Details

sample86.0ms

Algorithm

intervals

Results

21.0ms	100×	body	2560	nan
18.0ms	558×	body	80	nan
11.0ms	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

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`add-log-exp`
6×	`add-cube-cbrt`
4×	`pow1` `sqrt-prod`
3×	`add-exp-log` `expm1-log1p-u` `fma-def` `prod-diff` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `sqrt-div` `flip--` `difference-of-squares`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 54

Calls

3 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(- (* x x) 1.0)
5.0ms	(sqrt (- (* x x) 1.0))

series165.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(+ x (sqrt (- (* x x) 1.0)))
39.0ms	(- (* x x) 1.0)
55.0ms	(sqrt (- (* x x) 1.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	280	334
1	959	293
2	5002	289

prune126.0ms

Filtered

63 candidates to 51 candidates (81.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	1	64

Merged error: 0b

Counts

64 → 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))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`add-cube-cbrt` `associate-l`
6×	`pow1`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `fma-def` `pow-prod-down` `flip--`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 60

Calls

2 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series350.0ms

Counts

2 → 6

Calls

2 calls:

144.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	382	708
1	1369	643
2	5002	629

prune154.0ms

Filtered

66 candidates to 51 candidates (77.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	1	67

Merged error: 0b

Counts

67 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

587.0ms	3028×	body	2560	nan
549.0ms	16308×	body	80	nan
407.0ms	2544×	body	1280	nan
326.0ms	8000×	body	80	valid
160.0ms	1252×	body	640	nan
69.0ms	668×	body	320	nan
21.0ms	314×	body	160	nan