Average Error: 6.5 → 1.8
Time: 22.0s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\]
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(i \cdot c\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r803625 = 2.0;
        double r803626 = x;
        double r803627 = y;
        double r803628 = r803626 * r803627;
        double r803629 = z;
        double r803630 = t;
        double r803631 = r803629 * r803630;
        double r803632 = r803628 + r803631;
        double r803633 = a;
        double r803634 = b;
        double r803635 = c;
        double r803636 = r803634 * r803635;
        double r803637 = r803633 + r803636;
        double r803638 = r803637 * r803635;
        double r803639 = i;
        double r803640 = r803638 * r803639;
        double r803641 = r803632 - r803640;
        double r803642 = r803625 * r803641;
        return r803642;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r803643 = 2.0;
        double r803644 = x;
        double r803645 = y;
        double r803646 = r803644 * r803645;
        double r803647 = z;
        double r803648 = t;
        double r803649 = r803647 * r803648;
        double r803650 = r803646 + r803649;
        double r803651 = a;
        double r803652 = b;
        double r803653 = c;
        double r803654 = r803652 * r803653;
        double r803655 = r803651 + r803654;
        double r803656 = i;
        double r803657 = r803656 * r803653;
        double r803658 = r803655 * r803657;
        double r803659 = r803650 - r803658;
        double r803660 = r803643 * r803659;
        return r803660;
}

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. Simplified1.8

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

  5. Final simplification1.8

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

Reproduce

herbie shell --seed 2019350 
(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))))