Average Error: 3.3 → 2.0
Time: 6.6s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.4052837436924809 \cdot 10^{37}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -9.4052837436924809 \cdot 10^{37}:\\
\;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r778970 = x;
        double r778971 = y;
        double r778972 = z;
        double r778973 = 3.0;
        double r778974 = r778972 * r778973;
        double r778975 = r778971 / r778974;
        double r778976 = r778970 - r778975;
        double r778977 = t;
        double r778978 = r778974 * r778971;
        double r778979 = r778977 / r778978;
        double r778980 = r778976 + r778979;
        return r778980;
}
↓
double f(double x, double y, double z, double t) {
        double r778981 = t;
        double r778982 = -9.40528374369248e+37;
        bool r778983 = r778981 <= r778982;
        double r778984 = x;
        double r778985 = y;
        double r778986 = z;
        double r778987 = 3.0;
        double r778988 = r778986 * r778987;
        double r778989 = r778985 / r778988;
        double r778990 = r778984 - r778989;
        double r778991 = 0.3333333333333333;
        double r778992 = r778986 * r778985;
        double r778993 = r778981 / r778992;
        double r778994 = r778991 * r778993;
        double r778995 = r778990 + r778994;
        double r778996 = r778985 / r778987;
        double r778997 = r778996 / r778986;
        double r778998 = r778984 - r778997;
        double r778999 = 1.0;
        double r779000 = r778999 / r778986;
        double r779001 = r778981 / r778987;
        double r779002 = r778985 / r779001;
        double r779003 = r779000 / r779002;
        double r779004 = r778998 + r779003;
        double r779005 = r778983 ? r778995 : r779004;
        return r779005;
}

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

Original3.3
Target1.8
Herbie2.0
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -9.40528374369248e+37

    1. Initial program 0.7

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

    2. Taylor expanded around 0 0.8

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{0.333333333333333315 \cdot \frac{t}{z \cdot y}}\]

    if -9.40528374369248e+37 < t

    1. Initial program 3.9

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

    3. Applied associate-/r*1.5

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

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

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

    6. Applied times-frac1.5

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

    7. Applied associate-/l*2.3

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

    9. Applied *-un-lft-identity2.3

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

    10. Applied times-frac2.3

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

    12. Applied associate-*l/2.3

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

    13. Simplified2.3

      \[\leadsto \left(x - \frac{\color{blue}{\frac{y}{3}}}{z}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.4052837436924809 \cdot 10^{37}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{3}}{z}\right) + \frac{\frac{1}{z}}{\frac{y}{\frac{t}{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))