Average Error: 3.6 → 0
Time: 5.9s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(d + a\right)\right)
double f(double a, double b, double c, double d) {
        double r1387028 = a;
        double r1387029 = b;
        double r1387030 = c;
        double r1387031 = d;
        double r1387032 = r1387030 + r1387031;
        double r1387033 = r1387029 + r1387032;
        double r1387034 = r1387028 + r1387033;
        double r1387035 = 2.0;
        double r1387036 = r1387034 * r1387035;
        return r1387036;
}
↓
double f(double a, double b, double c, double d) {
        double r1387037 = 2.0;
        double r1387038 = b;
        double r1387039 = c;
        double r1387040 = r1387038 + r1387039;
        double r1387041 = d;
        double r1387042 = a;
        double r1387043 = r1387041 + r1387042;
        double r1387044 = r1387040 + r1387043;
        double r1387045 = r1387037 * r1387044;
        return r1387045;
}

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 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-log-exp2.8

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

  6. Applied add-log-exp2.8

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

  7. Applied add-log-exp2.8

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

  8. Applied sum-log2.8

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

  9. Applied sum-log2.8

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

  10. Applied add-log-exp2.8

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

  11. Applied sum-log1.5

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

  12. Simplified0.9

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

  14. Applied rem-log-exp0

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

  15. Final simplification0

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(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))