Details

sample49.0ms

Algorithm

intervals

Results

21.0ms	775×	body	80	nan
9.0ms	256×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	16	7
done	16	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 98

Calls

4 calls:

5.0ms	(sqrt (- 1.0 (* x x)))
31.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
37.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
12.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series568.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (- 1.0 (* x x)))
290.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
98.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
124.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify49.0ms

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	512	1016
1	1814	965
2	5002	961
done	5002	961

prune287.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(* (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (/ (cbrt (sqrt (- 1.0 (* x x)))) x))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
34×	`associate-r`
33×	`times-frac`
30×	`sqrt-div`
27×	`add-cube-cbrt` `*-un-lft-identity`
25×	`sqrt-prod`
24×	`cbrt-div`
23×	`cbrt-prod`
16×	`add-exp-log` `frac-times`
15×	`flip3--` `flip--`
12×	`pow1` `associate-*l/`
10×	`add-cbrt-cube`
6×	`prod-exp` `cbrt-unprod` `difference-of-squares`
5×	`associate-*r/`
4×	`add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`cbrt-undiv` `div-exp`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 122

Calls

4 calls:

6.0ms	(sqrt (- 1.0 (* x x)))
5.0ms	(sqrt (- 1.0 (* x x)))
5.0ms	(sqrt (- 1.0 (* x x)))
78.0ms	(* (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (/ (cbrt (sqrt (- 1.0 (* x x)))) x))

series310.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (- 1.0 (* x x)))
56.0ms	(sqrt (- 1.0 (* x x)))
64.0ms	(sqrt (- 1.0 (* x x)))
129.0ms	(* (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (/ (cbrt (sqrt (- 1.0 (* x x)))) x))

simplify70.0ms

Counts

134 → 134

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	620	1842
1	2635	1705
2	5001	1635
done	5001	1635

prune450.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	14	18
done	14	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

886.0ms	24216×	body	80	nan
278.0ms	8000×	body	80	valid