Details

sample685.0ms

Algorithm

intervals

Results

398.0ms	3810×	body	80	nan
73.0ms	175×	body	640	valid
16.0ms	45×	body	320	valid
3.0ms	17×	body	160	valid
2.0ms	16×	body	80	valid
2.0ms	3×	body	1280	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5005	31

prune20.0ms

Filtered

1 candidates to 1 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: 4.7b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite38.0ms

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))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series44.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
13.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify25.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5183	1378

prune263.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	5	90

Merged error: 0.3b

Counts

90 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite45.0ms

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:

13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
13.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify37.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5503	1792

prune333.0ms

Filtered

78 candidates to 119 candidates (-52.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Merged error: 0.2b

Counts

124 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite48.0ms

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:

11.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4882	2092
1	4882	2092

prune399.0ms

Filtered

90 candidates to 141 candidates (-56.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 0.1b

Counts

148 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
60×	`times-frac` `sqrt-prod` `distribute-lft-out`
46×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `difference-of-squares`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `distribute-lft-out--`
2×	`associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 151

Calls

4 calls:

11.0ms	(/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))
11.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 t)) (sqrt t)))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series41.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5777	2414

prune411.0ms

Filtered

101 candidates to 163 candidates (-61.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	163	8	171

Merged error: 0.0b

Counts

171 → 8

regimes1.3s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	39
1	42	39

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	15471×	body	80	nan
294.0ms	694×	body	640	valid
62.0ms	195×	body	320	valid
14.0ms	69×	body	160	valid
10.0ms	19×	body	1280	valid
8.0ms	76×	body	80	valid

Details

sample685.0ms

simplify31.0ms

prune20.0ms

localize24.0ms

rewrite38.0ms

series44.0ms

simplify25.0ms

prune263.0ms

localize27.0ms

rewrite45.0ms

series45.0ms

simplify37.0ms

prune333.0ms

localize32.0ms

rewrite48.0ms

series45.0ms

simplify68.0ms

prune399.0ms

localize29.0ms

rewrite53.0ms

series41.0ms

simplify61.0ms

prune411.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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