Average Error: 0.3 → 0.5
Time: 37.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r515875 = x;
        double r515876 = 0.5;
        double r515877 = r515875 * r515876;
        double r515878 = y;
        double r515879 = r515877 - r515878;
        double r515880 = z;
        double r515881 = 2.0;
        double r515882 = r515880 * r515881;
        double r515883 = sqrt(r515882);
        double r515884 = r515879 * r515883;
        double r515885 = t;
        double r515886 = r515885 * r515885;
        double r515887 = r515886 / r515881;
        double r515888 = exp(r515887);
        double r515889 = r515884 * r515888;
        return r515889;
}
↓
double f(double x, double y, double z, double t) {
        double r515890 = x;
        double r515891 = 0.5;
        double r515892 = r515890 * r515891;
        double r515893 = y;
        double r515894 = r515892 - r515893;
        double r515895 = z;
        double r515896 = sqrt(r515895);
        double r515897 = r515894 * r515896;
        double r515898 = 2.0;
        double r515899 = sqrt(r515898);
        double r515900 = cbrt(r515899);
        double r515901 = r515900 * r515900;
        double r515902 = r515897 * r515901;
        double r515903 = r515902 * r515900;
        double r515904 = exp(1.0);
        double r515905 = t;
        double r515906 = r515905 * r515905;
        double r515907 = r515906 / r515898;
        double r515908 = pow(r515904, r515907);
        double r515909 = r515903 * r515908;
        return r515909;
}

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

Original0.3
Target0.3
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 *-un-lft-identity0.3

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

  4. Applied exp-prod0.3

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

  5. Simplified0.3

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

  7. Applied sqrt-prod0.5

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

  8. Applied associate-*r*0.5

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

  10. Applied add-cube-cbrt0.5

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \sqrt[3]{\sqrt{2}}\right)}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]

  11. Applied associate-*r*0.5

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)} \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]

  12. Final simplification0.5

    \[\leadsto \left(\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))