Average Error: 0.3 → 0.5
Time: 32.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right) \cdot {e}^{\left(\frac{t \cdot t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\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 r1316829 = x;
        double r1316830 = 0.5;
        double r1316831 = r1316829 * r1316830;
        double r1316832 = y;
        double r1316833 = r1316831 - r1316832;
        double r1316834 = z;
        double r1316835 = 2.0;
        double r1316836 = r1316834 * r1316835;
        double r1316837 = sqrt(r1316836);
        double r1316838 = r1316833 * r1316837;
        double r1316839 = t;
        double r1316840 = r1316839 * r1316839;
        double r1316841 = r1316840 / r1316835;
        double r1316842 = exp(r1316841);
        double r1316843 = r1316838 * r1316842;
        return r1316843;
}
↓
double f(double x, double y, double z, double t) {
        double r1316844 = z;
        double r1316845 = sqrt(r1316844);
        double r1316846 = x;
        double r1316847 = 0.5;
        double r1316848 = r1316846 * r1316847;
        double r1316849 = y;
        double r1316850 = r1316848 - r1316849;
        double r1316851 = r1316845 * r1316850;
        double r1316852 = 2.0;
        double r1316853 = sqrt(r1316852);
        double r1316854 = cbrt(r1316853);
        double r1316855 = r1316854 * r1316854;
        double r1316856 = r1316851 * r1316855;
        double r1316857 = r1316856 * r1316854;
        double r1316858 = exp(1.0);
        double r1316859 = t;
        double r1316860 = r1316859 * r1316859;
        double r1316861 = r1316860 / r1316852;
        double r1316862 = pow(r1316858, r1316861);
        double r1316863 = r1316857 * r1316862;
        return r1316863;
}

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. Simplified0.5

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019199 
(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))))