Average Error: 7.2 → 7.2
Time: 1.6s
Precision: binary64
\[\frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]
↓
\[\frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]
\frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)
↓
\frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)
double code(double d, double a, double bc) {
	return ((double) (((double) (((double) (d / a)) * d)) - ((double) (0.333333343 * ((double) (((double) (1.0 / ((double) pow(a, 2.0)))) * bc))))));
}
↓
double code(double d, double a, double bc) {
	return ((double) (((double) (((double) (d / a)) * d)) - ((double) (0.333333343 * ((double) (((double) (1.0 / ((double) pow(a, 2.0)))) * bc))))));
}

Error

Bits error versus d

Bits error versus a

Bits error versus bc

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.2

    \[\frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]

  2. Final simplification7.2

    \[\leadsto \frac{d}{a} \cdot d - 0.333333343000000004 \cdot \left(\frac{1}{{a}^{2}} \cdot bc\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (d a bc)
  :name "(- (* (/ d a) d) (* 0.333333343 (* (/ 1 (pow a 2)) bc)))"
  :precision binary64
  (- (* (/ d a) d) (* 0.333333343 (* (/ 1.0 (pow a 2.0)) bc))))