Details

sample429.0ms

Algorithm

intervals

Results

246.0ms	3946×	body	80	nan
47.0ms	178×	body	640	valid
9.0ms	44×	body	320	valid
5.0ms	7×	body	1280	valid
1.0ms	10×	body	160	valid
1.0ms	17×	body	80	valid

simplify37.0ms

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 (100.0%)

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: 6.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
3.4b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite33.0ms

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

series310.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
77.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
77.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
79.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	463	702
1	1456	635
2	5001	620

prune334.0ms

Filtered

88 candidates to 56 candidates (36.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	81	7	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	7	89

Merged error: 0.8b

Counts

89 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite42.0ms

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

series387.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
77.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
78.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
80.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify72.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	625	1073
1	2296	978
2	5001	942

prune457.0ms

Filtered

119 candidates to 71 candidates (40.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	7	119
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	118	8	126

Merged error: 0.3b

Counts

126 → 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)))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))
1.9b	(- (sqrt (+ y 1.0)) (sqrt y))

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:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series469.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
156.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
79.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
80.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify83.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	712	1296
1	2657	1177
2	5001	1135

prune571.0ms

Filtered

141 candidates to 83 candidates (41.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Merged error: 0.3b

Counts

149 → 9

localize28.0ms

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)))
1.5b	(+ y (- 1.0 y))
1.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite43.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
15.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
6.0ms	(+ y (- 1.0 y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series392.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
158.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(+ y (- 1.0 y))
82.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify87.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	674	1181
1	2534	1073
2	5002	1005

prune549.0ms

Filtered

139 candidates to 83 candidates (40.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 0.1b

Counts

148 → 9

regimes616.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	17402×	body	80	nan
210.0ms	770×	body	640	valid
46.0ms	238×	body	320	valid
8.0ms	24×	body	1280	valid
7.0ms	52×	body	160	valid
5.0ms	82×	body	80	valid