Average Error: 3.7 → 2.8
Time: 15.5s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)\right) \cdot \log \left(e^{a} \cdot e^{\left(b + c\right) + d}\right)} \cdot 2\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
\sqrt[3]{\left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + a\right) + d\right)\right) \cdot \log \left(e^{a} \cdot e^{\left(b + c\right) + d}\right)} \cdot 2
double f(double a, double b, double c, double d) {
        double r2299202 = a;
        double r2299203 = b;
        double r2299204 = c;
        double r2299205 = d;
        double r2299206 = r2299204 + r2299205;
        double r2299207 = r2299203 + r2299206;
        double r2299208 = r2299202 + r2299207;
        double r2299209 = 2.0;
        double r2299210 = r2299208 * r2299209;
        return r2299210;
}
↓
double f(double a, double b, double c, double d) {
        double r2299211 = b;
        double r2299212 = c;
        double r2299213 = r2299211 + r2299212;
        double r2299214 = d;
        double r2299215 = r2299213 + r2299214;
        double r2299216 = a;
        double r2299217 = r2299215 + r2299216;
        double r2299218 = r2299213 + r2299216;
        double r2299219 = r2299218 + r2299214;
        double r2299220 = r2299217 * r2299219;
        double r2299221 = exp(r2299216);
        double r2299222 = exp(r2299215);
        double r2299223 = r2299221 * r2299222;
        double r2299224 = log(r2299223);
        double r2299225 = r2299220 * r2299224;
        double r2299226 = cbrt(r2299225);
        double r2299227 = 2.0;
        double r2299228 = r2299226 * r2299227;
        return r2299228;
}

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
Target3.8
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. Using strategy rm

  7. Applied associate-+r+2.7

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

  9. Applied add-log-exp2.7

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

  10. Applied add-log-exp2.7

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

  11. Applied sum-log2.8

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

  12. Final simplification2.8

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

Reproduce

herbie shell --seed 2019132 
(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))