Average Error: 6.3 → 1.9
Time: 6.8s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r750965 = 2.0;
        double r750966 = x;
        double r750967 = y;
        double r750968 = r750966 * r750967;
        double r750969 = z;
        double r750970 = t;
        double r750971 = r750969 * r750970;
        double r750972 = r750968 + r750971;
        double r750973 = a;
        double r750974 = b;
        double r750975 = c;
        double r750976 = r750974 * r750975;
        double r750977 = r750973 + r750976;
        double r750978 = r750977 * r750975;
        double r750979 = i;
        double r750980 = r750978 * r750979;
        double r750981 = r750972 - r750980;
        double r750982 = r750965 * r750981;
        return r750982;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r750983 = 2.0;
        double r750984 = x;
        double r750985 = y;
        double r750986 = r750984 * r750985;
        double r750987 = z;
        double r750988 = t;
        double r750989 = r750987 * r750988;
        double r750990 = r750986 + r750989;
        double r750991 = a;
        double r750992 = b;
        double r750993 = c;
        double r750994 = r750992 * r750993;
        double r750995 = r750991 + r750994;
        double r750996 = i;
        double r750997 = r750993 * r750996;
        double r750998 = r750995 * r750997;
        double r750999 = r750990 - r750998;
        double r751000 = r750983 * r750999;
        return r751000;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target1.9
Herbie1.9
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.3

    \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  2. Using strategy rm

  3. Applied associate-*l*1.9

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

  4. Final simplification1.9

    \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))