Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
7.0ms	267×	body	80	nan
4.0ms	38×	body	640	valid
3.0ms	128×	body	80	valid
1.0ms	20×	body	320	valid
1.0ms	15×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 30.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
3.8b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify30.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	282	318
1	1037	308
2	5001	297

prune72.0ms

Filtered

31 candidates to 41 candidates (-32.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	3	42

Merged error: 0.2b

Counts

42 → 3

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series17.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	514	800
1	2206	753
2	5001	721

prune159.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	82	10	92

Merged error: 0.0b

Counts

92 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
63×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
29×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
12×	`times-frac` `distribute-lft-out`
10×	`flip3-+` `associate-r` `associate-l` `flip-+`
9×	`pow-prod-up` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 167

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
17.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
15.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x 1.0)))
6.0ms	(sqrt (sqrt (+ x 1.0)))
9.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
4.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify109.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	679	1539
1	3301	1371
2	5002	1347

prune309.0ms

Filtered

96 candidates to 179 candidates (-86.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	178	11	189

Merged error: 0.0b

Counts

189 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))) (sqrt x)))
0.3b	(cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))
0.3b	(* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3)))
0.4b	(pow (sqrt (sqrt (+ x 1.0))) 3)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-prod`
89×	`add-sqr-sqrt`
76×	`cbrt-prod`
60×	`*-un-lft-identity`
39×	`unpow-prod-down` `cube-prod`
38×	`add-cube-cbrt`
32×	`sqrt-div`
29×	`associate-r`
27×	`unswap-sqr`
12×	`times-frac`
11×	`distribute-lft-out`
10×	`cube-div` `flip3-+` `associate-l` `flip-+`
9×	`pow1` `add-exp-log`
8×	`cbrt-div` `add-cbrt-cube`
6×	`sqr-pow`
5×	`pow-pow`
4×	`frac-times` `sqrt-pow1` `associate-/l*` `add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-/r*`
2×	`pow1/2` `associate-r/` `associate-l/` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow1/3` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `clear-num` `*-commutative` `sqrt-pow2` `rem-cbrt-cube` `cbrt-unprod` `div-inv` `rem-cube-cbrt`

Counts

4 → 201

Calls

4 calls:

19.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))) (sqrt x)))
6.0ms	(cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))
22.0ms	(* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3)))
6.0ms	(pow (sqrt (sqrt (+ x 1.0))) 3)

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))) (sqrt x)))
6.0ms	(cbrt (pow (sqrt (sqrt (+ x 1.0))) 3))
4.0ms	(* (sqrt (sqrt (+ x 1.0))) (cbrt (pow (sqrt (sqrt (+ x 1.0))) 3)))
11.0ms	(pow (sqrt (sqrt (+ x 1.0))) 3)

simplify130.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	919	2469
1	4241	1955
2	5002	1874

prune355.0ms

Filtered

105 candidates to 213 candidates (-102.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	213	11	224

Merged error: 0.0b

Counts

224 → 11

regimes141.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample967.0ms

Algorithm

intervals

Results

224.0ms	1778×	body	1280	valid
210.0ms	8182×	body	80	nan
124.0ms	1259×	body	640	valid
108.0ms	4064×	body	80	valid
46.0ms	575×	body	320	valid
16.0ms	324×	body	160	valid

Details

sample33.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite11.0ms

series13.0ms

simplify30.0ms

prune72.0ms

localize7.0ms

rewrite24.0ms

series17.0ms

simplify65.0ms

prune159.0ms

localize12.0ms

rewrite46.0ms

series25.0ms

simplify109.0ms

prune309.0ms

localize13.0ms

rewrite62.0ms

series30.0ms

simplify130.0ms

prune355.0ms

regimes141.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample967.0ms

Profiling