Average Error: 0.3 → 0.3
Time: 26.3s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{2 \cdot z}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
{\left(e^{t}\right)}^{\left(\frac{t}{2}\right)} \cdot \left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{2 \cdot z}\right)
double f(double x, double y, double z, double t) {
        double r1192092 = x;
        double r1192093 = 0.5;
        double r1192094 = r1192092 * r1192093;
        double r1192095 = y;
        double r1192096 = r1192094 - r1192095;
        double r1192097 = z;
        double r1192098 = 2.0;
        double r1192099 = r1192097 * r1192098;
        double r1192100 = sqrt(r1192099);
        double r1192101 = r1192096 * r1192100;
        double r1192102 = t;
        double r1192103 = r1192102 * r1192102;
        double r1192104 = r1192103 / r1192098;
        double r1192105 = exp(r1192104);
        double r1192106 = r1192101 * r1192105;
        return r1192106;
}
↓
double f(double x, double y, double z, double t) {
        double r1192107 = t;
        double r1192108 = exp(r1192107);
        double r1192109 = 2.0;
        double r1192110 = r1192107 / r1192109;
        double r1192111 = pow(r1192108, r1192110);
        double r1192112 = x;
        double r1192113 = 0.5;
        double r1192114 = r1192112 * r1192113;
        double r1192115 = y;
        double r1192116 = r1192114 - r1192115;
        double r1192117 = z;
        double r1192118 = r1192109 * r1192117;
        double r1192119 = sqrt(r1192118);
        double r1192120 = r1192116 * r1192119;
        double r1192121 = r1192111 * r1192120;
        return r1192121;
}

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. Using strategy rm

  8. Applied *-commutative0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A"

  :herbie-target
  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (pow (exp 1.0) (/ (* t t) 2.0)))

  (* (* (- (* x 0.5) y) (sqrt (* z 2.0))) (exp (/ (* t t) 2.0))))