Average Error: 0.3 → 0.3
Time: 25.7s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \left(\sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}} \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}\right)\right) \cdot \sqrt[3]{{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}}
double f(double x, double y, double z, double t) {
        double r529834 = x;
        double r529835 = 0.5;
        double r529836 = r529834 * r529835;
        double r529837 = y;
        double r529838 = r529836 - r529837;
        double r529839 = z;
        double r529840 = 2.0;
        double r529841 = r529839 * r529840;
        double r529842 = sqrt(r529841);
        double r529843 = r529838 * r529842;
        double r529844 = t;
        double r529845 = r529844 * r529844;
        double r529846 = r529845 / r529840;
        double r529847 = exp(r529846);
        double r529848 = r529843 * r529847;
        return r529848;
}
↓
double f(double x, double y, double z, double t) {
        double r529849 = x;
        double r529850 = 0.5;
        double r529851 = r529849 * r529850;
        double r529852 = y;
        double r529853 = r529851 - r529852;
        double r529854 = z;
        double r529855 = 2.0;
        double r529856 = r529854 * r529855;
        double r529857 = sqrt(r529856);
        double r529858 = r529853 * r529857;
        double r529859 = t;
        double r529860 = exp(r529859);
        double r529861 = r529859 / r529855;
        double r529862 = pow(r529860, r529861);
        double r529863 = cbrt(r529862);
        double r529864 = r529863 * r529863;
        double r529865 = r529858 * r529864;
        double r529866 = r529865 * r529863;
        return r529866;
}

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-cube-cbrt0.3

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

  9. Applied associate-*r*0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))))