Average Error: 0.3 → 0.3
Time: 28.5s
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 r519496 = x;
        double r519497 = 0.5;
        double r519498 = r519496 * r519497;
        double r519499 = y;
        double r519500 = r519498 - r519499;
        double r519501 = z;
        double r519502 = 2.0;
        double r519503 = r519501 * r519502;
        double r519504 = sqrt(r519503);
        double r519505 = r519500 * r519504;
        double r519506 = t;
        double r519507 = r519506 * r519506;
        double r519508 = r519507 / r519502;
        double r519509 = exp(r519508);
        double r519510 = r519505 * r519509;
        return r519510;
}
↓
double f(double x, double y, double z, double t) {
        double r519511 = x;
        double r519512 = 0.5;
        double r519513 = r519511 * r519512;
        double r519514 = y;
        double r519515 = r519513 - r519514;
        double r519516 = z;
        double r519517 = 2.0;
        double r519518 = r519516 * r519517;
        double r519519 = sqrt(r519518);
        double r519520 = r519515 * r519519;
        double r519521 = t;
        double r519522 = r519521 * r519521;
        double r519523 = r519522 / r519517;
        double r519524 = exp(r519523);
        double r519525 = r519520 * r519524;
        return r519525;
}

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 2019198 
(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))))