Average Error: 3.6 → 2.8
Time: 14.1s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r67141 = a;
        double r67142 = b;
        double r67143 = c;
        double r67144 = d;
        double r67145 = r67143 + r67144;
        double r67146 = r67142 + r67145;
        double r67147 = r67141 + r67146;
        double r67148 = 2.0;
        double r67149 = r67147 * r67148;
        return r67149;
}
↓
double f(double a, double b, double c, double d) {
        double r67150 = a;
        double r67151 = b;
        double r67152 = c;
        double r67153 = r67151 + r67152;
        double r67154 = d;
        double r67155 = r67153 + r67154;
        double r67156 = r67150 + r67155;
        double r67157 = expm1(r67156);
        double r67158 = log1p(r67157);
        double r67159 = 2.0;
        double r67160 = r67158 * r67159;
        return r67160;
}

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
Herbie2.8
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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 log1p-expm1-u2.8

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right)} \cdot 2\]

  6. Final simplification2.8

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot 2\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :precision binary64
  :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))