Average Error: 0.3 → 0.3
Time: 19.5s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}
double f(double x, double y, double z, double t) {
        double r15308381 = x;
        double r15308382 = 0.5;
        double r15308383 = r15308381 * r15308382;
        double r15308384 = y;
        double r15308385 = r15308383 - r15308384;
        double r15308386 = z;
        double r15308387 = 2.0;
        double r15308388 = r15308386 * r15308387;
        double r15308389 = sqrt(r15308388);
        double r15308390 = r15308385 * r15308389;
        double r15308391 = t;
        double r15308392 = r15308391 * r15308391;
        double r15308393 = r15308392 / r15308387;
        double r15308394 = exp(r15308393);
        double r15308395 = r15308390 * r15308394;
        return r15308395;
}
↓
double f(double x, double y, double z, double t) {
        double r15308396 = x;
        double r15308397 = 0.5;
        double r15308398 = r15308396 * r15308397;
        double r15308399 = y;
        double r15308400 = r15308398 - r15308399;
        double r15308401 = z;
        double r15308402 = 2.0;
        double r15308403 = r15308401 * r15308402;
        double r15308404 = sqrt(r15308403);
        double r15308405 = r15308400 * r15308404;
        double r15308406 = t;
        double r15308407 = exp(r15308406);
        double r15308408 = r15308406 / r15308402;
        double r15308409 = pow(r15308407, r15308408);
        double r15308410 = r15308405 * r15308409;
        return r15308410;
}

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
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{1}\right)}^{\left(\frac{t \cdot t}{2.0}\right)}\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{2.0}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2.0}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2.0}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2.0}\right)}}\]

  6. Simplified0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\color{blue}{\left(e^{t}\right)}}^{\left(\frac{t}{2.0}\right)}\]

  7. Final simplification0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2.0}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2.0}\right)}\]

Reproduce

herbie shell --seed 2019156 
(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) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))