Average Error: 25.2 → 25.2
Time: 2.1s
Precision: binary64
\[\sqrt{\left(a + b\right) \cdot \left(c + \left(d \cdot d\right) \cdot d\right)}\]
↓
\[\sqrt{\left(a + b\right) \cdot \left(c + \left(d \cdot d\right) \cdot d\right)}\]
\sqrt{\left(a + b\right) \cdot \left(c + \left(d \cdot d\right) \cdot d\right)}
↓
\sqrt{\left(a + b\right) \cdot \left(c + \left(d \cdot d\right) \cdot d\right)}
double code(double a, double b, double c, double d) {
	return ((double) sqrt(((double) (((double) (a + b)) * ((double) (c + ((double) (((double) (d * d)) * d))))))));
}
↓
double code(double a, double b, double c, double d) {
	return ((double) sqrt(((double) (((double) (a + b)) * ((double) (c + ((double) (((double) (d * d)) * d))))))));
}

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

Derivation

  1. Initial program 25.2

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

  2. Final simplification25.2

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

Reproduce

herbie shell --seed 2020153 
(FPCore (a b c d)
  :name "(sqrt (* (+ a b) (+ c (* (* d d) d))))"
  :precision binary64
  (sqrt (* (+ a b) (+ c (* (* d d) d)))))