Details

sample84.0ms

Algorithm

intervals

Results

34.0ms	281×	body	160	nan
16.0ms	569×	body	80	nan
10.0ms	256×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
2	11
1	10
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.3b	(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

14.0ms	(+ x (sqrt (- (* x x) 1.0)))
8.0ms	(sqrt (- (* x x) 1.0))

series183.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(+ x (sqrt (- (* x x) 1.0)))
89.0ms	(sqrt (- (* x x) 1.0))

simplify516.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
2	892
1	223
0	90

prune181.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

6.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
42.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

series546.0ms

Counts

2 → 6

Calls

2 calls:

216.0ms	(+ x (* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0)))))
330.0ms	(* (sqrt (+ (sqrt 1.0) x)) (sqrt (- x (sqrt 1.0))))

simplify799.0ms

Counts

59 → 59

Iterations

Iter	Nodes
done	5002
2	1488
1	381
0	159

prune392.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt (+ (sqrt 1.0) x))) (cbrt (sqrt (+ (sqrt 1.0) x))))
0.5b	(cbrt (sqrt (+ (sqrt 1.0) x)))
0.5b	(cbrt (sqrt (+ (sqrt 1.0) x)))
0.5b	(cbrt (sqrt (+ x (sqrt 1.0))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

69×	`cbrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`sqrt-prod`
22×	`add-cube-cbrt`
18×	`cbrt-div` `sqrt-div`
14×	`swap-sqr`
11×	`pow1`
10×	`associate-r` `associate-l`
9×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out` `unswap-sqr`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 120

Calls

4 calls:

54.0ms	(* (cbrt (sqrt (+ (sqrt 1.0) x))) (cbrt (sqrt (+ (sqrt 1.0) x))))
5.0ms	(cbrt (sqrt (+ (sqrt 1.0) x)))
5.0ms	(cbrt (sqrt (+ (sqrt 1.0) x)))
5.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (cbrt (sqrt (+ (sqrt 1.0) x))) (cbrt (sqrt (+ (sqrt 1.0) x))))
194.0ms	(cbrt (sqrt (+ (sqrt 1.0) x)))
158.0ms	(cbrt (sqrt (+ (sqrt 1.0) x)))
191.0ms	(cbrt (sqrt (+ x (sqrt 1.0))))

simplify1.3s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	1899
1	452
0	207

prune774.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
done	20
2	20
1	19
0	16

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	7472×	body	160	nan
954.0ms	16122×	body	80	nan
466.0ms	8000×	body	80	valid