Average Error: 5.9 → 0.3
Time: 3.4s
Precision: 64
\[x - \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x + y \cdot \frac{-\left(z - t\right)}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.12460364113996697 \cdot 10^{196}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\\ \end{array}\]
x - \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\
\;\;\;\;x + y \cdot \frac{-\left(z - t\right)}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 1.12460364113996697 \cdot 10^{196}:\\
\;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r418102 = x;
        double r418103 = y;
        double r418104 = z;
        double r418105 = t;
        double r418106 = r418104 - r418105;
        double r418107 = r418103 * r418106;
        double r418108 = a;
        double r418109 = r418107 / r418108;
        double r418110 = r418102 - r418109;
        return r418110;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r418111 = y;
        double r418112 = z;
        double r418113 = t;
        double r418114 = r418112 - r418113;
        double r418115 = r418111 * r418114;
        double r418116 = -inf.0;
        bool r418117 = r418115 <= r418116;
        double r418118 = x;
        double r418119 = -r418114;
        double r418120 = a;
        double r418121 = r418119 / r418120;
        double r418122 = r418111 * r418121;
        double r418123 = r418118 + r418122;
        double r418124 = 1.124603641139967e+196;
        bool r418125 = r418115 <= r418124;
        double r418126 = r418115 / r418120;
        double r418127 = r418118 - r418126;
        double r418128 = r418111 / r418120;
        double r418129 = -r418128;
        double r418130 = r418129 * r418114;
        double r418131 = r418118 + r418130;
        double r418132 = r418125 ? r418127 : r418131;
        double r418133 = r418117 ? r418123 : r418132;
        return r418133;
}

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

Original5.9
Target0.6
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -inf.0

    1. Initial program 64.0

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

    3. Applied clear-num64.0

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

    5. Applied sub-neg64.0

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

    6. Simplified0.2

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

    8. Applied div-inv0.4

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

    9. Applied distribute-rgt-neg-in0.4

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

    10. Applied associate-*l*0.3

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

    11. Simplified0.2

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

    if -inf.0 < (* y (- z t)) < 1.124603641139967e+196

    1. Initial program 0.3

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

    if 1.124603641139967e+196 < (* y (- z t))

    1. Initial program 28.4

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

    3. Applied clear-num28.5

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

    5. Applied sub-neg28.5

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

    6. Simplified0.6

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty:\\ \;\;\;\;x + y \cdot \frac{-\left(z - t\right)}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 1.12460364113996697 \cdot 10^{196}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(-\frac{y}{a}\right) \cdot \left(z - t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))