Average Error: 0.3 → 0.3
Time: 22.6s
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 r537207 = x;
        double r537208 = 0.5;
        double r537209 = r537207 * r537208;
        double r537210 = y;
        double r537211 = r537209 - r537210;
        double r537212 = z;
        double r537213 = 2.0;
        double r537214 = r537212 * r537213;
        double r537215 = sqrt(r537214);
        double r537216 = r537211 * r537215;
        double r537217 = t;
        double r537218 = r537217 * r537217;
        double r537219 = r537218 / r537213;
        double r537220 = exp(r537219);
        double r537221 = r537216 * r537220;
        return r537221;
}
↓
double f(double x, double y, double z, double t) {
        double r537222 = x;
        double r537223 = 0.5;
        double r537224 = r537222 * r537223;
        double r537225 = y;
        double r537226 = r537224 - r537225;
        double r537227 = z;
        double r537228 = 2.0;
        double r537229 = r537227 * r537228;
        double r537230 = sqrt(r537229);
        double r537231 = r537226 * r537230;
        double r537232 = t;
        double r537233 = r537232 + r537232;
        double r537234 = exp(r537233);
        double r537235 = r537232 / r537228;
        double r537236 = 2.0;
        double r537237 = r537235 / r537236;
        double r537238 = pow(r537234, r537237);
        double r537239 = r537231 * r537238;
        return r537239;
}

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))))