Average Error: 0.3 → 0.3
Time: 1.1m
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(\sqrt{z \cdot 2} \cdot \left(0.5 \cdot x - y\right)\right) \cdot e^{\frac{t \cdot t}{2}}
double f(double x, double y, double z, double t) {
        double r37480117 = x;
        double r37480118 = 0.5;
        double r37480119 = r37480117 * r37480118;
        double r37480120 = y;
        double r37480121 = r37480119 - r37480120;
        double r37480122 = z;
        double r37480123 = 2.0;
        double r37480124 = r37480122 * r37480123;
        double r37480125 = sqrt(r37480124);
        double r37480126 = r37480121 * r37480125;
        double r37480127 = t;
        double r37480128 = r37480127 * r37480127;
        double r37480129 = r37480128 / r37480123;
        double r37480130 = exp(r37480129);
        double r37480131 = r37480126 * r37480130;
        return r37480131;
}
↓
double f(double x, double y, double z, double t) {
        double r37480132 = z;
        double r37480133 = 2.0;
        double r37480134 = r37480132 * r37480133;
        double r37480135 = sqrt(r37480134);
        double r37480136 = 0.5;
        double r37480137 = x;
        double r37480138 = r37480136 * r37480137;
        double r37480139 = y;
        double r37480140 = r37480138 - r37480139;
        double r37480141 = r37480135 * r37480140;
        double r37480142 = t;
        double r37480143 = r37480142 * r37480142;
        double r37480144 = r37480143 / r37480133;
        double r37480145 = exp(r37480144);
        double r37480146 = r37480141 * r37480145;
        return r37480146;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019200 +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))))