Average Error: 3.7 → 0
Time: 8.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(a + d\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(a + d\right)\right)
double f(double a, double b, double c, double d) {
        double r65624 = a;
        double r65625 = b;
        double r65626 = c;
        double r65627 = d;
        double r65628 = r65626 + r65627;
        double r65629 = r65625 + r65628;
        double r65630 = r65624 + r65629;
        double r65631 = 2.0;
        double r65632 = r65630 * r65631;
        return r65632;
}
↓
double f(double a, double b, double c, double d) {
        double r65633 = 2.0;
        double r65634 = b;
        double r65635 = c;
        double r65636 = r65634 + r65635;
        double r65637 = a;
        double r65638 = d;
        double r65639 = r65637 + r65638;
        double r65640 = r65636 + r65639;
        double r65641 = r65633 * r65640;
        return r65641;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.7

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. Using strategy rm

  3. Applied associate-+r+2.8

    \[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
  4. Using strategy rm

  5. Applied add-cbrt-cube2.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]

  6. Simplified2.9

    \[\leadsto \sqrt[3]{\color{blue}{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}}} \cdot 2\]
  7. Using strategy rm

  8. Applied *-un-lft-identity2.9

    \[\leadsto \sqrt[3]{{\color{blue}{\left(1 \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right)}}^{3}} \cdot 2\]

  9. Applied unpow-prod-down2.9

    \[\leadsto \sqrt[3]{\color{blue}{{1}^{3} \cdot {\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}}} \cdot 2\]

  10. Applied cbrt-prod2.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}}\right)} \cdot 2\]

  11. Simplified2.9

    \[\leadsto \left(\color{blue}{1} \cdot \sqrt[3]{{\left(a + \left(\left(b + c\right) + d\right)\right)}^{3}}\right) \cdot 2\]

  12. Simplified0

    \[\leadsto \left(1 \cdot \color{blue}{\left(\left(b + c\right) + \left(a + d\right)\right)}\right) \cdot 2\]

  13. Final simplification0

    \[\leadsto 2 \cdot \left(\left(b + c\right) + \left(a + d\right)\right)\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))