Average Error: 0.3 → 0.5
Time: 24.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)
double f(double x, double y, double z, double t) {
        double r39162601 = x;
        double r39162602 = 0.5;
        double r39162603 = r39162601 * r39162602;
        double r39162604 = y;
        double r39162605 = r39162603 - r39162604;
        double r39162606 = z;
        double r39162607 = 2.0;
        double r39162608 = r39162606 * r39162607;
        double r39162609 = sqrt(r39162608);
        double r39162610 = r39162605 * r39162609;
        double r39162611 = t;
        double r39162612 = r39162611 * r39162611;
        double r39162613 = r39162612 / r39162607;
        double r39162614 = exp(r39162613);
        double r39162615 = r39162610 * r39162614;
        return r39162615;
}
↓
double f(double x, double y, double z, double t) {
        double r39162616 = t;
        double r39162617 = exp(r39162616);
        double r39162618 = 2.0;
        double r39162619 = r39162616 / r39162618;
        double r39162620 = pow(r39162617, r39162619);
        double r39162621 = sqrt(r39162618);
        double r39162622 = cbrt(r39162621);
        double r39162623 = r39162622 * r39162622;
        double r39162624 = z;
        double r39162625 = sqrt(r39162624);
        double r39162626 = x;
        double r39162627 = 0.5;
        double r39162628 = r39162626 * r39162627;
        double r39162629 = y;
        double r39162630 = r39162628 - r39162629;
        double r39162631 = r39162625 * r39162630;
        double r39162632 = r39162623 * r39162631;
        double r39162633 = r39162632 * r39162622;
        double r39162634 = r39162620 * r39162633;
        return r39162634;
}

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

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

  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 sqrt-prod0.5

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

  9. Applied associate-*r*0.5

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019192 
(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))))