Average Error: 0.3 → 0.3
Time: 24.0s
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 r558545 = x;
        double r558546 = 0.5;
        double r558547 = r558545 * r558546;
        double r558548 = y;
        double r558549 = r558547 - r558548;
        double r558550 = z;
        double r558551 = 2.0;
        double r558552 = r558550 * r558551;
        double r558553 = sqrt(r558552);
        double r558554 = r558549 * r558553;
        double r558555 = t;
        double r558556 = r558555 * r558555;
        double r558557 = r558556 / r558551;
        double r558558 = exp(r558557);
        double r558559 = r558554 * r558558;
        return r558559;
}
↓
double f(double x, double y, double z, double t) {
        double r558560 = x;
        double r558561 = 0.5;
        double r558562 = r558560 * r558561;
        double r558563 = y;
        double r558564 = r558562 - r558563;
        double r558565 = z;
        double r558566 = 2.0;
        double r558567 = r558565 * r558566;
        double r558568 = sqrt(r558567);
        double r558569 = r558564 * r558568;
        double r558570 = t;
        double r558571 = r558570 * r558570;
        double r558572 = r558571 / r558566;
        double r558573 = exp(r558572);
        double r558574 = sqrt(r558573);
        double r558575 = r558569 * r558574;
        double r558576 = r558575 * r558574;
        return r558576;
}

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 2019208 +o rules:numerics
(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))))