Average Error: 0.4 → 0.4
Time: 11.0s
Precision: 64
\[1 \le a \le 2 \le b \le 4 \le c \le 8 \le d \le 16 \le e \le 32\]
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
↓
\[\left(\left(d + \left(e + c\right)\right) + b\right) + a\]
\left(\left(\left(e + d\right) + c\right) + b\right) + a
↓
\left(\left(d + \left(e + c\right)\right) + b\right) + a
double f(double a, double b, double c, double d, double e) {
        double r87298 = e;
        double r87299 = d;
        double r87300 = r87298 + r87299;
        double r87301 = c;
        double r87302 = r87300 + r87301;
        double r87303 = b;
        double r87304 = r87302 + r87303;
        double r87305 = a;
        double r87306 = r87304 + r87305;
        return r87306;
}
↓
double f(double a, double b, double c, double d, double e) {
        double r87307 = d;
        double r87308 = e;
        double r87309 = c;
        double r87310 = r87308 + r87309;
        double r87311 = r87307 + r87310;
        double r87312 = b;
        double r87313 = r87311 + r87312;
        double r87314 = a;
        double r87315 = r87313 + r87314;
        return r87315;
}

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

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]

  2. Taylor expanded around 0 0.4

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

  3. Final simplification0.4

    \[\leadsto \left(\left(d + \left(e + c\right)\right) + b\right) + a\]

Reproduce

herbie shell --seed 2019303 
(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))