Average Error: 0.3 → 0.3
Time: 23.7s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{\frac{t \cdot t}{\sqrt{2}}}{\sqrt{2}}}\]
\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{\frac{t \cdot t}{\sqrt{2}}}{\sqrt{2}}}
double f(double x, double y, double z, double t) {
        double r36326250 = x;
        double r36326251 = 0.5;
        double r36326252 = r36326250 * r36326251;
        double r36326253 = y;
        double r36326254 = r36326252 - r36326253;
        double r36326255 = z;
        double r36326256 = 2.0;
        double r36326257 = r36326255 * r36326256;
        double r36326258 = sqrt(r36326257);
        double r36326259 = r36326254 * r36326258;
        double r36326260 = t;
        double r36326261 = r36326260 * r36326260;
        double r36326262 = r36326261 / r36326256;
        double r36326263 = exp(r36326262);
        double r36326264 = r36326259 * r36326263;
        return r36326264;
}
↓
double f(double x, double y, double z, double t) {
        double r36326265 = x;
        double r36326266 = 0.5;
        double r36326267 = r36326265 * r36326266;
        double r36326268 = y;
        double r36326269 = r36326267 - r36326268;
        double r36326270 = z;
        double r36326271 = 2.0;
        double r36326272 = r36326270 * r36326271;
        double r36326273 = sqrt(r36326272);
        double r36326274 = r36326269 * r36326273;
        double r36326275 = t;
        double r36326276 = r36326275 * r36326275;
        double r36326277 = sqrt(r36326271);
        double r36326278 = r36326276 / r36326277;
        double r36326279 = r36326278 / r36326277;
        double r36326280 = exp(r36326279);
        double r36326281 = r36326274 * r36326280;
        return r36326281;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}}\]

  4. Applied associate-/r*0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\frac{\frac{t \cdot t}{\sqrt{2}}}{\sqrt{2}}}}\]

  5. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{\frac{t \cdot t}{\sqrt{2}}}{\sqrt{2}}}\]

Reproduce

herbie shell --seed 2019169 
(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))))