Details

sample86.0ms

Algorithm

intervals

Results

18.0ms	100×	body	2560	nan
18.0ms	558×	body	80	nan
14.0ms	76×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	44×	body	640	nan
2.0ms	17×	body	320	nan
1.0ms	14×	body	160	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.4b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.0b	(- (* x x) 1.0)
30.1b	(sqrt (- (* x x) 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(- (* x x) 1.0)
4.0ms	(sqrt (- (* x x) 1.0))

series151.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(+ x (sqrt (- (* x x) 1.0)))
40.0ms	(- (* x x) 1.0)
51.0ms	(sqrt (- (* x x) 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	228	284
1	702	267
2	2784	261
3	5001	260

prune94.0ms

Filtered

50 candidates to 40 candidates (80.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	1	51

Merged error: 0b

Counts

51 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series350.0ms

Counts

2 → 6

Calls

2 calls:

135.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
215.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify43.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	360	656
1	1271	612
2	5002	600

prune127.0ms

Filtered

59 candidates to 44 candidates (74.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	1	60

Merged error: 0b

Counts

60 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

620.0ms	3028×	body	2560	nan
570.0ms	16308×	body	80	nan
420.0ms	2544×	body	1280	nan
338.0ms	8000×	body	80	valid
167.0ms	1252×	body	640	nan
72.0ms	668×	body	320	nan
22.0ms	314×	body	160	nan