Average Error: 3.8 → 0.6
Time: 12.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\

\mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r557071 = x;
        double r557072 = 2.0;
        double r557073 = r557071 * r557072;
        double r557074 = y;
        double r557075 = 9.0;
        double r557076 = r557074 * r557075;
        double r557077 = z;
        double r557078 = r557076 * r557077;
        double r557079 = t;
        double r557080 = r557078 * r557079;
        double r557081 = r557073 - r557080;
        double r557082 = a;
        double r557083 = 27.0;
        double r557084 = r557082 * r557083;
        double r557085 = b;
        double r557086 = r557084 * r557085;
        double r557087 = r557081 + r557086;
        return r557087;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r557088 = y;
        double r557089 = 9.0;
        double r557090 = r557088 * r557089;
        double r557091 = -3.338893372507657e-32;
        bool r557092 = r557090 <= r557091;
        double r557093 = x;
        double r557094 = 2.0;
        double r557095 = r557093 * r557094;
        double r557096 = sqrt(r557089);
        double r557097 = z;
        double r557098 = t;
        double r557099 = r557097 * r557098;
        double r557100 = r557096 * r557099;
        double r557101 = r557096 * r557100;
        double r557102 = r557088 * r557101;
        double r557103 = r557095 - r557102;
        double r557104 = 27.0;
        double r557105 = a;
        double r557106 = b;
        double r557107 = r557105 * r557106;
        double r557108 = r557104 * r557107;
        double r557109 = r557103 + r557108;
        double r557110 = 2.4139872172489993e-42;
        bool r557111 = r557090 <= r557110;
        double r557112 = r557090 * r557097;
        double r557113 = r557112 * r557098;
        double r557114 = r557095 - r557113;
        double r557115 = r557104 * r557106;
        double r557116 = r557105 * r557115;
        double r557117 = r557114 + r557116;
        double r557118 = r557090 * r557099;
        double r557119 = r557095 - r557118;
        double r557120 = sqrt(r557104);
        double r557121 = r557120 * r557107;
        double r557122 = r557120 * r557121;
        double r557123 = r557119 + r557122;
        double r557124 = r557111 ? r557117 : r557123;
        double r557125 = r557092 ? r557109 : r557124;
        return r557125;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.8
Target2.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y 9.0) < -3.338893372507657e-32

    1. Initial program 7.1

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.8

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around 0 0.8

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
    5. Using strategy rm

    6. Applied associate-*l*0.7

      \[\leadsto \left(x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + 27 \cdot \left(a \cdot b\right)\]
    7. Using strategy rm

    8. Applied add-sqr-sqrt0.7

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\color{blue}{\left(\sqrt{9} \cdot \sqrt{9}\right)} \cdot \left(z \cdot t\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\]

    9. Applied associate-*l*0.8

      \[\leadsto \left(x \cdot 2 - y \cdot \color{blue}{\left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)}\right) + 27 \cdot \left(a \cdot b\right)\]

    if -3.338893372507657e-32 < (* y 9.0) < 2.4139872172489993e-42

    1. Initial program 0.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.5

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{a \cdot \left(27 \cdot b\right)}\]

    if 2.4139872172489993e-42 < (* y 9.0)

    1. Initial program 7.2

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*0.7

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around 0 0.7

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
    5. Using strategy rm

    6. Applied add-sqr-sqrt0.7

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{\left(\sqrt{27} \cdot \sqrt{27}\right)} \cdot \left(a \cdot b\right)\]

    7. Applied associate-*l*0.8

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))