Average Error: 0.3 → 0.3
Time: 8.7s
Precision: 64
\[\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}\]
↓
\[\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z \cdot 2} \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right)\]
\left(\left(x \cdot 0.5 - y\right) \cdot \sqrt{z \cdot 2}\right) \cdot e^{\frac{t \cdot t}{2}}
↓
\left(x \cdot 0.5 - y\right) \cdot \left(\left(\sqrt{z \cdot 2} \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right) \cdot \sqrt{e^{\frac{t \cdot t}{2}}}\right)
double f(double x, double y, double z, double t) {
        double r792940 = x;
        double r792941 = 0.5;
        double r792942 = r792940 * r792941;
        double r792943 = y;
        double r792944 = r792942 - r792943;
        double r792945 = z;
        double r792946 = 2.0;
        double r792947 = r792945 * r792946;
        double r792948 = sqrt(r792947);
        double r792949 = r792944 * r792948;
        double r792950 = t;
        double r792951 = r792950 * r792950;
        double r792952 = r792951 / r792946;
        double r792953 = exp(r792952);
        double r792954 = r792949 * r792953;
        return r792954;
}
↓
double f(double x, double y, double z, double t) {
        double r792955 = x;
        double r792956 = 0.5;
        double r792957 = r792955 * r792956;
        double r792958 = y;
        double r792959 = r792957 - r792958;
        double r792960 = z;
        double r792961 = 2.0;
        double r792962 = r792960 * r792961;
        double r792963 = sqrt(r792962);
        double r792964 = t;
        double r792965 = r792964 * r792964;
        double r792966 = r792965 / r792961;
        double r792967 = exp(r792966);
        double r792968 = sqrt(r792967);
        double r792969 = r792963 * r792968;
        double r792970 = r792969 * r792968;
        double r792971 = r792959 * r792970;
        return r792971;
}

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 associate-*l*0.3

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

  5. Applied add-sqr-sqrt0.3

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

  6. Applied associate-*r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020081 +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))))