Details

sample98.0ms

Algorithm

intervals

Results

23.0ms	122×	body	2560	nan
20.0ms	612×	body	80	nan
15.0ms	96×	body	1280	nan
13.0ms	256×	body	80	valid
6.0ms	49×	body	640	nan
3.0ms	29×	body	320	nan
1.0ms	9×	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: 31.4b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.0b	(- (* x x) 1.0)
29.2b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
7.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(- (* x x) 1.0)
5.0ms	(sqrt (- (* x x) 1.0))

series366.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
70.0ms	(+ x (sqrt (- (* x x) 1.0)))
38.0ms	(- (* x x) 1.0)
55.0ms	(sqrt (- (* x x) 1.0))

simplify138.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	327	471
1	1087	435
2	4892	422
3	5001	422

prune142.0ms

Filtered

68 candidates to 55 candidates (80.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	2	69

Merged error: 0b

Counts

69 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
3.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
14.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series645.0ms

Counts

3 → 9

Calls

3 calls:

150.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
290.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
204.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	440	941
1	1553	864
2	5001	848

prune371.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Merged error: 0b

Counts

78 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x x) 1.0)
0.0b	(- (* x x) 1.0)
29.2b	(sqrt (- (* x x) 1.0))
29.2b	(sqrt (- (* x x) 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 58

Calls

4 calls:

4.0ms	(- (* x x) 1.0)
5.0ms	(- (* x x) 1.0)
5.0ms	(sqrt (- (* x x) 1.0))
5.0ms	(sqrt (- (* x x) 1.0))

series191.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* x x) 1.0)
46.0ms	(- (* x x) 1.0)
56.0ms	(sqrt (- (* x x) 1.0))
51.0ms	(sqrt (- (* x x) 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	154	352
1	484	334
2	2036	330
3	5001	328

prune210.0ms

Filtered

70 candidates to 54 candidates (77.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	70	2	72

Merged error: 0b

Counts

72 → 2

regimes28.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

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

558.0ms	2940×	body	2560	nan
540.0ms	16061×	body	80	nan
392.0ms	2511×	body	1280	nan
318.0ms	8000×	body	80	valid
158.0ms	1251×	body	640	nan
64.0ms	661×	body	320	nan
22.0ms	301×	body	160	nan