Average Error: 0.3 → 0.5
Time: 25.2s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(\left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right) \cdot \left(\sqrt{z} \cdot \left(x \cdot 0.5 - y\right)\right)\right) \cdot \sqrt[3]{\sqrt{2}}\right)
double f(double x, double y, double z, double t) {
        double r37035051 = x;
        double r37035052 = 0.5;
        double r37035053 = r37035051 * r37035052;
        double r37035054 = y;
        double r37035055 = r37035053 - r37035054;
        double r37035056 = z;
        double r37035057 = 2.0;
        double r37035058 = r37035056 * r37035057;
        double r37035059 = sqrt(r37035058);
        double r37035060 = r37035055 * r37035059;
        double r37035061 = t;
        double r37035062 = r37035061 * r37035061;
        double r37035063 = r37035062 / r37035057;
        double r37035064 = exp(r37035063);
        double r37035065 = r37035060 * r37035064;
        return r37035065;
}
↓
double f(double x, double y, double z, double t) {
        double r37035066 = t;
        double r37035067 = exp(r37035066);
        double r37035068 = 2.0;
        double r37035069 = r37035066 / r37035068;
        double r37035070 = pow(r37035067, r37035069);
        double r37035071 = sqrt(r37035068);
        double r37035072 = cbrt(r37035071);
        double r37035073 = r37035072 * r37035072;
        double r37035074 = z;
        double r37035075 = sqrt(r37035074);
        double r37035076 = x;
        double r37035077 = 0.5;
        double r37035078 = r37035076 * r37035077;
        double r37035079 = y;
        double r37035080 = r37035078 - r37035079;
        double r37035081 = r37035075 * r37035080;
        double r37035082 = r37035073 * r37035081;
        double r37035083 = r37035082 * r37035072;
        double r37035084 = r37035070 * r37035083;
        return r37035084;
}

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
Herbie0.5
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2}\right)}\]

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 sqrt-prod0.5

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

  9. Applied associate-*r*0.5

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

  11. Applied add-cube-cbrt0.5

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

  12. Applied associate-*r*0.5

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

  13. Final simplification0.5

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

Reproduce

herbie shell --seed 2019192 +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 1.0) (/ (* t t) 2.0)))

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