Average Error: 0.3 → 0.3
Time: 22.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{{t}^{2}}{2}} \cdot \sqrt{z \cdot 2}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{{t}^{2}}{2}} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r515241 = x;
        double r515242 = 0.5;
        double r515243 = r515241 * r515242;
        double r515244 = y;
        double r515245 = r515243 - r515244;
        double r515246 = z;
        double r515247 = 2.0;
        double r515248 = r515246 * r515247;
        double r515249 = sqrt(r515248);
        double r515250 = r515245 * r515249;
        double r515251 = t;
        double r515252 = r515251 * r515251;
        double r515253 = r515252 / r515247;
        double r515254 = exp(r515253);
        double r515255 = r515250 * r515254;
        return r515255;
}
↓
double f(double x, double y, double z, double t) {
        double r515256 = x;
        double r515257 = 0.5;
        double r515258 = r515256 * r515257;
        double r515259 = y;
        double r515260 = r515258 - r515259;
        double r515261 = t;
        double r515262 = 2.0;
        double r515263 = pow(r515261, r515262);
        double r515264 = 2.0;
        double r515265 = r515263 / r515264;
        double r515266 = exp(r515265);
        double r515267 = z;
        double r515268 = r515267 * r515264;
        double r515269 = sqrt(r515268);
        double r515270 = r515266 * r515269;
        double r515271 = r515260 * r515270;
        return r515271;
}

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 associate-*l*0.3

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 +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))))