Average Error: 3.7 → 0
Time: 8.5s
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 r3356112 = a;
        double r3356113 = b;
        double r3356114 = c;
        double r3356115 = d;
        double r3356116 = r3356114 + r3356115;
        double r3356117 = r3356113 + r3356116;
        double r3356118 = r3356112 + r3356117;
        double r3356119 = 2.0;
        double r3356120 = r3356118 * r3356119;
        return r3356120;
}
↓
double f(double a, double b, double c, double d) {
        double r3356121 = 2.0;
        double r3356122 = b;
        double r3356123 = c;
        double r3356124 = r3356122 + r3356123;
        double r3356125 = d;
        double r3356126 = a;
        double r3356127 = r3356125 + r3356126;
        double r3356128 = r3356124 + r3356127;
        double r3356129 = r3356121 * r3356128;
        return r3356129;
}

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

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

  7. Applied sum-log2.8

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

  8. Applied add-log-exp2.8

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

  9. Applied sum-log1.4

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

  10. Simplified0.9

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

  12. Applied exp-sum1.2

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

  13. Applied log-prod0.8

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

  14. Simplified0.5

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

  15. Simplified0

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

  16. Final simplification0

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

Reproduce

herbie shell --seed 2019151 +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))