Average Error: 0.3 → 0.3
Time: 8.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt[3]{{\left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)}^{3}}\]
\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 \sqrt[3]{{\left({\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\right)}^{3}}
double f(double x, double y, double z, double t) {
        double r813764 = x;
        double r813765 = 0.5;
        double r813766 = r813764 * r813765;
        double r813767 = y;
        double r813768 = r813766 - r813767;
        double r813769 = z;
        double r813770 = 2.0;
        double r813771 = r813769 * r813770;
        double r813772 = sqrt(r813771);
        double r813773 = r813768 * r813772;
        double r813774 = t;
        double r813775 = r813774 * r813774;
        double r813776 = r813775 / r813770;
        double r813777 = exp(r813776);
        double r813778 = r813773 * r813777;
        return r813778;
}
↓
double f(double x, double y, double z, double t) {
        double r813779 = x;
        double r813780 = 0.5;
        double r813781 = r813779 * r813780;
        double r813782 = y;
        double r813783 = r813781 - r813782;
        double r813784 = z;
        double r813785 = 2.0;
        double r813786 = r813784 * r813785;
        double r813787 = sqrt(r813786);
        double r813788 = r813783 * r813787;
        double r813789 = t;
        double r813790 = exp(r813789);
        double r813791 = r813789 / r813785;
        double r813792 = pow(r813790, r813791);
        double r813793 = 3.0;
        double r813794 = pow(r813792, r813793);
        double r813795 = cbrt(r813794);
        double r813796 = r813788 * r813795;
        return r813796;
}

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 add-cbrt-cube0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019362 
(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))))