Average Error: 6.0 → 1.0
Time: 4.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -2.81789439071592 \cdot 10^{45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 1.71734560352234823 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;y \le 3.25053680246434249 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \le -2.81789439071592 \cdot 10^{45}:\\
\;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\

\mathbf{elif}\;y \le 1.71734560352234823 \cdot 10^{-179}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

\mathbf{elif}\;y \le 3.25053680246434249 \cdot 10^{-65}:\\
\;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r347142 = x;
        double r347143 = y;
        double r347144 = z;
        double r347145 = t;
        double r347146 = r347144 - r347145;
        double r347147 = r347143 * r347146;
        double r347148 = a;
        double r347149 = r347147 / r347148;
        double r347150 = r347142 + r347149;
        return r347150;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r347151 = y;
        double r347152 = -2.817894390715925e+45;
        bool r347153 = r347151 <= r347152;
        double r347154 = x;
        double r347155 = a;
        double r347156 = z;
        double r347157 = t;
        double r347158 = r347156 - r347157;
        double r347159 = r347155 / r347158;
        double r347160 = r347151 / r347159;
        double r347161 = r347154 + r347160;
        double r347162 = 1.7173456035223482e-179;
        bool r347163 = r347151 <= r347162;
        double r347164 = r347151 * r347158;
        double r347165 = r347164 / r347155;
        double r347166 = r347154 + r347165;
        double r347167 = 3.2505368024643425e-65;
        bool r347168 = r347151 <= r347167;
        double r347169 = r347151 / r347155;
        double r347170 = r347169 * r347158;
        double r347171 = r347154 + r347170;
        double r347172 = r347158 / r347155;
        double r347173 = r347151 * r347172;
        double r347174 = r347154 + r347173;
        double r347175 = r347168 ? r347171 : r347174;
        double r347176 = r347163 ? r347166 : r347175;
        double r347177 = r347153 ? r347161 : r347176;
        return r347177;
}

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

Original6.0
Target0.7
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if y < -2.817894390715925e+45

    1. Initial program 17.9

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

    3. Applied associate-/l*1.1

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

    if -2.817894390715925e+45 < y < 1.7173456035223482e-179

    1. Initial program 0.7

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

    if 1.7173456035223482e-179 < y < 3.2505368024643425e-65

    1. Initial program 0.4

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

    3. Applied associate-/l*7.2

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

    5. Applied associate-/r/1.4

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

    if 3.2505368024643425e-65 < y

    1. Initial program 11.3

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

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

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

    4. Applied times-frac1.4

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

    5. Simplified1.4

      \[\leadsto x + \color{blue}{y} \cdot \frac{z - t}{a}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.81789439071592 \cdot 10^{45}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;y \le 1.71734560352234823 \cdot 10^{-179}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;y \le 3.25053680246434249 \cdot 10^{-65}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :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)))