Average Error: 3.7 → 2.8
Time: 47.8s
Precision: 64
\[-14 \le a \le -13 \land -3 \le b \le -2 \land 3 \le c \le 3.5 \land 12.5 \le d \le 13.5\]
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[2 \cdot \sqrt[3]{\log \left(e^{\left(a + c\right) + \left(b + d\right)}\right) \cdot \left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\right)}\]
\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2
↓
2 \cdot \sqrt[3]{\log \left(e^{\left(a + c\right) + \left(b + d\right)}\right) \cdot \left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\right)}
double f(double a, double b, double c, double d) {
        double r12322369 = a;
        double r12322370 = b;
        double r12322371 = c;
        double r12322372 = d;
        double r12322373 = r12322371 + r12322372;
        double r12322374 = r12322370 + r12322373;
        double r12322375 = r12322369 + r12322374;
        double r12322376 = 2.0;
        double r12322377 = r12322375 * r12322376;
        return r12322377;
}
↓
double f(double a, double b, double c, double d) {
        double r12322378 = 2.0;
        double r12322379 = a;
        double r12322380 = c;
        double r12322381 = r12322379 + r12322380;
        double r12322382 = b;
        double r12322383 = d;
        double r12322384 = r12322382 + r12322383;
        double r12322385 = r12322381 + r12322384;
        double r12322386 = exp(r12322385);
        double r12322387 = log(r12322386);
        double r12322388 = r12322382 + r12322380;
        double r12322389 = r12322388 + r12322383;
        double r12322390 = r12322389 + r12322379;
        double r12322391 = r12322390 * r12322390;
        double r12322392 = r12322387 * r12322391;
        double r12322393 = cbrt(r12322392);
        double r12322394 = r12322378 * r12322393;
        return r12322394;
}

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. Using strategy rm

  7. Applied associate-+r+2.8

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

  9. Applied add-log-exp2.8

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

  10. Applied add-log-exp2.8

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

  11. Applied sum-log2.8

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

  12. Simplified2.8

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

  13. Final simplification2.8

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

Reproduce

herbie shell --seed 2019104 
(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))