Average Error: 41.1 → 41.1
Time: 7.1s
Precision: binary64
\[\sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}\]
↓
\[\sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}\]
\sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}
↓
\sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}
double code(double b, double M, double a, double d) {
	return ((double) sqrt(((double) (((double) (((double) (((double) (((double) (4.0 * b)) * b)) * M)) * M)) - ((double) (((double) (((double) (a * a)) + ((double) (b * b)))) * ((double) (((double) (b * b)) + ((double) (((double) (a - d)) * ((double) (a - d))))))))))));
}
↓
double code(double b, double M, double a, double d) {
	return ((double) sqrt(((double) (((double) (((double) (((double) (((double) (4.0 * b)) * b)) * M)) * M)) - ((double) (((double) (((double) (a * a)) + ((double) (b * b)))) * ((double) (((double) (b * b)) + ((double) (((double) (a - d)) * ((double) (a - d))))))))))));
}

Error

Bits error versus b

Bits error versus M

Bits error versus a

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 41.1

    \[\sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}\]

  2. Final simplification41.1

    \[\leadsto \sqrt{\left(\left(\left(4 \cdot b\right) \cdot b\right) \cdot M\right) \cdot M - \left(a \cdot a + b \cdot b\right) \cdot \left(b \cdot b + \left(a - d\right) \cdot \left(a - d\right)\right)}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (b M a d)
  :name "(sqrt (- (* (* (* (* 4.0 b) b) M) M) (* (+ (* a a) (* b b)) (+ (* b b) (* (- a d) (- a d))))))"
  :precision binary64
  (sqrt (- (* (* (* (* 4.0 b) b) M) M) (* (+ (* a a) (* b b)) (+ (* b b) (* (- a d) (- a d)))))))