Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r34737539 = x;
        double r34737540 = 0.5;
        double r34737541 = r34737539 * r34737540;
        double r34737542 = y;
        double r34737543 = r34737541 - r34737542;
        double r34737544 = z;
        double r34737545 = 2.0;
        double r34737546 = r34737544 * r34737545;
        double r34737547 = sqrt(r34737546);
        double r34737548 = r34737543 * r34737547;
        double r34737549 = t;
        double r34737550 = r34737549 * r34737549;
        double r34737551 = r34737550 / r34737545;
        double r34737552 = exp(r34737551);
        double r34737553 = r34737548 * r34737552;
        return r34737553;
}
↓
double f(double x, double y, double z, double t) {
        double r34737554 = z;
        double r34737555 = 2.0;
        double r34737556 = r34737554 * r34737555;
        double r34737557 = sqrt(r34737556);
        double r34737558 = 0.5;
        double r34737559 = x;
        double r34737560 = r34737558 * r34737559;
        double r34737561 = y;
        double r34737562 = r34737560 - r34737561;
        double r34737563 = r34737557 * r34737562;
        double r34737564 = t;
        double r34737565 = r34737564 * r34737564;
        double r34737566 = r34737565 / r34737555;
        double r34737567 = exp(r34737566);
        double r34737568 = r34737563 * r34737567;
        return r34737568;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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))))