Average Error: 0.3 → 0.3
Time: 22.6s
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 r575525 = x;
        double r575526 = 0.5;
        double r575527 = r575525 * r575526;
        double r575528 = y;
        double r575529 = r575527 - r575528;
        double r575530 = z;
        double r575531 = 2.0;
        double r575532 = r575530 * r575531;
        double r575533 = sqrt(r575532);
        double r575534 = r575529 * r575533;
        double r575535 = t;
        double r575536 = r575535 * r575535;
        double r575537 = r575536 / r575531;
        double r575538 = exp(r575537);
        double r575539 = r575534 * r575538;
        return r575539;
}
↓
double f(double x, double y, double z, double t) {
        double r575540 = x;
        double r575541 = 0.5;
        double r575542 = r575540 * r575541;
        double r575543 = y;
        double r575544 = r575542 - r575543;
        double r575545 = z;
        double r575546 = 2.0;
        double r575547 = r575545 * r575546;
        double r575548 = sqrt(r575547);
        double r575549 = r575544 * r575548;
        double r575550 = t;
        double r575551 = r575550 * r575550;
        double r575552 = r575551 / r575546;
        double r575553 = exp(r575552);
        double r575554 = r575549 * r575553;
        return r575554;
}

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 2019306 
(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))))