Average Error: 0.3 → 0.3
Time: 6.8s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}
double f(double x, double y, double z, double t) {
        double r891397 = x;
        double r891398 = 0.5;
        double r891399 = r891397 * r891398;
        double r891400 = y;
        double r891401 = r891399 - r891400;
        double r891402 = z;
        double r891403 = 2.0;
        double r891404 = r891402 * r891403;
        double r891405 = sqrt(r891404);
        double r891406 = r891401 * r891405;
        double r891407 = t;
        double r891408 = r891407 * r891407;
        double r891409 = r891408 / r891403;
        double r891410 = exp(r891409);
        double r891411 = r891406 * r891410;
        return r891411;
}
↓
double f(double x, double y, double z, double t) {
        double r891412 = x;
        double r891413 = 0.5;
        double r891414 = r891412 * r891413;
        double r891415 = y;
        double r891416 = r891414 - r891415;
        double r891417 = z;
        double r891418 = 2.0;
        double r891419 = r891417 * r891418;
        double r891420 = sqrt(r891419);
        double r891421 = r891416 * r891420;
        double r891422 = t;
        double r891423 = exp(r891422);
        double r891424 = r891422 / r891418;
        double r891425 = pow(r891423, r891424);
        double r891426 = r891421 * r891425;
        return r891426;
}

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 *-un-lft-identity0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{\color{blue}{1 \cdot 2}}}\]

  4. Applied times-frac0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\color{blue}{\frac{t}{1} \cdot \frac{t}{2}}}\]

  5. Applied exp-prod0.3

    \[\leadsto \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot \color{blue}{{\left(e^{\frac{t}{1}}\right)}^{\left(\frac{t}{2}\right)}}\]

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020025 
(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))))