Average Error: 0.3 → 0.3
Time: 7.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r763570 = x;
        double r763571 = 0.5;
        double r763572 = r763570 * r763571;
        double r763573 = y;
        double r763574 = r763572 - r763573;
        double r763575 = z;
        double r763576 = 2.0;
        double r763577 = r763575 * r763576;
        double r763578 = sqrt(r763577);
        double r763579 = r763574 * r763578;
        double r763580 = t;
        double r763581 = r763580 * r763580;
        double r763582 = r763581 / r763576;
        double r763583 = exp(r763582);
        double r763584 = r763579 * r763583;
        return r763584;
}
↓
double f(double x, double y, double z, double t) {
        double r763585 = x;
        double r763586 = 0.5;
        double r763587 = r763585 * r763586;
        double r763588 = y;
        double r763589 = r763587 - r763588;
        double r763590 = z;
        double r763591 = 2.0;
        double r763592 = r763590 * r763591;
        double r763593 = sqrt(r763592);
        double r763594 = r763589 * r763593;
        double r763595 = t;
        double r763596 = r763595 * r763595;
        double r763597 = r763596 / r763591;
        double r763598 = exp(r763597);
        double r763599 = r763594 * r763598;
        return r763599;
}

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

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

Reproduce

herbie shell --seed 2020060 
(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))))