Average Error: 6.0 → 1.6
Time: 7.5s
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 r638195 = 2.0;
        double r638196 = x;
        double r638197 = y;
        double r638198 = r638196 * r638197;
        double r638199 = z;
        double r638200 = t;
        double r638201 = r638199 * r638200;
        double r638202 = r638198 + r638201;
        double r638203 = a;
        double r638204 = b;
        double r638205 = c;
        double r638206 = r638204 * r638205;
        double r638207 = r638203 + r638206;
        double r638208 = r638207 * r638205;
        double r638209 = i;
        double r638210 = r638208 * r638209;
        double r638211 = r638202 - r638210;
        double r638212 = r638195 * r638211;
        return r638212;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r638213 = 2.0;
        double r638214 = x;
        double r638215 = y;
        double r638216 = r638214 * r638215;
        double r638217 = z;
        double r638218 = t;
        double r638219 = r638217 * r638218;
        double r638220 = r638216 + r638219;
        double r638221 = a;
        double r638222 = b;
        double r638223 = c;
        double r638224 = r638222 * r638223;
        double r638225 = r638221 + r638224;
        double r638226 = i;
        double r638227 = r638223 * r638226;
        double r638228 = r638225 * r638227;
        double r638229 = r638220 - r638228;
        double r638230 = r638213 * r638229;
        return r638230;
}

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

Original6.0
Target1.6
Herbie1.6
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.0

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

  3. Applied associate-*l*1.6

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

  4. Final simplification1.6

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

Reproduce

herbie shell --seed 2020039 
(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))))