Average Error: 3.8 → 0.4
Time: 4.1s
Precision: 64
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 2.41708142255612862 \cdot 10^{-32}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]
\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 2.41708142255612862 \cdot 10^{-32}\right):\\
\;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r731102 = x;
        double r731103 = y;
        double r731104 = z;
        double r731105 = 3.0;
        double r731106 = r731104 * r731105;
        double r731107 = r731103 / r731106;
        double r731108 = r731102 - r731107;
        double r731109 = t;
        double r731110 = r731106 * r731103;
        double r731111 = r731109 / r731110;
        double r731112 = r731108 + r731111;
        return r731112;
}
↓
double f(double x, double y, double z, double t) {
        double r731113 = t;
        double r731114 = -5.633804011750121e+26;
        bool r731115 = r731113 <= r731114;
        double r731116 = 2.4170814225561286e-32;
        bool r731117 = r731113 <= r731116;
        double r731118 = !r731117;
        bool r731119 = r731115 || r731118;
        double r731120 = x;
        double r731121 = y;
        double r731122 = z;
        double r731123 = r731121 / r731122;
        double r731124 = 3.0;
        double r731125 = r731123 / r731124;
        double r731126 = r731120 - r731125;
        double r731127 = 0.3333333333333333;
        double r731128 = r731122 * r731121;
        double r731129 = r731113 / r731128;
        double r731130 = r731127 * r731129;
        double r731131 = r731126 + r731130;
        double r731132 = 1.0;
        double r731133 = r731132 / r731122;
        double r731134 = r731113 / r731124;
        double r731135 = r731134 / r731121;
        double r731136 = r731133 * r731135;
        double r731137 = r731126 + r731136;
        double r731138 = r731119 ? r731131 : r731137;
        return r731138;
}

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

Original3.8
Target1.8
Herbie0.4
\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -5.633804011750121e+26 or 2.4170814225561286e-32 < t

    1. Initial program 0.6

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

    3. Applied associate-/r*2.4

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

    5. Applied associate-/r*2.4

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

    6. Taylor expanded around 0 0.7

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

    if -5.633804011750121e+26 < t < 2.4170814225561286e-32

    1. Initial program 6.1

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

    3. Applied associate-/r*1.3

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

    5. Applied associate-/r*1.3

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

    7. Applied *-un-lft-identity1.3

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

    8. Applied *-un-lft-identity1.3

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

    9. Applied times-frac1.3

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

    10. Applied times-frac0.3

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

    11. Simplified0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.63380401175012114 \cdot 10^{26} \lor \neg \left(t \le 2.41708142255612862 \cdot 10^{-32}\right):\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + 0.333333333333333315 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{1}{z} \cdot \frac{\frac{t}{3}}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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))))