Average Error: 3.7 → 2.8
Time: 4.2s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\sqrt[3]{a + \left(\left(b + c\right) + d\right)} \cdot \sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)}\right) \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\left(\sqrt[3]{a + \left(\left(b + c\right) + d\right)} \cdot \sqrt[3]{\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(\left(a + \left(b + c\right)\right) + d\right)}\right) \cdot 2
double f(double a, double b, double c, double d) {
        double r134079 = a;
        double r134080 = b;
        double r134081 = c;
        double r134082 = d;
        double r134083 = r134081 + r134082;
        double r134084 = r134080 + r134083;
        double r134085 = r134079 + r134084;
        double r134086 = 2.0;
        double r134087 = r134085 * r134086;
        return r134087;
}
↓
double f(double a, double b, double c, double d) {
        double r134088 = a;
        double r134089 = b;
        double r134090 = c;
        double r134091 = r134089 + r134090;
        double r134092 = d;
        double r134093 = r134091 + r134092;
        double r134094 = r134088 + r134093;
        double r134095 = cbrt(r134094);
        double r134096 = r134088 + r134091;
        double r134097 = r134096 + r134092;
        double r134098 = r134094 * r134097;
        double r134099 = cbrt(r134098);
        double r134100 = r134095 * r134099;
        double r134101 = 2.0;
        double r134102 = r134100 * r134101;
        return r134102;
}

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

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-cbrt-cube2.9

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

  6. Simplified2.9

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

  8. Applied cube-mult2.9

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

  9. Applied cbrt-prod3.0

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

  11. Applied associate-+r+2.8

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

  12. Final simplification2.8

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

Reproduce

herbie shell --seed 2020033 
(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))