Average Error: 0.4 → 0.3
Time: 2.5s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[e + \left(d + \sqrt{a + \left(b + c\right)} \cdot \sqrt{a + \left(b + c\right)}\right)\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
e + \left(d + \sqrt{a + \left(b + c\right)} \cdot \sqrt{a + \left(b + c\right)}\right)
double f(double a, double b, double c, double d, double e) {
        double r94146 = e;
        double r94147 = d;
        double r94148 = r94146 + r94147;
        double r94149 = c;
        double r94150 = r94148 + r94149;
        double r94151 = b;
        double r94152 = r94150 + r94151;
        double r94153 = a;
        double r94154 = r94152 + r94153;
        return r94154;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r94155 = e;
        double r94156 = d;
        double r94157 = a;
        double r94158 = b;
        double r94159 = c;
        double r94160 = r94158 + r94159;
        double r94161 = r94157 + r94160;
        double r94162 = sqrt(r94161);
        double r94163 = r94162 * r94162;
        double r94164 = r94156 + r94163;
        double r94165 = r94155 + r94164;
        return r94165;
}

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

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

  5. Applied associate-+l+0.3

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

  6. Simplified0.3

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

  8. Applied associate-+l+0.2

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

  10. Applied add-sqr-sqrt0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2020020 
(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))