Average Error: 0.3 → 0.3
Time: 21.9s
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 r476486 = x;
        double r476487 = 0.5;
        double r476488 = r476486 * r476487;
        double r476489 = y;
        double r476490 = r476488 - r476489;
        double r476491 = z;
        double r476492 = 2.0;
        double r476493 = r476491 * r476492;
        double r476494 = sqrt(r476493);
        double r476495 = r476490 * r476494;
        double r476496 = t;
        double r476497 = r476496 * r476496;
        double r476498 = r476497 / r476492;
        double r476499 = exp(r476498);
        double r476500 = r476495 * r476499;
        return r476500;
}
↓
double f(double x, double y, double z, double t) {
        double r476501 = x;
        double r476502 = 0.5;
        double r476503 = r476501 * r476502;
        double r476504 = y;
        double r476505 = r476503 - r476504;
        double r476506 = z;
        double r476507 = 2.0;
        double r476508 = r476506 * r476507;
        double r476509 = sqrt(r476508);
        double r476510 = r476505 * r476509;
        double r476511 = t;
        double r476512 = r476511 * r476511;
        double r476513 = r476512 / r476507;
        double r476514 = exp(r476513);
        double r476515 = r476510 * r476514;
        return r476515;
}

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 +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))))