Average Error: 0.3 → 0.3
Time: 6.9s
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 r725230 = x;
        double r725231 = 0.5;
        double r725232 = r725230 * r725231;
        double r725233 = y;
        double r725234 = r725232 - r725233;
        double r725235 = z;
        double r725236 = 2.0;
        double r725237 = r725235 * r725236;
        double r725238 = sqrt(r725237);
        double r725239 = r725234 * r725238;
        double r725240 = t;
        double r725241 = r725240 * r725240;
        double r725242 = r725241 / r725236;
        double r725243 = exp(r725242);
        double r725244 = r725239 * r725243;
        return r725244;
}
↓
double f(double x, double y, double z, double t) {
        double r725245 = x;
        double r725246 = 0.5;
        double r725247 = r725245 * r725246;
        double r725248 = y;
        double r725249 = r725247 - r725248;
        double r725250 = z;
        double r725251 = 2.0;
        double r725252 = r725250 * r725251;
        double r725253 = sqrt(r725252);
        double r725254 = r725249 * r725253;
        double r725255 = t;
        double r725256 = exp(r725255);
        double r725257 = r725255 / r725251;
        double r725258 = pow(r725256, r725257);
        double r725259 = r725254 * r725258;
        return r725259;
}

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. 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 2020024 
(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))))