Average Error: 0.3 → 0.3
Time: 24.9s
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 r41923396 = x;
        double r41923397 = 0.5;
        double r41923398 = r41923396 * r41923397;
        double r41923399 = y;
        double r41923400 = r41923398 - r41923399;
        double r41923401 = z;
        double r41923402 = 2.0;
        double r41923403 = r41923401 * r41923402;
        double r41923404 = sqrt(r41923403);
        double r41923405 = r41923400 * r41923404;
        double r41923406 = t;
        double r41923407 = r41923406 * r41923406;
        double r41923408 = r41923407 / r41923402;
        double r41923409 = exp(r41923408);
        double r41923410 = r41923405 * r41923409;
        return r41923410;
}
↓
double f(double x, double y, double z, double t) {
        double r41923411 = x;
        double r41923412 = 0.5;
        double r41923413 = r41923411 * r41923412;
        double r41923414 = y;
        double r41923415 = r41923413 - r41923414;
        double r41923416 = z;
        double r41923417 = 2.0;
        double r41923418 = r41923416 * r41923417;
        double r41923419 = sqrt(r41923418);
        double r41923420 = r41923415 * r41923419;
        double r41923421 = t;
        double r41923422 = r41923421 * r41923421;
        double r41923423 = r41923422 / r41923417;
        double r41923424 = exp(r41923423);
        double r41923425 = r41923420 * r41923424;
        return r41923425;
}

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 
(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))))