Details

sample52.0ms

Algorithm

intervals

Results

13.0ms	552×	body	80	nan
12.0ms	261×	body	160	nan
10.0ms	256×	body	80	valid

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: 30.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
5×	`difference-of-squares`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `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 → 34

Calls

2 calls:

11.0ms	(+ x (sqrt (- (* x x) 1.0)))
9.0ms	(sqrt (- (* x x) 1.0))

series126.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ x (sqrt (- (* x x) 1.0)))
57.0ms	(sqrt (- (* x x) 1.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	228	257
1	748	245
2	2972	239
3	5002	236

prune70.0ms

Filtered

40 candidates to 30 candidates (75.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	1	41

Merged error: 0b

Counts

41 → 1

localize13.0ms

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

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
14×	`*-un-lft-identity`
12×	`sqrt-div`
9×	`associate-r`
8×	`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--` `distribute-lft-out`
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--`

Counts

2 → 55

Calls

2 calls:

15.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series357.0ms

Counts

2 → 6

Calls

2 calls:

150.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	354	672
1	1244	628
2	5001	616

prune127.0ms

Filtered

61 candidates to 44 candidates (72.1%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	1	62

Merged error: 0b

Counts

62 → 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

371.0ms	16356×	body	80	nan
362.0ms	7635×	body	160	nan
230.0ms	8000×	body	80	valid