Details

sample552.0ms

Algorithm

intervals

Results

354.0ms	4042×	body	80	nan
56.0ms	155×	body	640	valid
16.0ms	60×	body	320	valid
2.0ms	25×	body	80	valid
2.0ms	12×	body	160	valid
2.0ms	4×	body	1280	valid

simplify25.0ms

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: 4.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))
4.4b	(- (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:

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

series282.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
67.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (33.0ms)

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

prune378.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 0.5b

Counts

89 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
3.4b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite47.0ms

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 (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
13.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series358.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify79.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	634	1071
1	2335	978
2	5001	942

prune494.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	119	9	128

Merged error: 0.2b

Counts

128 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.6b	(- (sqrt (+ z 1.0)) (sqrt z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite43.0ms

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 (+ y 1.0)) (sqrt y)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series628.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
336.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
78.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
76.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify87.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	728	1296
1	2722	1176
2	5001	1134

prune570.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	139	11	150

Merged error: 0.2b

Counts

150 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b	(+ z (- 1.0 z))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

116×	`*-un-lft-identity`
46×	`distribute-lft-out`
44×	`sqrt-prod`
42×	`times-frac`
35×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
12×	`associate-/r*`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
4×	`pow1` `flip3-+` `associate-/r/` `flip-+` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `associate-+r+` `frac-2neg` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
6.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series349.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms	(+ z (- 1.0 z))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify78.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	683	1179
1	2548	1073
2	5002	1031

prune546.0ms

Filtered

139 candidates to 82 candidates (59.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Merged error: 0.1b

Counts

150 → 9

regimes723.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	23
1	50	23
2	50	23

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s	16067×	body	80	nan
244.0ms	647×	body	640	valid
54.0ms	197×	body	320	valid
11.0ms	63×	body	160	valid
9.0ms	93×	body	80	valid
7.0ms	15×	body	1280	valid

Details

sample552.0ms

simplify25.0ms

prune5.0ms

localize22.0ms

rewrite35.0ms

series282.0ms

simplify41.0ms

prune378.0ms

localize29.0ms

rewrite47.0ms

series358.0ms

simplify79.0ms

prune494.0ms

localize31.0ms

rewrite43.0ms

series628.0ms

simplify87.0ms

prune570.0ms

localize30.0ms

rewrite44.0ms

series349.0ms

simplify78.0ms

prune546.0ms

regimes723.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling