Average Error: 0.3 → 0.3
Time: 23.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}\right) \cdot e^{t \cdot \frac{\frac{t}{2}}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}\right) \cdot e^{t \cdot \frac{\frac{t}{2}}{2}}
double f(double x, double y, double z, double t) {
        double r473907 = x;
        double r473908 = 0.5;
        double r473909 = r473907 * r473908;
        double r473910 = y;
        double r473911 = r473909 - r473910;
        double r473912 = z;
        double r473913 = 2.0;
        double r473914 = r473912 * r473913;
        double r473915 = sqrt(r473914);
        double r473916 = r473911 * r473915;
        double r473917 = t;
        double r473918 = r473917 * r473917;
        double r473919 = r473918 / r473913;
        double r473920 = exp(r473919);
        double r473921 = r473916 * r473920;
        return r473921;
}
↓
double f(double x, double y, double z, double t) {
        double r473922 = x;
        double r473923 = 0.5;
        double r473924 = r473922 * r473923;
        double r473925 = y;
        double r473926 = r473924 - r473925;
        double r473927 = z;
        double r473928 = 2.0;
        double r473929 = r473927 * r473928;
        double r473930 = sqrt(r473929);
        double r473931 = r473926 * r473930;
        double r473932 = t;
        double r473933 = exp(r473932);
        double r473934 = r473932 / r473928;
        double r473935 = 2.0;
        double r473936 = r473934 / r473935;
        double r473937 = pow(r473933, r473936);
        double r473938 = r473931 * r473937;
        double r473939 = r473932 * r473936;
        double r473940 = exp(r473939);
        double r473941 = r473938 * r473940;
        return r473941;
}

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

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 *-un-lft-identity0.3

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

  4. Applied times-frac0.3

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

  5. Applied exp-prod0.3

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

  6. Simplified0.3

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

  8. Applied sqr-pow0.3

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

  9. Applied associate-*r*0.3

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

  11. Applied pow-exp0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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))))