4. Final simplification10.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.957149557496558218367445688194546540827 \cdot 10^{-126} \lor \neg \left(a \le 4.003498980487542433224415809653995536148 \cdot 10^{-122}\right):\\ \;\;\;\;x + \frac{y - x}{\left(a - t\right) \cdot \frac{1}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(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))))