Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	552×	body	80	nan
12.0ms	261×	body	160	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 30.1b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
28.0b	(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `sqrt-prod`
5×	`difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-l` `sum-log` `*-commutative` `flip--` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 41

Calls

2 calls:

11.0ms	(+ x (sqrt (- (* x x) 1.0)))
11.0ms	(sqrt (- (* x x) 1.0))

series122.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(+ x (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	248	275
1	841	258
2	3314	253
3	5002	249

prune85.0ms

Filtered

47 candidates to 37 candidates (78.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	1	48

Merged error: 0b

Counts

48 → 1

localize12.0ms

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))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `sqrt-prod`
12×	`sqrt-div`
9×	`associate-r`
8×	`associate-l`
7×	`add-cube-cbrt`
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--` `distribute-lft-out`
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--`

Counts

2 → 62

Calls

2 calls:

14.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series341.0ms

Counts

2 → 6

Calls

2 calls:

145.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
196.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify41.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	376	724
1	1337	657
2	5002	643

prune152.0ms

Filtered

68 candidates to 52 candidates (76.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	1	69

Merged error: 0b

Counts

69 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

368.0ms	16356×	body	80	nan
356.0ms	7635×	body	160	nan
224.0ms	8000×	body	80	valid