Average Error: 3.6 → 0
Time: 5.8s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(a + d\right) + c\right) + b\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(\left(a + d\right) + c\right) + b\right)
double f(double a, double b, double c, double d) {
        double r3079389 = a;
        double r3079390 = b;
        double r3079391 = c;
        double r3079392 = d;
        double r3079393 = r3079391 + r3079392;
        double r3079394 = r3079390 + r3079393;
        double r3079395 = r3079389 + r3079394;
        double r3079396 = 2.0;
        double r3079397 = r3079395 * r3079396;
        return r3079397;
}
↓
double f(double a, double b, double c, double d) {
        double r3079398 = 2.0;
        double r3079399 = a;
        double r3079400 = d;
        double r3079401 = r3079399 + r3079400;
        double r3079402 = c;
        double r3079403 = r3079401 + r3079402;
        double r3079404 = b;
        double r3079405 = r3079403 + r3079404;
        double r3079406 = r3079398 * r3079405;
        return r3079406;
}

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

Original3.6
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

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

  3. Applied add-log-exp3.6

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

  4. Applied add-log-exp3.6

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

  5. Applied sum-log3.6

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

  6. Applied add-log-exp3.6

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

  7. Applied sum-log2.8

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

  8. Applied add-log-exp2.8

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

  9. Applied sum-log1.5

    \[\leadsto \color{blue}{\log \left(e^{a} \cdot \left(e^{b} \cdot \left(e^{c} \cdot e^{d}\right)\right)\right)} \cdot 2\]

  10. Simplified0.9

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

  12. Applied rem-log-exp0.0

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

  14. Applied associate-+l+0

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

  15. Final simplification0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (a b c d)
  :name "Expression, p6"
  :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))