Average Error: 0.3 → 0.3
Time: 13.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)\]
\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(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)
double f(double x, double y, double z, double t) {
        double r892281 = x;
        double r892282 = 0.5;
        double r892283 = r892281 * r892282;
        double r892284 = y;
        double r892285 = r892283 - r892284;
        double r892286 = z;
        double r892287 = 2.0;
        double r892288 = r892286 * r892287;
        double r892289 = sqrt(r892288);
        double r892290 = r892285 * r892289;
        double r892291 = t;
        double r892292 = r892291 * r892291;
        double r892293 = r892292 / r892287;
        double r892294 = exp(r892293);
        double r892295 = r892290 * r892294;
        return r892295;
}
↓
double f(double x, double y, double z, double t) {
        double r892296 = x;
        double r892297 = 0.5;
        double r892298 = r892296 * r892297;
        double r892299 = y;
        double r892300 = r892298 - r892299;
        double r892301 = z;
        double r892302 = 2.0;
        double r892303 = r892301 * r892302;
        double r892304 = sqrt(r892303);
        double r892305 = t;
        double r892306 = r892305 * r892305;
        double r892307 = r892306 / r892302;
        double r892308 = exp(r892307);
        double r892309 = r892304 * r892308;
        double r892310 = r892300 * r892309;
        return r892310;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +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))))