Average Error: 0.3 → 0.3
Time: 29.1s
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 r36548412 = x;
        double r36548413 = 0.5;
        double r36548414 = r36548412 * r36548413;
        double r36548415 = y;
        double r36548416 = r36548414 - r36548415;
        double r36548417 = z;
        double r36548418 = 2.0;
        double r36548419 = r36548417 * r36548418;
        double r36548420 = sqrt(r36548419);
        double r36548421 = r36548416 * r36548420;
        double r36548422 = t;
        double r36548423 = r36548422 * r36548422;
        double r36548424 = r36548423 / r36548418;
        double r36548425 = exp(r36548424);
        double r36548426 = r36548421 * r36548425;
        return r36548426;
}
↓
double f(double x, double y, double z, double t) {
        double r36548427 = x;
        double r36548428 = 0.5;
        double r36548429 = r36548427 * r36548428;
        double r36548430 = y;
        double r36548431 = r36548429 - r36548430;
        double r36548432 = z;
        double r36548433 = 2.0;
        double r36548434 = r36548432 * r36548433;
        double r36548435 = sqrt(r36548434);
        double r36548436 = r36548431 * r36548435;
        double r36548437 = t;
        double r36548438 = r36548437 * r36548437;
        double r36548439 = r36548438 / r36548433;
        double r36548440 = exp(r36548439);
        double r36548441 = r36548436 * r36548440;
        return r36548441;
}

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 2019174 +o rules:numerics
(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))))