Average Error: 0.3 → 0.3
Time: 18.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(e^{\frac{t}{\frac{2}{t}}} \cdot \sqrt{z \cdot 2}\right)\]
\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(e^{\frac{t}{\frac{2}{t}}} \cdot \sqrt{z \cdot 2}\right)
double f(double x, double y, double z, double t) {
        double r701527 = x;
        double r701528 = 0.5;
        double r701529 = r701527 * r701528;
        double r701530 = y;
        double r701531 = r701529 - r701530;
        double r701532 = z;
        double r701533 = 2.0;
        double r701534 = r701532 * r701533;
        double r701535 = sqrt(r701534);
        double r701536 = r701531 * r701535;
        double r701537 = t;
        double r701538 = r701537 * r701537;
        double r701539 = r701538 / r701533;
        double r701540 = exp(r701539);
        double r701541 = r701536 * r701540;
        return r701541;
}
↓
double f(double x, double y, double z, double t) {
        double r701542 = x;
        double r701543 = 0.5;
        double r701544 = r701542 * r701543;
        double r701545 = y;
        double r701546 = r701544 - r701545;
        double r701547 = t;
        double r701548 = 2.0;
        double r701549 = r701548 / r701547;
        double r701550 = r701547 / r701549;
        double r701551 = exp(r701550);
        double r701552 = z;
        double r701553 = r701552 * r701548;
        double r701554 = sqrt(r701553);
        double r701555 = r701551 * r701554;
        double r701556 = r701546 * r701555;
        return r701556;
}

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. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019350 +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))))