Average Error: 0.3 → 0.3
Time: 10.9s
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 r817273 = x;
        double r817274 = 0.5;
        double r817275 = r817273 * r817274;
        double r817276 = y;
        double r817277 = r817275 - r817276;
        double r817278 = z;
        double r817279 = 2.0;
        double r817280 = r817278 * r817279;
        double r817281 = sqrt(r817280);
        double r817282 = r817277 * r817281;
        double r817283 = t;
        double r817284 = r817283 * r817283;
        double r817285 = r817284 / r817279;
        double r817286 = exp(r817285);
        double r817287 = r817282 * r817286;
        return r817287;
}
↓
double f(double x, double y, double z, double t) {
        double r817288 = x;
        double r817289 = 0.5;
        double r817290 = r817288 * r817289;
        double r817291 = y;
        double r817292 = r817290 - r817291;
        double r817293 = z;
        double r817294 = 2.0;
        double r817295 = r817293 * r817294;
        double r817296 = sqrt(r817295);
        double r817297 = r817292 * r817296;
        double r817298 = t;
        double r817299 = r817298 * r817298;
        double r817300 = r817299 / r817294;
        double r817301 = exp(r817300);
        double r817302 = r817297 * r817301;
        return r817302;
}

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 2019354 +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))))