Average Error: 0.3 → 0.3
Time: 9.6s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{\sqrt[3]{\frac{t \cdot t}{2}} \cdot \sqrt[3]{\frac{t \cdot t}{2}}}\right)}^{\left(\sqrt[3]{\frac{t \cdot t}{2}}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{\sqrt[3]{\frac{t \cdot t}{2}} \cdot \sqrt[3]{\frac{t \cdot t}{2}}}\right)}^{\left(\sqrt[3]{\frac{t \cdot t}{2}}\right)}
double f(double x, double y, double z, double t) {
        double r746973 = x;
        double r746974 = 0.5;
        double r746975 = r746973 * r746974;
        double r746976 = y;
        double r746977 = r746975 - r746976;
        double r746978 = z;
        double r746979 = 2.0;
        double r746980 = r746978 * r746979;
        double r746981 = sqrt(r746980);
        double r746982 = r746977 * r746981;
        double r746983 = t;
        double r746984 = r746983 * r746983;
        double r746985 = r746984 / r746979;
        double r746986 = exp(r746985);
        double r746987 = r746982 * r746986;
        return r746987;
}
↓
double f(double x, double y, double z, double t) {
        double r746988 = x;
        double r746989 = 0.5;
        double r746990 = r746988 * r746989;
        double r746991 = y;
        double r746992 = r746990 - r746991;
        double r746993 = z;
        double r746994 = 2.0;
        double r746995 = r746993 * r746994;
        double r746996 = sqrt(r746995);
        double r746997 = r746992 * r746996;
        double r746998 = t;
        double r746999 = r746998 * r746998;
        double r747000 = r746999 / r746994;
        double r747001 = cbrt(r747000);
        double r747002 = r747001 * r747001;
        double r747003 = exp(r747002);
        double r747004 = pow(r747003, r747001);
        double r747005 = r746997 * r747004;
        return r747005;
}

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 add-cube-cbrt0.3

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

  4. Applied exp-prod0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020021 
(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))))