Average Error: 0.3 → 0.3
Time: 23.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\left(x \cdot 0.5\right) \cdot \sqrt{z \cdot 2} + \left(-y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\left(x \cdot 0.5\right) \cdot \sqrt{z \cdot 2} + \left(-y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}
double f(double x, double y, double z, double t) {
        double r539872 = x;
        double r539873 = 0.5;
        double r539874 = r539872 * r539873;
        double r539875 = y;
        double r539876 = r539874 - r539875;
        double r539877 = z;
        double r539878 = 2.0;
        double r539879 = r539877 * r539878;
        double r539880 = sqrt(r539879);
        double r539881 = r539876 * r539880;
        double r539882 = t;
        double r539883 = r539882 * r539882;
        double r539884 = r539883 / r539878;
        double r539885 = exp(r539884);
        double r539886 = r539881 * r539885;
        return r539886;
}
↓
double f(double x, double y, double z, double t) {
        double r539887 = t;
        double r539888 = exp(r539887);
        double r539889 = pow(r539888, r539887);
        double r539890 = 0.5;
        double r539891 = 2.0;
        double r539892 = r539890 / r539891;
        double r539893 = pow(r539889, r539892);
        double r539894 = x;
        double r539895 = 0.5;
        double r539896 = r539894 * r539895;
        double r539897 = z;
        double r539898 = r539897 * r539891;
        double r539899 = sqrt(r539898);
        double r539900 = r539896 * r539899;
        double r539901 = y;
        double r539902 = -r539901;
        double r539903 = r539902 * r539899;
        double r539904 = r539900 + r539903;
        double r539905 = r539893 * r539904;
        double r539906 = 1.0;
        double r539907 = r539906 / r539891;
        double r539908 = 2.0;
        double r539909 = r539907 / r539908;
        double r539910 = pow(r539889, r539909);
        double r539911 = r539905 * r539910;
        return r539911;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.3
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
  2. Using strategy rm

  3. Applied div-inv0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\left(t \cdot t\right) \cdot \frac{1}{2}}}\]

  4. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{t \cdot t}\right)}^{\left(\frac{1}{2}\right)}}\]
  5. Using strategy rm

  6. Applied add-log-exp0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{\color{blue}{\log \left(e^{t}\right)} \cdot t}\right)}^{\left(\frac{1}{2}\right)}\]

  7. Applied exp-to-pow0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\color{blue}{\left({\left(e^{t}\right)}^{t}\right)}}^{\left(\frac{1}{2}\right)}\]
  8. Using strategy rm

  9. Applied sqr-pow0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{\left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}\]

  10. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}}\]

  11. Simplified0.3

    \[\leadsto \color{blue}{\left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5 - y\right)\right)\right)} \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]
  12. Using strategy rm

  13. Applied sub-neg0.3

    \[\leadsto \left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\sqrt{z \cdot 2} \cdot \color{blue}{\left(x \cdot 0.5 + \left(-y\right)\right)}\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]

  14. Applied distribute-lft-in0.3

    \[\leadsto \left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \color{blue}{\left(\sqrt{z \cdot 2} \cdot \left(x \cdot 0.5\right) + \sqrt{z \cdot 2} \cdot \left(-y\right)\right)}\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]

  15. Simplified0.3

    \[\leadsto \left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\color{blue}{\left(x \cdot 0.5\right) \cdot \sqrt{z \cdot 2}} + \sqrt{z \cdot 2} \cdot \left(-y\right)\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]

  16. Simplified0.3

    \[\leadsto \left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\left(x \cdot 0.5\right) \cdot \sqrt{z \cdot 2} + \color{blue}{\left(-y\right) \cdot \sqrt{z \cdot 2}}\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]

  17. Final simplification0.3

    \[\leadsto \left({\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \left(\left(x \cdot 0.5\right) \cdot \sqrt{z \cdot 2} + \left(-y\right) \cdot \sqrt{z \cdot 2}\right)\right) \cdot {\left({\left(e^{t}\right)}^{t}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"
  :precision binary64

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (pow (exp 1) (/ (* t t) 2)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2))) (exp (/ (* t t) 2))))