Details

sample567.0ms

Algorithm

intervals

Results

316.0ms	3559×	body	80	nan
62.0ms	168×	body	640	valid
15.0ms	55×	body	320	valid
2.0ms	21×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	8×	body	160	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

prune8.0ms

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: 5.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite32.0ms

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 (+ t 1.0)) (sqrt t))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
7.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series42.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify64.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	864
1	2941	824
2	5001	824

prune779.0ms

Filtered

88 candidates to 60 candidates (31.8%)

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: 4.7b

Counts

89 → 8

localize27.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.2b	(+ z (- 1.0 z))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
24×	`sqrt-prod`
15×	`add-log-exp`
12×	`difference-of-squares`
10×	`distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`associate-+r+` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

7.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
5.0ms	(+ z (- 1.0 z))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
1.0ms	(+ z (- 1.0 z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	601	708
1	2432	673
2	5001	673

prune705.0ms

Filtered

86 candidates to 59 candidates (31.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Merged error: 2.6b

Counts

94 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.7b	(- (sqrt (+ y 1.0)) (sqrt y))
1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`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`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

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

series41.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
12.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify76.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	813	1082
1	3573	1020
2	5002	1003

prune1.0s

Filtered

110 candidates to 72 candidates (34.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	105	5	110
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	106	13	119

Merged error: 2.6b

Counts

119 → 13

localize35.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (+ t 1.0)) (sqrt t))
2.5b	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
9.9b	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
64×	`sqrt-prod`
57×	`associate-l`
53×	`distribute-lft-out`
52×	`times-frac`
48×	`sqrt-div`
47×	`add-sqr-sqrt`
36×	`unpow-prod-down` `cube-prod`
34×	`frac-times`
32×	`frac-add`
27×	`flip3-+` `flip-+`
26×	`add-cube-cbrt` `associate-*r/`
19×	`flip3--` `flip--`
10×	`add-log-exp`
9×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
8×	`difference-of-squares`
6×	`pow1` `distribute-lft-out--`
3×	`sub-neg` `diff-log` `associate-r` `sum-cubes`
2×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `distribute-rgt-in` `distribute-rgt-out--` `distribute-lft-in` `div-exp` `pow-prod-down` `*-commutative` `div-inv`

Counts

4 → 165

Calls

4 calls:

7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
5.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
49.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
13.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
19.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1823	4243
1	5002	4019

prune3.1s

Filtered

177 candidates to 113 candidates (36.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	174	16	190

Merged error: 2.6b

Counts

190 → 16

regimes2.2s

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	28
1	40	28

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.0s	44482×	body	80	nan
737.0ms	1962×	body	640	valid
152.0ms	545×	body	320	valid
30.0ms	160×	body	160	valid
22.0ms	47×	body	1280	valid
20.0ms	204×	body	80	valid

Details

sample567.0ms

simplify25.0ms

prune8.0ms

localize25.0ms

rewrite32.0ms

series42.0ms

simplify64.0ms

prune779.0ms

localize27.0ms

rewrite30.0ms

series33.0ms

simplify55.0ms

prune705.0ms

localize23.0ms

rewrite35.0ms

series41.0ms

simplify76.0ms

prune1.0s

localize35.0ms

rewrite84.0ms

series51.0ms

simplify73.0ms

prune3.1s

regimes2.2s

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.8s

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