Average Error: 0.3 → 0.3
Time: 26.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}
double f(double x, double y, double z, double t) {
        double r41040679 = x;
        double r41040680 = 0.5;
        double r41040681 = r41040679 * r41040680;
        double r41040682 = y;
        double r41040683 = r41040681 - r41040682;
        double r41040684 = z;
        double r41040685 = 2.0;
        double r41040686 = r41040684 * r41040685;
        double r41040687 = sqrt(r41040686);
        double r41040688 = r41040683 * r41040687;
        double r41040689 = t;
        double r41040690 = r41040689 * r41040689;
        double r41040691 = r41040690 / r41040685;
        double r41040692 = exp(r41040691);
        double r41040693 = r41040688 * r41040692;
        return r41040693;
}
↓
double f(double x, double y, double z, double t) {
        double r41040694 = t;
        double r41040695 = cbrt(r41040694);
        double r41040696 = r41040695 * r41040695;
        double r41040697 = exp(r41040696);
        double r41040698 = 2.0;
        double r41040699 = r41040694 / r41040698;
        double r41040700 = r41040699 * r41040695;
        double r41040701 = pow(r41040697, r41040700);
        double r41040702 = sqrt(r41040701);
        double r41040703 = x;
        double r41040704 = 0.5;
        double r41040705 = r41040703 * r41040704;
        double r41040706 = y;
        double r41040707 = r41040705 - r41040706;
        double r41040708 = z;
        double r41040709 = r41040708 * r41040698;
        double r41040710 = sqrt(r41040709);
        double r41040711 = r41040707 * r41040710;
        double r41040712 = r41040702 * r41040711;
        double r41040713 = exp(r41040694);
        double r41040714 = pow(r41040713, r41040699);
        double r41040715 = sqrt(r41040714);
        double r41040716 = r41040712 * r41040715;
        return r41040716;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2.0}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2.0}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2.0}\right)}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{\left(\sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)}\]

  9. Applied associate-*r*0.3

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\left(e^{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\right)}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  12. Applied exp-prod0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{{\color{blue}{\left({\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t}\right)}\right)}}^{\left(\frac{t}{2.0}\right)}}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  13. Applied pow-pow0.3

    \[\leadsto \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \sqrt{\color{blue}{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\sqrt[3]{t} \cdot \frac{t}{2.0}\right)}}}\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  14. Final simplification0.3

    \[\leadsto \left(\sqrt{{\left(e^{\sqrt[3]{t} \cdot \sqrt[3]{t}}\right)}^{\left(\frac{t}{2.0} \cdot \sqrt[3]{t}\right)}} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right)\right) \cdot \sqrt{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\]

Reproduce

herbie shell --seed 2019163 
(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) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))