Average Error: 0.4 → 0.3
Time: 17.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \sqrt[3]{c \cdot \left(\left(c + \left(b + a\right)\right) \cdot \left(c + \left(b + a\right)\right)\right) + \left(b + a\right) \cdot \left(\left(c + \left(b + a\right)\right) \cdot \left(c + \left(b + a\right)\right)\right)}\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \sqrt[3]{c \cdot \left(\left(c + \left(b + a\right)\right) \cdot \left(c + \left(b + a\right)\right)\right) + \left(b + a\right) \cdot \left(\left(c + \left(b + a\right)\right) \cdot \left(c + \left(b + a\right)\right)\right)}
double f(double a, double b, double c, double d, double e) {
        double r14977625 = e;
        double r14977626 = d;
        double r14977627 = r14977625 + r14977626;
        double r14977628 = c;
        double r14977629 = r14977627 + r14977628;
        double r14977630 = b;
        double r14977631 = r14977629 + r14977630;
        double r14977632 = a;
        double r14977633 = r14977631 + r14977632;
        return r14977633;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r14977634 = e;
        double r14977635 = d;
        double r14977636 = r14977634 + r14977635;
        double r14977637 = c;
        double r14977638 = b;
        double r14977639 = a;
        double r14977640 = r14977638 + r14977639;
        double r14977641 = r14977637 + r14977640;
        double r14977642 = r14977641 * r14977641;
        double r14977643 = r14977637 * r14977642;
        double r14977644 = r14977640 * r14977642;
        double r14977645 = r14977643 + r14977644;
        double r14977646 = cbrt(r14977645);
        double r14977647 = r14977636 + r14977646;
        return r14977647;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

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

  3. Applied associate-+l+0.3

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

  5. Applied associate-+l+0.3

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

  7. Applied add-cbrt-cube0.3

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

  9. Applied distribute-rgt-in0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019173 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))