Details

sample114.0ms

Algorithm

intervals

Results

89.0ms

729×

body

valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
6	3785
5	1494
4	533
3	147
2	51
1	26
0	12

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
0.0b	(* (* b b) 4)
0.3b	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
11×	`add-sqr-sqrt`
10×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`flip3-+` `flip-+`
6×	`associate-r`
5×	`add-log-exp`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`swap-sqr` `insert-posit16`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-l/` `associate-r/` `*-commutative` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

3 → 70

Calls

3 calls:

32.0ms	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
27.0ms	(* (* b b) 4)
66.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

series706.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(+ (* (* b b) 4) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))
63.0ms	(* (* b b) 4)
525.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

simplify4.7s

Counts

79 → 79

Iterations

Iter	Nodes
3	7980
2	1696
1	424
0	124

prune656.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b)))) (sqrt (+ (* a a) (* b b))))
0.2b	(* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b))))
9.8b	(sqrt (+ (* a a) (* b b)))
9.8b	(sqrt (+ (* a a) (* b b)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
35×	`flip3-+` `flip-+`
32×	`frac-times`
25×	`pow1`
20×	`add-sqr-sqrt`
16×	`associate-*l/`
13×	`sqrt-prod`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
10×	`associate-*r/`
7×	`sqrt-pow1` `pow1/2`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow3`
2×	`rem-sqrt-square` `*-commutative` `unswap-sqr`
1×	`pow-plus`

Counts

4 → 120

Calls

4 calls:

129.0ms	(* (* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b)))) (sqrt (+ (* a a) (* b b))))
56.0ms	(* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b))))
7.0ms	(sqrt (+ (* a a) (* b b)))
6.0ms	(sqrt (+ (* a a) (* b b)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b)))) (sqrt (+ (* a a) (* b b))))
163.0ms	(* (+ (* a a) (* b b)) (sqrt (+ (* a a) (* b b))))
53.0ms	(sqrt (+ (* a a) (* b b)))
47.0ms	(sqrt (+ (* a a) (* b b)))

simplify4.1s

Counts

132 → 132

Iterations

Iter	Nodes
3	6927
2	1794
1	426
0	157

prune1.4s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
0.0b	(pow (sqrt (+ (* a a) (* b b))) 4)
0.0b	(* (* b b) 4)
9.8b	(sqrt (+ (* a a) (* b b)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `pow-pow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `associate-l` `pow-exp` `*-commutative` `sqrt-pow2` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

53.0ms	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
14.0ms	(pow (sqrt (+ (* a a) (* b b))) 4)
32.0ms	(* (* b b) 4)
11.0ms	(sqrt (+ (* a a) (* b b)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))
89.0ms	(pow (sqrt (+ (* a a) (* b b))) 4)
41.0ms	(* (* b b) 4)
58.0ms	(sqrt (+ (* a a) (* b b)))

simplify2.9s

Counts

84 → 84

Iterations

Iter	Nodes
3	3355
2	1031
1	328
0	127

prune719.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.3s

20501×

body

valid