Average Error: 0.3 → 0.3
Time: 26.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
double f(double x, double y, double z, double t) {
        double r31711356 = x;
        double r31711357 = 0.5;
        double r31711358 = r31711356 * r31711357;
        double r31711359 = y;
        double r31711360 = r31711358 - r31711359;
        double r31711361 = z;
        double r31711362 = 2.0;
        double r31711363 = r31711361 * r31711362;
        double r31711364 = sqrt(r31711363);
        double r31711365 = r31711360 * r31711364;
        double r31711366 = t;
        double r31711367 = r31711366 * r31711366;
        double r31711368 = r31711367 / r31711362;
        double r31711369 = exp(r31711368);
        double r31711370 = r31711365 * r31711369;
        return r31711370;
}
↓
double f(double x, double y, double z, double t) {
        double r31711371 = x;
        double r31711372 = 0.5;
        double r31711373 = r31711371 * r31711372;
        double r31711374 = y;
        double r31711375 = r31711373 - r31711374;
        double r31711376 = z;
        double r31711377 = 2.0;
        double r31711378 = r31711376 * r31711377;
        double r31711379 = sqrt(r31711378);
        double r31711380 = r31711375 * r31711379;
        double r31711381 = t;
        double r31711382 = r31711381 * r31711381;
        double r31711383 = r31711382 / r31711377;
        double r31711384 = exp(r31711383);
        double r31711385 = r31711380 * r31711384;
        return r31711385;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]

  2. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))