Average Error: 3.7 → 0
Time: 2.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(d + a\right) + \left(b + c\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(d + a\right) + \left(b + c\right)\right)
double f(double a, double b, double c, double d) {
        double r69382 = a;
        double r69383 = b;
        double r69384 = c;
        double r69385 = d;
        double r69386 = r69384 + r69385;
        double r69387 = r69383 + r69386;
        double r69388 = r69382 + r69387;
        double r69389 = 2.0;
        double r69390 = r69388 * r69389;
        return r69390;
}
↓
double f(double a, double b, double c, double d) {
        double r69391 = 2.0;
        double r69392 = d;
        double r69393 = a;
        double r69394 = r69392 + r69393;
        double r69395 = b;
        double r69396 = c;
        double r69397 = r69395 + r69396;
        double r69398 = r69394 + r69397;
        double r69399 = r69391 * r69398;
        return r69399;
}

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 *-un-lft-identity3.7

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

  4. Applied *-un-lft-identity3.7

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

  5. Applied distribute-lft-out3.7

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

  6. Simplified2.8

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

  8. Applied distribute-lft-in2.8

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

  9. Applied associate-+r+0

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2020045 
(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))