Average Error: 3.6 → 0.8
Time: 15.3s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -6.04040118693943595803771657159403407899 \cdot 10^{54}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{elif}\;t \le 17403769.191135458648204803466796875:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\\ \end{array}\]
\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}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\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 r52982976 = x;
        double r52982977 = y;
        double r52982978 = z;
        double r52982979 = 3.0;
        double r52982980 = r52982978 * r52982979;
        double r52982981 = r52982977 / r52982980;
        double r52982982 = r52982976 - r52982981;
        double r52982983 = t;
        double r52982984 = r52982980 * r52982977;
        double r52982985 = r52982983 / r52982984;
        double r52982986 = r52982982 + r52982985;
        return r52982986;
}
↓
double f(double x, double y, double z, double t) {
        double r52982987 = t;
        double r52982988 = -6.040401186939436e+54;
        bool r52982989 = r52982987 <= r52982988;
        double r52982990 = x;
        double r52982991 = y;
        double r52982992 = z;
        double r52982993 = 3.0;
        double r52982994 = r52982992 * r52982993;
        double r52982995 = r52982991 / r52982994;
        double r52982996 = r52982990 - r52982995;
        double r52982997 = r52982993 * r52982991;
        double r52982998 = r52982992 * r52982997;
        double r52982999 = r52982987 / r52982998;
        double r52983000 = r52982996 + r52982999;
        double r52983001 = 17403769.19113546;
        bool r52983002 = r52982987 <= r52983001;
        double r52983003 = 1.0;
        double r52983004 = r52983003 / r52982992;
        double r52983005 = r52982987 / r52982993;
        double r52983006 = r52983005 / r52982991;
        double r52983007 = r52983004 * r52983006;
        double r52983008 = r52982996 + r52983007;
        double r52983009 = r52982991 / r52982992;
        double r52983010 = r52983009 / r52982993;
        double r52983011 = r52982990 - r52983010;
        double r52983012 = r52982987 / r52982994;
        double r52983013 = r52983012 / r52982991;
        double r52983014 = r52983011 + r52983013;
        double r52983015 = r52983002 ? r52983008 : r52983014;
        double r52983016 = r52982989 ? r52983000 : r52983015;
        return r52983016;
}

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

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

Reproduce

herbie shell --seed 2019174 
(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))))