Average Error: 0.3 → 0.3
Time: 48.9s
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 r39146394 = x;
        double r39146395 = 0.5;
        double r39146396 = r39146394 * r39146395;
        double r39146397 = y;
        double r39146398 = r39146396 - r39146397;
        double r39146399 = z;
        double r39146400 = 2.0;
        double r39146401 = r39146399 * r39146400;
        double r39146402 = sqrt(r39146401);
        double r39146403 = r39146398 * r39146402;
        double r39146404 = t;
        double r39146405 = r39146404 * r39146404;
        double r39146406 = r39146405 / r39146400;
        double r39146407 = exp(r39146406);
        double r39146408 = r39146403 * r39146407;
        return r39146408;
}
↓
double f(double x, double y, double z, double t) {
        double r39146409 = x;
        double r39146410 = 0.5;
        double r39146411 = r39146409 * r39146410;
        double r39146412 = y;
        double r39146413 = r39146411 - r39146412;
        double r39146414 = z;
        double r39146415 = 2.0;
        double r39146416 = r39146414 * r39146415;
        double r39146417 = sqrt(r39146416);
        double r39146418 = r39146413 * r39146417;
        double r39146419 = t;
        double r39146420 = r39146419 * r39146419;
        double r39146421 = r39146420 / r39146415;
        double r39146422 = exp(r39146421);
        double r39146423 = r39146418 * r39146422;
        return r39146423;
}

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 2019168 +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 1.0) (/ (* t t) 2.0)))

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