Average Error: 3.7 → 0.6
Time: 9.0s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{{\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{{\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}} \cdot 2
double f(double a, double b, double c, double d) {
        double r81348 = a;
        double r81349 = b;
        double r81350 = c;
        double r81351 = d;
        double r81352 = r81350 + r81351;
        double r81353 = r81349 + r81352;
        double r81354 = r81348 + r81353;
        double r81355 = 2.0;
        double r81356 = r81354 * r81355;
        return r81356;
}
↓
double f(double a, double b, double c, double d) {
        double r81357 = a;
        double r81358 = d;
        double r81359 = r81357 + r81358;
        double r81360 = b;
        double r81361 = c;
        double r81362 = r81360 + r81361;
        double r81363 = r81359 + r81362;
        double r81364 = 3.0;
        double r81365 = pow(r81363, r81364);
        double r81366 = cbrt(r81365);
        double r81367 = 2.0;
        double r81368 = r81366 * r81367;
        return r81368;
}

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
Herbie0.6
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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

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

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

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

  10. Applied distribute-lft-out2.9

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

  11. Simplified2.9

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

  13. Applied associate-+r+0.6

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

  14. Simplified0.6

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

  15. Final simplification0.6

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

Reproduce

herbie shell --seed 2019235 
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))