Average Error: 3.7 → 0.6
Time: 3.0s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\left(d + a\right) + \left(b + c\right)\right)\right)}^{3}}\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\left(d + a\right) + \left(b + c\right)\right)\right)}^{3}}\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r118262 = a;
        double r118263 = b;
        double r118264 = c;
        double r118265 = d;
        double r118266 = r118264 + r118265;
        double r118267 = r118263 + r118266;
        double r118268 = r118262 + r118267;
        double r118269 = 2.0;
        double r118270 = r118268 * r118269;
        return r118270;
}
↓
double f(double a, double b, double c, double d) {
        double r118271 = d;
        double r118272 = a;
        double r118273 = r118271 + r118272;
        double r118274 = b;
        double r118275 = c;
        double r118276 = r118274 + r118275;
        double r118277 = r118273 + r118276;
        double r118278 = expm1(r118277);
        double r118279 = 3.0;
        double r118280 = pow(r118278, r118279);
        double r118281 = cbrt(r118280);
        double r118282 = log1p(r118281);
        double r118283 = 2.0;
        double r118284 = r118282 * r118283;
        return r118284;
}

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
Target3.9
Herbie0.6
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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 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. Using strategy rm

  7. Applied add-cbrt-cube2.9

    \[\leadsto \mathsf{log1p}\left(\color{blue}{\sqrt[3]{\left(\mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \mathsf{expm1}\left(a + \left(\left(b + c\right) + d\right)\right)}}\right) \cdot 2\]

  8. Simplified2.9

    \[\leadsto \mathsf{log1p}\left(\sqrt[3]{\color{blue}{{\left(\mathsf{expm1}\left(d + \left(a + \left(b + c\right)\right)\right)\right)}^{3}}}\right) \cdot 2\]
  9. Using strategy rm

  10. Applied associate-+r+0.6

    \[\leadsto \mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\color{blue}{\left(d + a\right) + \left(b + c\right)}\right)\right)}^{3}}\right) \cdot 2\]

  11. Final simplification0.6

    \[\leadsto \mathsf{log1p}\left(\sqrt[3]{{\left(\mathsf{expm1}\left(\left(d + a\right) + \left(b + c\right)\right)\right)}^{3}}\right) \cdot 2\]

Reproduce

herbie shell --seed 2019356 +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))