Average Error: 6.0 → 0.7
Time: 8.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.7422788828719246 \cdot 10^{161}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{a}\right) + \frac{y}{a} \cdot \left(-t\right)\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -3.7422788828719246 \cdot 10^{161}:\\
\;\;\;\;x + y \cdot \frac{z - t}{a}\\

\mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\
\;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\

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

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r374090 = x;
        double r374091 = y;
        double r374092 = z;
        double r374093 = t;
        double r374094 = r374092 - r374093;
        double r374095 = r374091 * r374094;
        double r374096 = a;
        double r374097 = r374095 / r374096;
        double r374098 = r374090 + r374097;
        return r374098;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r374099 = y;
        double r374100 = z;
        double r374101 = t;
        double r374102 = r374100 - r374101;
        double r374103 = r374099 * r374102;
        double r374104 = -3.7422788828719246e+161;
        bool r374105 = r374103 <= r374104;
        double r374106 = x;
        double r374107 = a;
        double r374108 = r374102 / r374107;
        double r374109 = r374099 * r374108;
        double r374110 = r374106 + r374109;
        double r374111 = 2.424193312752178e+192;
        bool r374112 = r374103 <= r374111;
        double r374113 = 1.0;
        double r374114 = r374107 / r374103;
        double r374115 = r374113 / r374114;
        double r374116 = r374106 + r374115;
        double r374117 = r374099 / r374107;
        double r374118 = r374100 * r374117;
        double r374119 = r374106 + r374118;
        double r374120 = -r374101;
        double r374121 = r374117 * r374120;
        double r374122 = r374119 + r374121;
        double r374123 = r374112 ? r374116 : r374122;
        double r374124 = r374105 ? r374110 : r374123;
        return r374124;
}

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
Target0.6
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y (- z t)) < -3.7422788828719246e+161

    1. Initial program 21.2

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

    3. Applied *-un-lft-identity21.2

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

    4. Applied times-frac1.7

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

    5. Simplified1.7

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

    if -3.7422788828719246e+161 < (* y (- z t)) < 2.424193312752178e+192

    1. Initial program 0.4

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

    3. Applied clear-num0.4

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

    if 2.424193312752178e+192 < (* y (- z t))

    1. Initial program 26.2

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

    3. Applied associate-/l*1.1

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

    5. Applied associate-/r/1.0

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

    7. Applied sub-neg1.0

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

    8. Applied distribute-lft-in1.0

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

    9. Applied associate-+r+1.0

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

    10. Simplified1.0

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -3.7422788828719246 \cdot 10^{161}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \le 2.424193312752178 \cdot 10^{192}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \frac{y}{a}\right) + \frac{y}{a} \cdot \left(-t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))