Average Error: 0.3 → 0.3
Time: 8.1s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot {\left(e^{t}\right)}^{\left(\frac{t}{2}\right)}\]
\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 r894228 = x;
        double r894229 = 0.5;
        double r894230 = r894228 * r894229;
        double r894231 = y;
        double r894232 = r894230 - r894231;
        double r894233 = z;
        double r894234 = 2.0;
        double r894235 = r894233 * r894234;
        double r894236 = sqrt(r894235);
        double r894237 = r894232 * r894236;
        double r894238 = t;
        double r894239 = r894238 * r894238;
        double r894240 = r894239 / r894234;
        double r894241 = exp(r894240);
        double r894242 = r894237 * r894241;
        return r894242;
}
↓
double f(double x, double y, double z, double t) {
        double r894243 = x;
        double r894244 = 0.5;
        double r894245 = r894243 * r894244;
        double r894246 = y;
        double r894247 = r894245 - r894246;
        double r894248 = z;
        double r894249 = 2.0;
        double r894250 = r894248 * r894249;
        double r894251 = sqrt(r894250);
        double r894252 = r894247 * r894251;
        double r894253 = t;
        double r894254 = exp(r894253);
        double r894255 = r894253 / r894249;
        double r894256 = pow(r894254, r894255);
        double r894257 = r894252 * r894256;
        return r894257;
}

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

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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 +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))))