Average Error: 0.3 → 0.3
Time: 23.9s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t + t}\right)}^{\left(\frac{\frac{t}{2}}{2}\right)}
double f(double x, double y, double z, double t) {
        double r480155 = x;
        double r480156 = 0.5;
        double r480157 = r480155 * r480156;
        double r480158 = y;
        double r480159 = r480157 - r480158;
        double r480160 = z;
        double r480161 = 2.0;
        double r480162 = r480160 * r480161;
        double r480163 = sqrt(r480162);
        double r480164 = r480159 * r480163;
        double r480165 = t;
        double r480166 = r480165 * r480165;
        double r480167 = r480166 / r480161;
        double r480168 = exp(r480167);
        double r480169 = r480164 * r480168;
        return r480169;
}
↓
double f(double x, double y, double z, double t) {
        double r480170 = x;
        double r480171 = 0.5;
        double r480172 = r480170 * r480171;
        double r480173 = y;
        double r480174 = r480172 - r480173;
        double r480175 = z;
        double r480176 = 2.0;
        double r480177 = r480175 * r480176;
        double r480178 = sqrt(r480177);
        double r480179 = r480174 * r480178;
        double r480180 = t;
        double r480181 = r480180 + r480180;
        double r480182 = exp(r480181);
        double r480183 = r480180 / r480176;
        double r480184 = 2.0;
        double r480185 = r480183 / r480184;
        double r480186 = pow(r480182, r480185);
        double r480187 = r480179 * r480186;
        return r480187;
}

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 sqr-pow0.3

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

  10. Applied pow-prod-down0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019326 +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))))