Average Error: 3.7 → 0
Time: 7.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(b + c\right) + \left(a + d\right)\right)\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \left(\left(b + c\right) + \left(a + d\right)\right)
double f(double a, double b, double c, double d) {
        double r4048560 = a;
        double r4048561 = b;
        double r4048562 = c;
        double r4048563 = d;
        double r4048564 = r4048562 + r4048563;
        double r4048565 = r4048561 + r4048564;
        double r4048566 = r4048560 + r4048565;
        double r4048567 = 2.0;
        double r4048568 = r4048566 * r4048567;
        return r4048568;
}
↓
double f(double a, double b, double c, double d) {
        double r4048569 = 2.0;
        double r4048570 = b;
        double r4048571 = c;
        double r4048572 = r4048570 + r4048571;
        double r4048573 = a;
        double r4048574 = d;
        double r4048575 = r4048573 + r4048574;
        double r4048576 = r4048572 + r4048575;
        double r4048577 = r4048569 * r4048576;
        return r4048577;
}

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 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 exp-sum1.2

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

  15. Applied log-prod0.8

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

  16. Simplified0.5

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

  17. Simplified0

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

  18. Final simplification0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14.0 a -13.0) (<= -3.0 b -2.0) (<= 3.0 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2.0) (* (+ c d) 2.0))

  (* (+ a (+ b (+ c d))) 2.0))