Details

sample544.0ms

Algorithm

intervals

Results

346.0ms	3730×	body	80	nan
63.0ms	171×	body	640	valid
13.0ms	48×	body	320	valid
3.0ms	16×	body	160	valid
2.0ms	18×	body	80	valid
1.0ms	3×	body	1280	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite35.0ms

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:

9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune364.0ms

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: 1.0b

Counts

89 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.4b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

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

series362.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify80.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	634	1071
1	2333	978
2	5002	942

prune512.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Merged error: 0.6b

Counts

127 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.4b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite45.0ms

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:

12.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series428.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify95.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (75.0ms)

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

prune585.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Merged error: 0.6b

Counts

149 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.3b	(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))))
2.4b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

670×	`sqrt-prod`
537×	`*-un-lft-identity`
406×	`times-frac`
369×	`add-sqr-sqrt`
194×	`distribute-lft-out`
171×	`add-cube-cbrt`
126×	`swap-sqr`
60×	`associate-r` `associate-l`
25×	`unswap-sqr`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`associate-/r/`
8×	`sqrt-div` `add-log-exp` `difference-of-squares`
6×	`associate-/r*` `distribute-lft-out--`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`sqrt-undiv` `prod-exp` `cbrt-unprod`
3×	`associate-/l*`
2×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 376

Calls

4 calls:

11.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
72.0ms	(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series457.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
174.0ms	(* (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))) (/ (sqrt 1.0) (sqrt (+ (sqrt (+ t 1.0)) (sqrt t)))))
65.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
75.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify96.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1292	7808
1	5001	6601

prune1.0s

Filtered

388 candidates to 143 candidates (36.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	386	2	388
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	387	9	396

Merged error: 0.5b

Counts

396 → 9

regimes715.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	31
1	38	31

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	17135×	body	80	nan
307.0ms	815×	body	640	valid
59.0ms	218×	body	320	valid
11.0ms	63×	body	160	valid
8.0ms	17×	body	1280	valid
8.0ms	82×	body	80	valid

Details

sample544.0ms

simplify30.0ms

prune5.0ms

localize25.0ms

rewrite35.0ms

series282.0ms

simplify46.0ms

prune364.0ms

localize23.0ms

rewrite43.0ms

series362.0ms

simplify80.0ms

prune512.0ms

localize25.0ms

rewrite45.0ms

series428.0ms

simplify95.0ms

prune585.0ms

localize29.0ms

rewrite142.0ms

series457.0ms

simplify96.0ms

prune1.0s

regimes715.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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