Average Error: 3.7 → 0.6
Time: 7.4s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{{\left(\left(d + a\right) + \left(b + c\right)\right)}^{3}} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{{\left(\left(d + a\right) + \left(b + c\right)\right)}^{3}} \cdot 2
double f(double a, double b, double c, double d) {
        double r156556 = a;
        double r156557 = b;
        double r156558 = c;
        double r156559 = d;
        double r156560 = r156558 + r156559;
        double r156561 = r156557 + r156560;
        double r156562 = r156556 + r156561;
        double r156563 = 2.0;
        double r156564 = r156562 * r156563;
        return r156564;
}
↓
double f(double a, double b, double c, double d) {
        double r156565 = d;
        double r156566 = a;
        double r156567 = r156565 + r156566;
        double r156568 = b;
        double r156569 = c;
        double r156570 = r156568 + r156569;
        double r156571 = r156567 + r156570;
        double r156572 = 3.0;
        double r156573 = pow(r156571, r156572);
        double r156574 = cbrt(r156573);
        double r156575 = 2.0;
        double r156576 = r156574 * r156575;
        return r156576;
}

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
Target3.9
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. Final simplification0.6

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

Reproduce

herbie shell --seed 2020043 
(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))