Average Error: 0.3 → 0.3
Time: 23.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}}\right)\right)
double f(double x, double y, double z, double t) {
        double r37217785 = x;
        double r37217786 = 0.5;
        double r37217787 = r37217785 * r37217786;
        double r37217788 = y;
        double r37217789 = r37217787 - r37217788;
        double r37217790 = z;
        double r37217791 = 2.0;
        double r37217792 = r37217790 * r37217791;
        double r37217793 = sqrt(r37217792);
        double r37217794 = r37217789 * r37217793;
        double r37217795 = t;
        double r37217796 = r37217795 * r37217795;
        double r37217797 = r37217796 / r37217791;
        double r37217798 = exp(r37217797);
        double r37217799 = r37217794 * r37217798;
        return r37217799;
}
↓
double f(double x, double y, double z, double t) {
        double r37217800 = t;
        double r37217801 = exp(r37217800);
        double r37217802 = 2.0;
        double r37217803 = r37217800 / r37217802;
        double r37217804 = pow(r37217801, r37217803);
        double r37217805 = cbrt(r37217804);
        double r37217806 = x;
        double r37217807 = 0.5;
        double r37217808 = r37217806 * r37217807;
        double r37217809 = y;
        double r37217810 = r37217808 - r37217809;
        double r37217811 = z;
        double r37217812 = r37217811 * r37217802;
        double r37217813 = sqrt(r37217812);
        double r37217814 = r37217810 * r37217813;
        double r37217815 = r37217805 * r37217805;
        double r37217816 = r37217814 * r37217815;
        double r37217817 = r37217805 * r37217816;
        return r37217817;
}

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-cube-cbrt0.3

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(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))))