Average Error: 0.3 → 0.3
Time: 21.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}
double f(double x, double y, double z, double t) {
        double r542862 = x;
        double r542863 = 0.5;
        double r542864 = r542862 * r542863;
        double r542865 = y;
        double r542866 = r542864 - r542865;
        double r542867 = z;
        double r542868 = 2.0;
        double r542869 = r542867 * r542868;
        double r542870 = sqrt(r542869);
        double r542871 = r542866 * r542870;
        double r542872 = t;
        double r542873 = r542872 * r542872;
        double r542874 = r542873 / r542868;
        double r542875 = exp(r542874);
        double r542876 = r542871 * r542875;
        return r542876;
}
↓
double f(double x, double y, double z, double t) {
        double r542877 = x;
        double r542878 = 0.5;
        double r542879 = r542877 * r542878;
        double r542880 = y;
        double r542881 = r542879 - r542880;
        double r542882 = z;
        double r542883 = 2.0;
        double r542884 = r542882 * r542883;
        double r542885 = sqrt(r542884);
        double r542886 = r542881 * r542885;
        double r542887 = t;
        double r542888 = r542887 + r542887;
        double r542889 = exp(r542888);
        double r542890 = r542887 / r542883;
        double r542891 = 2.0;
        double r542892 = r542890 / r542891;
        double r542893 = pow(r542889, r542892);
        double r542894 = r542886 * r542893;
        return r542894;
}

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. Using strategy rm

  10. Applied pow-prod-down0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 
(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))))