Average Error: 24.9 → 11.4
Time: 5.7s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -4.8101418718325989 \cdot 10^{-48} \lor \neg \left(a \le 1.72111488913343407 \cdot 10^{-177}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}
↓
\begin{array}{l}
\mathbf{if}\;a \le -4.8101418718325989 \cdot 10^{-48} \lor \neg \left(a \le 1.72111488913343407 \cdot 10^{-177}\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 r643933 = x;
        double r643934 = y;
        double r643935 = r643934 - r643933;
        double r643936 = z;
        double r643937 = t;
        double r643938 = r643936 - r643937;
        double r643939 = r643935 * r643938;
        double r643940 = a;
        double r643941 = r643940 - r643937;
        double r643942 = r643939 / r643941;
        double r643943 = r643933 + r643942;
        return r643943;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r643944 = a;
        double r643945 = -4.810141871832599e-48;
        bool r643946 = r643944 <= r643945;
        double r643947 = 1.721114889133434e-177;
        bool r643948 = r643944 <= r643947;
        double r643949 = !r643948;
        bool r643950 = r643946 || r643949;
        double r643951 = x;
        double r643952 = y;
        double r643953 = r643952 - r643951;
        double r643954 = z;
        double r643955 = t;
        double r643956 = r643954 - r643955;
        double r643957 = r643944 - r643955;
        double r643958 = r643956 / r643957;
        double r643959 = r643953 * r643958;
        double r643960 = r643951 + r643959;
        double r643961 = r643951 * r643954;
        double r643962 = r643961 / r643955;
        double r643963 = r643952 + r643962;
        double r643964 = r643954 * r643952;
        double r643965 = r643964 / r643955;
        double r643966 = r643963 - r643965;
        double r643967 = r643950 ? r643960 : r643966;
        return r643967;
}

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

Original24.9
Target9.3
Herbie11.4
\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -4.810141871832599e-48 or 1.721114889133434e-177 < a

    1. Initial program 23.0

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

    3. Applied *-un-lft-identity23.0

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

    4. Applied times-frac9.0

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

    5. Simplified9.0

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

    if -4.810141871832599e-48 < a < 1.721114889133434e-177

    1. Initial program 29.4

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

    2. Taylor expanded around inf 17.1

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

  4. Final simplification11.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.8101418718325989 \cdot 10^{-48} \lor \neg \left(a \le 1.72111488913343407 \cdot 10^{-177}\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y + \frac{x \cdot z}{t}\right) - \frac{z \cdot y}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))