Average Error: 0.3 → 0.3
Time: 7.7s
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 r941245 = x;
        double r941246 = 0.5;
        double r941247 = r941245 * r941246;
        double r941248 = y;
        double r941249 = r941247 - r941248;
        double r941250 = z;
        double r941251 = 2.0;
        double r941252 = r941250 * r941251;
        double r941253 = sqrt(r941252);
        double r941254 = r941249 * r941253;
        double r941255 = t;
        double r941256 = r941255 * r941255;
        double r941257 = r941256 / r941251;
        double r941258 = exp(r941257);
        double r941259 = r941254 * r941258;
        return r941259;
}
↓
double f(double x, double y, double z, double t) {
        double r941260 = x;
        double r941261 = 0.5;
        double r941262 = r941260 * r941261;
        double r941263 = y;
        double r941264 = r941262 - r941263;
        double r941265 = z;
        double r941266 = 2.0;
        double r941267 = r941265 * r941266;
        double r941268 = sqrt(r941267);
        double r941269 = r941264 * r941268;
        double r941270 = t;
        double r941271 = r941270 * r941270;
        double r941272 = r941271 / r941266;
        double r941273 = exp(r941272);
        double r941274 = r941269 * r941273;
        return r941274;
}

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 2020065 +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))))