Average Error: 20.7 → 19.2
Time: 14.7s
Precision: 64
\[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}\]
↓
\[\begin{array}{l} \mathbf{if}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 1.009936411466954 \cdot 10^{275}\right):\\ \;\;\;\;\log \left({\left(e^{2 \cdot \sqrt{x}}\right)}^{\left(\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) - \sin y \cdot \sin \left(-0.333333333333333315 \cdot \left(t \cdot z\right)\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]
\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3}
↓
\begin{array}{l}
\mathbf{if}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 1.009936411466954 \cdot 10^{275}\right):\\
\;\;\;\;\log \left({\left(e^{2 \cdot \sqrt{x}}\right)}^{\left(\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)}\right) - \frac{a}{b \cdot 3}\\

\mathbf{else}:\\
\;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) - \sin y \cdot \sin \left(-0.333333333333333315 \cdot \left(t \cdot z\right)\right)\right) - \frac{a}{b \cdot 3}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r800002 = 2.0;
        double r800003 = x;
        double r800004 = sqrt(r800003);
        double r800005 = r800002 * r800004;
        double r800006 = y;
        double r800007 = z;
        double r800008 = t;
        double r800009 = r800007 * r800008;
        double r800010 = 3.0;
        double r800011 = r800009 / r800010;
        double r800012 = r800006 - r800011;
        double r800013 = cos(r800012);
        double r800014 = r800005 * r800013;
        double r800015 = a;
        double r800016 = b;
        double r800017 = r800016 * r800010;
        double r800018 = r800015 / r800017;
        double r800019 = r800014 - r800018;
        return r800019;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r800020 = y;
        double r800021 = z;
        double r800022 = t;
        double r800023 = r800021 * r800022;
        double r800024 = 3.0;
        double r800025 = r800023 / r800024;
        double r800026 = r800020 - r800025;
        double r800027 = -inf.0;
        bool r800028 = r800026 <= r800027;
        double r800029 = 1.009936411466954e+275;
        bool r800030 = r800026 <= r800029;
        double r800031 = !r800030;
        bool r800032 = r800028 || r800031;
        double r800033 = 2.0;
        double r800034 = x;
        double r800035 = sqrt(r800034);
        double r800036 = r800033 * r800035;
        double r800037 = exp(r800036);
        double r800038 = sin(r800025);
        double r800039 = sin(r800020);
        double r800040 = r800038 * r800039;
        double r800041 = cos(r800020);
        double r800042 = cos(r800025);
        double r800043 = r800041 * r800042;
        double r800044 = r800040 + r800043;
        double r800045 = pow(r800037, r800044);
        double r800046 = log(r800045);
        double r800047 = a;
        double r800048 = b;
        double r800049 = r800048 * r800024;
        double r800050 = r800047 / r800049;
        double r800051 = r800046 - r800050;
        double r800052 = cbrt(r800042);
        double r800053 = r800052 * r800052;
        double r800054 = r800053 * r800052;
        double r800055 = r800041 * r800054;
        double r800056 = 0.3333333333333333;
        double r800057 = r800022 * r800021;
        double r800058 = r800056 * r800057;
        double r800059 = -r800058;
        double r800060 = sin(r800059);
        double r800061 = r800039 * r800060;
        double r800062 = r800055 - r800061;
        double r800063 = r800036 * r800062;
        double r800064 = r800063 - r800050;
        double r800065 = r800032 ? r800051 : r800064;
        return r800065;
}

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

Original20.7
Target18.7
Herbie19.2
\[\begin{array}{l} \mathbf{if}\;z \lt -1.379333748723514 \cdot 10^{129}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\frac{1}{y} - \frac{\frac{0.333333333333333315}{z}}{t}\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{elif}\;z \lt 3.51629061355598715 \cdot 10^{106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - \frac{\frac{0.333333333333333315}{z}}{t}\right) \cdot \left(2 \cdot \sqrt{x}\right) - \frac{\frac{a}{b}}{3}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- y (/ (* z t) 3.0)) < -inf.0 or 1.009936411466954e+275 < (- y (/ (* z t) 3.0))

    1. Initial program 53.9

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

    3. Applied sub-neg53.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y + \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3}\]

    4. Applied cos-sum53.7

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(-\frac{z \cdot t}{3}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3}\]

    5. Simplified53.7

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)} - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3}\]
    6. Using strategy rm

    7. Applied add-log-exp60.3

      \[\leadsto \color{blue}{\log \left(e^{\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right)}\right)} - \frac{a}{b \cdot 3}\]

    8. Simplified46.7

      \[\leadsto \log \color{blue}{\left({\left(e^{2 \cdot \sqrt{x}}\right)}^{\left(\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)}\right)} - \frac{a}{b \cdot 3}\]

    if -inf.0 < (- y (/ (* z t) 3.0)) < 1.009936411466954e+275

    1. Initial program 14.4

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

    3. Applied sub-neg14.4

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \color{blue}{\left(y + \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3}\]

    4. Applied cos-sum13.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(-\frac{z \cdot t}{3}\right) - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right)} - \frac{a}{b \cdot 3}\]

    5. Simplified13.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)} - \sin y \cdot \sin \left(-\frac{z \cdot t}{3}\right)\right) - \frac{a}{b \cdot 3}\]

    6. Taylor expanded around inf 13.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) - \sin y \cdot \color{blue}{\sin \left(-0.333333333333333315 \cdot \left(t \cdot z\right)\right)}\right) - \frac{a}{b \cdot 3}\]
    7. Using strategy rm

    8. Applied add-cube-cbrt13.9

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \color{blue}{\left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right)} - \sin y \cdot \sin \left(-0.333333333333333315 \cdot \left(t \cdot z\right)\right)\right) - \frac{a}{b \cdot 3}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification19.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y - \frac{z \cdot t}{3} = -\infty \lor \neg \left(y - \frac{z \cdot t}{3} \le 1.009936411466954 \cdot 10^{275}\right):\\ \;\;\;\;\log \left({\left(e^{2 \cdot \sqrt{x}}\right)}^{\left(\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)}\right) - \frac{a}{b \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \left(\left(\sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)} \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) \cdot \sqrt[3]{\cos \left(\frac{z \cdot t}{3}\right)}\right) - \sin y \cdot \sin \left(-0.333333333333333315 \cdot \left(t \cdot z\right)\right)\right) - \frac{a}{b \cdot 3}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.379333748723514e+129) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3))))

  (- (* (* 2 (sqrt x)) (cos (- y (/ (* z t) 3)))) (/ a (* b 3))))