Average Error: 5.6 → 0.7
Time: 10.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.0994806737492123 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \le 1.3603908647454576 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{\left(-t \cdot y\right) + z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.0994806737492123 \cdot 10^{-51}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \le 1.3603908647454576 \cdot 10^{-28}:\\
\;\;\;\;x - \frac{\left(-t \cdot y\right) + z \cdot y}{a}\\

\mathbf{else}:\\
\;\;\;\;x - y \cdot \frac{z - t}{a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r5937034 = x;
        double r5937035 = y;
        double r5937036 = z;
        double r5937037 = t;
        double r5937038 = r5937036 - r5937037;
        double r5937039 = r5937035 * r5937038;
        double r5937040 = a;
        double r5937041 = r5937039 / r5937040;
        double r5937042 = r5937034 - r5937041;
        return r5937042;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r5937043 = y;
        double r5937044 = -2.0994806737492123e-51;
        bool r5937045 = r5937043 <= r5937044;
        double r5937046 = x;
        double r5937047 = z;
        double r5937048 = t;
        double r5937049 = r5937047 - r5937048;
        double r5937050 = a;
        double r5937051 = r5937049 / r5937050;
        double r5937052 = r5937043 * r5937051;
        double r5937053 = r5937046 - r5937052;
        double r5937054 = 1.3603908647454576e-28;
        bool r5937055 = r5937043 <= r5937054;
        double r5937056 = r5937048 * r5937043;
        double r5937057 = -r5937056;
        double r5937058 = r5937047 * r5937043;
        double r5937059 = r5937057 + r5937058;
        double r5937060 = r5937059 / r5937050;
        double r5937061 = r5937046 - r5937060;
        double r5937062 = r5937055 ? r5937061 : r5937053;
        double r5937063 = r5937045 ? r5937053 : r5937062;
        return r5937063;
}

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

Original5.6
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -2.0994806737492123e-51 or 1.3603908647454576e-28 < y

    1. Initial program 11.8

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

    3. Applied *-un-lft-identity11.8

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

    4. Applied times-frac1.0

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

    5. Simplified1.0

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

    if -2.0994806737492123e-51 < y < 1.3603908647454576e-28

    1. Initial program 0.4

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

    3. Applied sub-neg0.4

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

    4. Applied distribute-lft-in0.4

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.0994806737492123 \cdot 10^{-51}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \le 1.3603908647454576 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{\left(-t \cdot y\right) + z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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