Average Error: 6.4 → 0.7
Time: 12.8s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -9.109595270522021579671391139995883067258 \cdot 10^{140} \lor \neg \left(\left(z - t\right) \cdot y \le 4.07478987407041983829874325238341798776 \cdot 10^{191}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;\left(z - t\right) \cdot y \le -9.109595270522021579671391139995883067258 \cdot 10^{140} \lor \neg \left(\left(z - t\right) \cdot y \le 4.07478987407041983829874325238341798776 \cdot 10^{191}\right):\\
\;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r225948 = x;
        double r225949 = y;
        double r225950 = z;
        double r225951 = t;
        double r225952 = r225950 - r225951;
        double r225953 = r225949 * r225952;
        double r225954 = a;
        double r225955 = r225953 / r225954;
        double r225956 = r225948 - r225955;
        return r225956;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r225957 = z;
        double r225958 = t;
        double r225959 = r225957 - r225958;
        double r225960 = y;
        double r225961 = r225959 * r225960;
        double r225962 = -9.109595270522022e+140;
        bool r225963 = r225961 <= r225962;
        double r225964 = 4.07478987407042e+191;
        bool r225965 = r225961 <= r225964;
        double r225966 = !r225965;
        bool r225967 = r225963 || r225966;
        double r225968 = x;
        double r225969 = a;
        double r225970 = r225958 - r225957;
        double r225971 = r225969 / r225970;
        double r225972 = r225960 / r225971;
        double r225973 = r225968 + r225972;
        double r225974 = r225961 / r225969;
        double r225975 = r225968 - r225974;
        double r225976 = r225967 ? r225973 : r225975;
        return r225976;
}

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

Original6.4
Target0.7
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -9.109595270522022e+140 or 4.07478987407042e+191 < (* y (- z t))

    1. Initial program 23.6

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

    2. Simplified1.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t - z, x\right)}\]
    3. Using strategy rm

    4. Applied fma-udef1.2

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

    5. Simplified1.4

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

    if -9.109595270522022e+140 < (* y (- z t)) < 4.07478987407042e+191

    1. Initial program 0.5

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \le -9.109595270522021579671391139995883067258 \cdot 10^{140} \lor \neg \left(\left(z - t\right) \cdot y \le 4.07478987407041983829874325238341798776 \cdot 10^{191}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 +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 (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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