Average Error: 0.4 → 0.3
Time: 14.8s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\frac{\left(\left(c + \left(e + d\right)\right) - \left(b + a\right)\right) \cdot \left(\left(c + d\right) + \left(\left(b + e\right) + a\right)\right)}{\left(c + \left(e + d\right)\right) - \left(b + a\right)}\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\frac{\left(\left(c + \left(e + d\right)\right) - \left(b + a\right)\right) \cdot \left(\left(c + d\right) + \left(\left(b + e\right) + a\right)\right)}{\left(c + \left(e + d\right)\right) - \left(b + a\right)}
double f(double a, double b, double c, double d, double e) {
        double r251531 = e;
        double r251532 = d;
        double r251533 = r251531 + r251532;
        double r251534 = c;
        double r251535 = r251533 + r251534;
        double r251536 = b;
        double r251537 = r251535 + r251536;
        double r251538 = a;
        double r251539 = r251537 + r251538;
        return r251539;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r251540 = c;
        double r251541 = e;
        double r251542 = d;
        double r251543 = r251541 + r251542;
        double r251544 = r251540 + r251543;
        double r251545 = b;
        double r251546 = a;
        double r251547 = r251545 + r251546;
        double r251548 = r251544 - r251547;
        double r251549 = r251540 + r251542;
        double r251550 = r251545 + r251541;
        double r251551 = r251550 + r251546;
        double r251552 = r251549 + r251551;
        double r251553 = r251548 * r251552;
        double r251554 = r251553 / r251548;
        return r251554;
}

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. Simplified0.3

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

  4. Applied flip-+0.5

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

  5. Simplified0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1.0 a 2.0 b 4.0 c 8.0 d 16.0 e 32.0)

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

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