Average Error: 6.5 → 1.8
Time: 21.1s
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 r909657 = 2.0;
        double r909658 = x;
        double r909659 = y;
        double r909660 = r909658 * r909659;
        double r909661 = z;
        double r909662 = t;
        double r909663 = r909661 * r909662;
        double r909664 = r909660 + r909663;
        double r909665 = a;
        double r909666 = b;
        double r909667 = c;
        double r909668 = r909666 * r909667;
        double r909669 = r909665 + r909668;
        double r909670 = r909669 * r909667;
        double r909671 = i;
        double r909672 = r909670 * r909671;
        double r909673 = r909664 - r909672;
        double r909674 = r909657 * r909673;
        return r909674;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r909675 = 2.0;
        double r909676 = x;
        double r909677 = y;
        double r909678 = r909676 * r909677;
        double r909679 = z;
        double r909680 = t;
        double r909681 = r909679 * r909680;
        double r909682 = r909678 + r909681;
        double r909683 = a;
        double r909684 = b;
        double r909685 = c;
        double r909686 = r909684 * r909685;
        double r909687 = r909683 + r909686;
        double r909688 = i;
        double r909689 = r909685 * r909688;
        double r909690 = r909687 * r909689;
        double r909691 = r909682 - r909690;
        double r909692 = r909675 * r909691;
        return r909692;
}

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

Original6.5
Target1.8
Herbie1.8
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Initial program 6.5

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

  3. Applied associate-*l*1.8

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

  4. Final simplification1.8

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(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))))