Average Error: 0.3 → 0.3
Time: 24.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}
double f(double x, double y, double z, double t) {
        double r55015408 = x;
        double r55015409 = 0.5;
        double r55015410 = r55015408 * r55015409;
        double r55015411 = y;
        double r55015412 = r55015410 - r55015411;
        double r55015413 = z;
        double r55015414 = 2.0;
        double r55015415 = r55015413 * r55015414;
        double r55015416 = sqrt(r55015415);
        double r55015417 = r55015412 * r55015416;
        double r55015418 = t;
        double r55015419 = r55015418 * r55015418;
        double r55015420 = r55015419 / r55015414;
        double r55015421 = exp(r55015420);
        double r55015422 = r55015417 * r55015421;
        return r55015422;
}
↓
double f(double x, double y, double z, double t) {
        double r55015423 = x;
        double r55015424 = 0.5;
        double r55015425 = r55015423 * r55015424;
        double r55015426 = y;
        double r55015427 = r55015425 - r55015426;
        double r55015428 = z;
        double r55015429 = 2.0;
        double r55015430 = r55015428 * r55015429;
        double r55015431 = sqrt(r55015430);
        double r55015432 = r55015427 * r55015431;
        double r55015433 = t;
        double r55015434 = r55015433 * r55015433;
        double r55015435 = r55015434 / r55015429;
        double r55015436 = exp(r55015435);
        double r55015437 = sqrt(r55015436);
        double r55015438 = r55015432 * r55015437;
        double r55015439 = r55015438 * r55015437;
        return r55015439;
}

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

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

  4. Applied associate-*r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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))))