Details

sample626.0ms

Algorithm

intervals

Results

412.0ms	3925×	body	80	nan
71.0ms	168×	body	640	valid
18.0ms	55×	body	320	valid
2.0ms	4×	body	1280	valid
2.0ms	10×	body	160	valid
2.0ms	19×	body	80	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

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: 5.6b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))
3.3b	(- (sqrt (+ t 1.0)) (sqrt t))
3.4b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series272.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune363.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 0.5b

Counts

89 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))
3.3b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
44×	`sqrt-prod`
40×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `associate-/l*`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 107

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series341.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
65.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify73.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	627	1069
1	2306	979
2	5002	943

prune491.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	118	9	127

Merged error: 0.3b

Counts

127 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series420.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
136.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify79.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	721	1294
1	2693	1177
2	5001	1135

prune572.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	141	9	150

Merged error: 0.3b

Counts

150 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.3b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
12.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series420.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
136.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify79.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	721	1294
1	2695	1177
2	5001	1135

prune544.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	140	10	150

Merged error: 0.3b

Counts

150 → 10

regimes892.0ms

bsearch373.0ms

Steps

Iters	Range		Point
9	5.52153243089643e+58	2.1038718490204522e+64	7.59843173084999e+62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	52
1	63	52
2	63	52

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	18642×	body	80	nan
348.0ms	803×	body	640	valid
89.0ms	268×	body	320	valid
15.0ms	69×	body	160	valid
11.0ms	94×	body	80	valid
8.0ms	15×	body	1280	valid

Details

sample626.0ms

simplify26.0ms

prune5.0ms

localize24.0ms

rewrite34.0ms

series272.0ms

simplify43.0ms

prune363.0ms

localize27.0ms

rewrite43.0ms

series341.0ms

simplify73.0ms

prune491.0ms

localize28.0ms

rewrite47.0ms

series420.0ms

simplify79.0ms

prune572.0ms

localize28.0ms

rewrite47.0ms

series420.0ms

simplify79.0ms

prune544.0ms

regimes892.0ms

bsearch373.0ms

simplify2.0ms

end0.0ms

sample3.0s

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