Average Error: 3.6 → 0
Time: 6.7s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \left(\left(\left(a + d\right) + c\right) + b\right)\]
\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 r3246091 = a;
        double r3246092 = b;
        double r3246093 = c;
        double r3246094 = d;
        double r3246095 = r3246093 + r3246094;
        double r3246096 = r3246092 + r3246095;
        double r3246097 = r3246091 + r3246096;
        double r3246098 = 2.0;
        double r3246099 = r3246097 * r3246098;
        return r3246099;
}
↓
double f(double a, double b, double c, double d) {
        double r3246100 = 2.0;
        double r3246101 = a;
        double r3246102 = d;
        double r3246103 = r3246101 + r3246102;
        double r3246104 = c;
        double r3246105 = r3246103 + r3246104;
        double r3246106 = b;
        double r3246107 = r3246105 + r3246106;
        double r3246108 = r3246100 * r3246107;
        return r3246108;
}

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-exp3.0

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

  7. Applied pow13.0

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

  8. Applied log-pow3.0

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

  9. Simplified0

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

  10. Final simplification0

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

Reproduce

herbie shell --seed 2019133 
(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))