Average Error: 0.3 → 0.3
Time: 23.7s
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 r546483 = x;
        double r546484 = 0.5;
        double r546485 = r546483 * r546484;
        double r546486 = y;
        double r546487 = r546485 - r546486;
        double r546488 = z;
        double r546489 = 2.0;
        double r546490 = r546488 * r546489;
        double r546491 = sqrt(r546490);
        double r546492 = r546487 * r546491;
        double r546493 = t;
        double r546494 = r546493 * r546493;
        double r546495 = r546494 / r546489;
        double r546496 = exp(r546495);
        double r546497 = r546492 * r546496;
        return r546497;
}
↓
double f(double x, double y, double z, double t) {
        double r546498 = x;
        double r546499 = 0.5;
        double r546500 = r546498 * r546499;
        double r546501 = y;
        double r546502 = r546500 - r546501;
        double r546503 = z;
        double r546504 = 2.0;
        double r546505 = r546503 * r546504;
        double r546506 = sqrt(r546505);
        double r546507 = t;
        double r546508 = r546507 * r546507;
        double r546509 = r546508 / r546504;
        double r546510 = exp(r546509);
        double r546511 = r546506 * r546510;
        double r546512 = r546502 * r546511;
        return r546512;
}

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))))