Average Error: 0.3 → 0.3
Time: 23.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot e^{\frac{t \cdot t}{2}}\right)
double f(double x, double y, double z, double t) {
        double r520632 = x;
        double r520633 = 0.5;
        double r520634 = r520632 * r520633;
        double r520635 = y;
        double r520636 = r520634 - r520635;
        double r520637 = z;
        double r520638 = 2.0;
        double r520639 = r520637 * r520638;
        double r520640 = sqrt(r520639);
        double r520641 = r520636 * r520640;
        double r520642 = t;
        double r520643 = r520642 * r520642;
        double r520644 = r520643 / r520638;
        double r520645 = exp(r520644);
        double r520646 = r520641 * r520645;
        return r520646;
}
↓
double f(double x, double y, double z, double t) {
        double r520647 = x;
        double r520648 = 0.5;
        double r520649 = r520647 * r520648;
        double r520650 = y;
        double r520651 = r520649 - r520650;
        double r520652 = z;
        double r520653 = 2.0;
        double r520654 = r520652 * r520653;
        double r520655 = sqrt(r520654);
        double r520656 = t;
        double r520657 = r520656 * r520656;
        double r520658 = r520657 / r520653;
        double r520659 = exp(r520658);
        double r520660 = r520655 * r520659;
        double r520661 = r520651 * r520660;
        return r520661;
}

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 associate-*l*0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(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))))