Average Error: 0.3 → 0.3
Time: 16.0s
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 r1019361 = x;
        double r1019362 = 0.5;
        double r1019363 = r1019361 * r1019362;
        double r1019364 = y;
        double r1019365 = r1019363 - r1019364;
        double r1019366 = z;
        double r1019367 = 2.0;
        double r1019368 = r1019366 * r1019367;
        double r1019369 = sqrt(r1019368);
        double r1019370 = r1019365 * r1019369;
        double r1019371 = t;
        double r1019372 = r1019371 * r1019371;
        double r1019373 = r1019372 / r1019367;
        double r1019374 = exp(r1019373);
        double r1019375 = r1019370 * r1019374;
        return r1019375;
}
↓
double f(double x, double y, double z, double t) {
        double r1019376 = x;
        double r1019377 = 0.5;
        double r1019378 = r1019376 * r1019377;
        double r1019379 = y;
        double r1019380 = r1019378 - r1019379;
        double r1019381 = z;
        double r1019382 = 2.0;
        double r1019383 = r1019381 * r1019382;
        double r1019384 = sqrt(r1019383);
        double r1019385 = r1019380 * r1019384;
        double r1019386 = t;
        double r1019387 = r1019386 * r1019386;
        double r1019388 = r1019387 / r1019382;
        double r1019389 = exp(r1019388);
        double r1019390 = r1019385 * r1019389;
        return r1019390;
}

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 2019351 +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))))