Average Error: 0.3 → 0.3
Time: 7.3s
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 r782268 = x;
        double r782269 = 0.5;
        double r782270 = r782268 * r782269;
        double r782271 = y;
        double r782272 = r782270 - r782271;
        double r782273 = z;
        double r782274 = 2.0;
        double r782275 = r782273 * r782274;
        double r782276 = sqrt(r782275);
        double r782277 = r782272 * r782276;
        double r782278 = t;
        double r782279 = r782278 * r782278;
        double r782280 = r782279 / r782274;
        double r782281 = exp(r782280);
        double r782282 = r782277 * r782281;
        return r782282;
}
↓
double f(double x, double y, double z, double t) {
        double r782283 = x;
        double r782284 = 0.5;
        double r782285 = r782283 * r782284;
        double r782286 = y;
        double r782287 = r782285 - r782286;
        double r782288 = z;
        double r782289 = 2.0;
        double r782290 = r782288 * r782289;
        double r782291 = sqrt(r782290);
        double r782292 = t;
        double r782293 = r782292 * r782292;
        double r782294 = r782293 / r782289;
        double r782295 = exp(r782294);
        double r782296 = r782291 * r782295;
        double r782297 = r782287 * r782296;
        return r782297;
}

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 2020018 
(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))))