Average Error: 0.3 → 0.3
Time: 9.8s
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 r993361 = x;
        double r993362 = 0.5;
        double r993363 = r993361 * r993362;
        double r993364 = y;
        double r993365 = r993363 - r993364;
        double r993366 = z;
        double r993367 = 2.0;
        double r993368 = r993366 * r993367;
        double r993369 = sqrt(r993368);
        double r993370 = r993365 * r993369;
        double r993371 = t;
        double r993372 = r993371 * r993371;
        double r993373 = r993372 / r993367;
        double r993374 = exp(r993373);
        double r993375 = r993370 * r993374;
        return r993375;
}
↓
double f(double x, double y, double z, double t) {
        double r993376 = x;
        double r993377 = 0.5;
        double r993378 = r993376 * r993377;
        double r993379 = y;
        double r993380 = r993378 - r993379;
        double r993381 = z;
        double r993382 = 2.0;
        double r993383 = r993381 * r993382;
        double r993384 = sqrt(r993383);
        double r993385 = r993380 * r993384;
        double r993386 = t;
        double r993387 = r993386 * r993386;
        double r993388 = r993387 / r993382;
        double r993389 = exp(r993388);
        double r993390 = r993385 * r993389;
        return r993390;
}

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 2019353 
(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))))