Average Error: 3.6 → 0.8
Time: 19.3s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.04040118693943595803771657159403407899 \cdot 10^{54}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{elif}\;t \le 17403769.191135458648204803466796875:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -6.04040118693943595803771657159403407899 \cdot 10^{54}:\\
\;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\

\mathbf{elif}\;t \le 17403769.191135458648204803466796875:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r32306211 = x;
        double r32306212 = y;
        double r32306213 = z;
        double r32306214 = 3.0;
        double r32306215 = r32306213 * r32306214;
        double r32306216 = r32306212 / r32306215;
        double r32306217 = r32306211 - r32306216;
        double r32306218 = t;
        double r32306219 = r32306215 * r32306212;
        double r32306220 = r32306218 / r32306219;
        double r32306221 = r32306217 + r32306220;
        return r32306221;
}
↓
double f(double x, double y, double z, double t) {
        double r32306222 = t;
        double r32306223 = -6.040401186939436e+54;
        bool r32306224 = r32306222 <= r32306223;
        double r32306225 = z;
        double r32306226 = 3.0;
        double r32306227 = y;
        double r32306228 = r32306226 * r32306227;
        double r32306229 = r32306225 * r32306228;
        double r32306230 = r32306222 / r32306229;
        double r32306231 = x;
        double r32306232 = r32306225 * r32306226;
        double r32306233 = r32306227 / r32306232;
        double r32306234 = r32306231 - r32306233;
        double r32306235 = r32306230 + r32306234;
        double r32306236 = 17403769.19113546;
        bool r32306237 = r32306222 <= r32306236;
        double r32306238 = 1.0;
        double r32306239 = r32306238 / r32306225;
        double r32306240 = r32306222 / r32306226;
        double r32306241 = r32306240 / r32306227;
        double r32306242 = r32306239 * r32306241;
        double r32306243 = r32306234 + r32306242;
        double r32306244 = r32306227 / r32306225;
        double r32306245 = r32306244 / r32306226;
        double r32306246 = r32306231 - r32306245;
        double r32306247 = r32306222 / r32306232;
        double r32306248 = r32306247 / r32306227;
        double r32306249 = r32306246 + r32306248;
        double r32306250 = r32306237 ? r32306243 : r32306249;
        double r32306251 = r32306224 ? r32306235 : r32306250;
        return r32306251;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.6
Target1.6
Herbie0.8
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -6.040401186939436e+54

    1. Initial program 0.7

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-*l*0.6

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}}\]

    if -6.040401186939436e+54 < t < 17403769.19113546

    1. Initial program 5.3

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*1.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity1.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{\color{blue}{1 \cdot y}}\]

    6. Applied *-un-lft-identity1.0

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\color{blue}{1 \cdot t}}{z \cdot 3}}{1 \cdot y}\]

    7. Applied times-frac1.1

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{1}{z} \cdot \frac{t}{3}}}{1 \cdot y}\]

    8. Applied times-frac0.3

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{1}{z}}{1} \cdot \frac{\frac{t}{3}}{y}}\]

    9. Simplified0.3

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{1}{z}} \cdot \frac{\frac{t}{3}}{y}\]

    if 17403769.19113546 < t

    1. Initial program 0.8

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
    2. Using strategy rm

    3. Applied associate-/r*2.1

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}}\]
    4. Using strategy rm

    5. Applied associate-/r*2.1

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -6.04040118693943595803771657159403407899 \cdot 10^{54}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{elif}\;t \le 17403769.191135458648204803466796875:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))