Average Error: 0.3 → 0.3
Time: 18.0s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\sqrt{z \cdot 2} \cdot {\left(\sqrt{e^{t}}\right)}^{\left(2 \cdot \frac{t}{2}\right)}\right)\]
\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 {\left(\sqrt{e^{t}}\right)}^{\left(2 \cdot \frac{t}{2}\right)}\right)
double f(double x, double y, double z, double t) {
        double r525591 = x;
        double r525592 = 0.5;
        double r525593 = r525591 * r525592;
        double r525594 = y;
        double r525595 = r525593 - r525594;
        double r525596 = z;
        double r525597 = 2.0;
        double r525598 = r525596 * r525597;
        double r525599 = sqrt(r525598);
        double r525600 = r525595 * r525599;
        double r525601 = t;
        double r525602 = r525601 * r525601;
        double r525603 = r525602 / r525597;
        double r525604 = exp(r525603);
        double r525605 = r525600 * r525604;
        return r525605;
}
↓
double f(double x, double y, double z, double t) {
        double r525606 = x;
        double r525607 = 0.5;
        double r525608 = r525606 * r525607;
        double r525609 = y;
        double r525610 = r525608 - r525609;
        double r525611 = z;
        double r525612 = 2.0;
        double r525613 = r525611 * r525612;
        double r525614 = sqrt(r525613);
        double r525615 = t;
        double r525616 = exp(r525615);
        double r525617 = sqrt(r525616);
        double r525618 = 2.0;
        double r525619 = r525615 / r525612;
        double r525620 = r525618 * r525619;
        double r525621 = pow(r525617, r525620);
        double r525622 = r525614 * r525621;
        double r525623 = r525610 * r525622;
        return r525623;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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. Using strategy rm

  8. Applied add-sqr-sqrt0.3

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

  9. Applied unpow-prod-down0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019291 
(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))))