Average Error: 3.6 → 2.7
Time: 13.5s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(d + \left(\left(b + c\right) + a\right)\right)\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(d + \left(\left(b + c\right) + a\right)\right) \cdot \left(d + \left(\left(b + c\right) + a\right)\right)\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r2226061 = a;
        double r2226062 = b;
        double r2226063 = c;
        double r2226064 = d;
        double r2226065 = r2226063 + r2226064;
        double r2226066 = r2226062 + r2226065;
        double r2226067 = r2226061 + r2226066;
        double r2226068 = 2.0;
        double r2226069 = r2226067 * r2226068;
        return r2226069;
}
↓
double f(double a, double b, double c, double d) {
        double r2226070 = a;
        double r2226071 = b;
        double r2226072 = c;
        double r2226073 = r2226071 + r2226072;
        double r2226074 = d;
        double r2226075 = r2226073 + r2226074;
        double r2226076 = r2226070 + r2226075;
        double r2226077 = r2226073 + r2226070;
        double r2226078 = r2226074 + r2226077;
        double r2226079 = r2226078 * r2226078;
        double r2226080 = r2226076 * r2226079;
        double r2226081 = cbrt(r2226080);
        double r2226082 = 2.0;
        double r2226083 = r2226081 * r2226082;
        return r2226083;
}

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
Herbie2.7
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

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 associate-+r+2.8

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

  7. Applied add-cbrt-cube2.9

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

  9. Applied associate-+l+2.7

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

  10. Final simplification2.7

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

Reproduce

herbie shell --seed 2019130 +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))