Average Error: 0.3 → 0.3
Time: 7.1s
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 r1043447 = x;
        double r1043448 = 0.5;
        double r1043449 = r1043447 * r1043448;
        double r1043450 = y;
        double r1043451 = r1043449 - r1043450;
        double r1043452 = z;
        double r1043453 = 2.0;
        double r1043454 = r1043452 * r1043453;
        double r1043455 = sqrt(r1043454);
        double r1043456 = r1043451 * r1043455;
        double r1043457 = t;
        double r1043458 = r1043457 * r1043457;
        double r1043459 = r1043458 / r1043453;
        double r1043460 = exp(r1043459);
        double r1043461 = r1043456 * r1043460;
        return r1043461;
}
↓
double f(double x, double y, double z, double t) {
        double r1043462 = x;
        double r1043463 = 0.5;
        double r1043464 = r1043462 * r1043463;
        double r1043465 = y;
        double r1043466 = r1043464 - r1043465;
        double r1043467 = z;
        double r1043468 = 2.0;
        double r1043469 = r1043467 * r1043468;
        double r1043470 = sqrt(r1043469);
        double r1043471 = r1043466 * r1043470;
        double r1043472 = t;
        double r1043473 = r1043472 * r1043472;
        double r1043474 = r1043473 / r1043468;
        double r1043475 = exp(r1043474);
        double r1043476 = r1043471 * r1043475;
        return r1043476;
}

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 2020060 +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))))