Average Error: 0.3 → 0.3
Time: 10.4s
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 r802376 = x;
        double r802377 = 0.5;
        double r802378 = r802376 * r802377;
        double r802379 = y;
        double r802380 = r802378 - r802379;
        double r802381 = z;
        double r802382 = 2.0;
        double r802383 = r802381 * r802382;
        double r802384 = sqrt(r802383);
        double r802385 = r802380 * r802384;
        double r802386 = t;
        double r802387 = r802386 * r802386;
        double r802388 = r802387 / r802382;
        double r802389 = exp(r802388);
        double r802390 = r802385 * r802389;
        return r802390;
}
↓
double f(double x, double y, double z, double t) {
        double r802391 = x;
        double r802392 = 0.5;
        double r802393 = r802391 * r802392;
        double r802394 = y;
        double r802395 = r802393 - r802394;
        double r802396 = z;
        double r802397 = 2.0;
        double r802398 = r802396 * r802397;
        double r802399 = sqrt(r802398);
        double r802400 = r802395 * r802399;
        double r802401 = t;
        double r802402 = r802401 * r802401;
        double r802403 = r802402 / r802397;
        double r802404 = exp(r802403);
        double r802405 = r802400 * r802404;
        return r802405;
}

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 2020003 
(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))))