Average Error: 0.4 → 0.3
Time: 2.9s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(e + d\right) + \sqrt{a + \left(b + c\right)} \cdot \sqrt{a + \left(b + c\right)}\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(e + d\right) + \sqrt{a + \left(b + c\right)} \cdot \sqrt{a + \left(b + c\right)}
double f(double a, double b, double c, double d, double e) {
        double r92120 = e;
        double r92121 = d;
        double r92122 = r92120 + r92121;
        double r92123 = c;
        double r92124 = r92122 + r92123;
        double r92125 = b;
        double r92126 = r92124 + r92125;
        double r92127 = a;
        double r92128 = r92126 + r92127;
        return r92128;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r92129 = e;
        double r92130 = d;
        double r92131 = r92129 + r92130;
        double r92132 = a;
        double r92133 = b;
        double r92134 = c;
        double r92135 = r92133 + r92134;
        double r92136 = r92132 + r92135;
        double r92137 = sqrt(r92136);
        double r92138 = r92137 * r92137;
        double r92139 = r92131 + r92138;
        return r92139;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.3
\[\left(d + \left(c + \left(a + b\right)\right)\right) + e\]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
  2. Using strategy rm

  3. Applied associate-+l+0.3

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

  5. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\left(e + d\right) + \left(\left(c + b\right) + a\right)}\]

  6. Simplified0.3

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

  8. Applied add-sqr-sqrt0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :precision binary64
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))