Average Error: 0.3 → 0.3
Time: 8.4s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\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 e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r770310 = x;
        double r770311 = 0.5;
        double r770312 = r770310 * r770311;
        double r770313 = y;
        double r770314 = r770312 - r770313;
        double r770315 = z;
        double r770316 = 2.0;
        double r770317 = r770315 * r770316;
        double r770318 = sqrt(r770317);
        double r770319 = r770314 * r770318;
        double r770320 = t;
        double r770321 = r770320 * r770320;
        double r770322 = r770321 / r770316;
        double r770323 = exp(r770322);
        double r770324 = r770319 * r770323;
        return r770324;
}
↓
double f(double x, double y, double z, double t) {
        double r770325 = x;
        double r770326 = 0.5;
        double r770327 = r770325 * r770326;
        double r770328 = y;
        double r770329 = r770327 - r770328;
        double r770330 = z;
        double r770331 = 2.0;
        double r770332 = r770330 * r770331;
        double r770333 = sqrt(r770332);
        double r770334 = r770329 * r770333;
        double r770335 = t;
        double r770336 = r770335 * r770335;
        double r770337 = r770336 / r770331;
        double r770338 = exp(r770337);
        double r770339 = r770334 * r770338;
        return r770339;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2020039 +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))))