Average Error: 0.3 → 0.3
Time: 7.1s
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 r787030 = x;
        double r787031 = 0.5;
        double r787032 = r787030 * r787031;
        double r787033 = y;
        double r787034 = r787032 - r787033;
        double r787035 = z;
        double r787036 = 2.0;
        double r787037 = r787035 * r787036;
        double r787038 = sqrt(r787037);
        double r787039 = r787034 * r787038;
        double r787040 = t;
        double r787041 = r787040 * r787040;
        double r787042 = r787041 / r787036;
        double r787043 = exp(r787042);
        double r787044 = r787039 * r787043;
        return r787044;
}
↓
double f(double x, double y, double z, double t) {
        double r787045 = x;
        double r787046 = 0.5;
        double r787047 = r787045 * r787046;
        double r787048 = y;
        double r787049 = r787047 - r787048;
        double r787050 = z;
        double r787051 = 2.0;
        double r787052 = r787050 * r787051;
        double r787053 = sqrt(r787052);
        double r787054 = r787049 * r787053;
        double r787055 = t;
        double r787056 = exp(r787055);
        double r787057 = r787055 / r787051;
        double r787058 = pow(r787056, r787057);
        double r787059 = 3.0;
        double r787060 = pow(r787058, r787059);
        double r787061 = cbrt(r787060);
        double r787062 = r787054 * r787061;
        return r787062;
}

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 2020024 +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))))