Details

analyze1.1s (18.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	216×	body	80	valid
2.0ms	10×	body	1280	valid
2.0ms	11×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	29×	body	80	invalid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4892	13
1	4892	13

prune18.0ms (0.3%)

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: 9.8b

Counts

2 → 2

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
6.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

18.0ms	(* (- y z) (/ (- t x) (- a z)))
8.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

series102.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
38.0ms	(* (- y z) (/ (- t x) (- a z)))
13.0ms	(/ (- t x) (- a z))

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5183	1602

prune209.0ms (3.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	13	130

Merged error: 2.6b

Counts

130 → 13

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.4b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

39.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series167.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
55.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
27.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5314	2524

prune218.0ms (3.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	146	13	159

Merged error: 2.6b

Counts

159 → 13

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
6.2b	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite154.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

332×	`cbrt-div`
137×	`frac-times`
111×	`flip3--` `flip--`
89×	`associate-l`
84×	`add-sqr-sqrt`
82×	`associate-/r/`
78×	`cbrt-prod`
73×	`*-un-lft-identity`
63×	`times-frac`
61×	`associate-r`
60×	`add-exp-log`
45×	`associate-r/` `associate-l/`
38×	`add-cbrt-cube`
35×	`add-cube-cbrt`
28×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
4×	`unswap-sqr`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 231

Calls

4 calls:

118.0ms	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
5.0ms	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series169.0ms (3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
52.0ms	(+ x (* (/ (- y z) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))
29.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

243 → 243

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5070	7455

prune451.0ms (7.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	241	2	243
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	242	14	256

Merged error: 2.4b

Counts

256 → 14

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

2.8b	(* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z)))))
6.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
6.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
6.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite156.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

328×	`cbrt-div`
137×	`frac-times`
109×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
78×	`add-sqr-sqrt`
69×	`associate-*r/`
68×	`cbrt-prod`
67×	`*-un-lft-identity`
63×	`times-frac`
61×	`associate-r`
49×	`add-exp-log`
33×	`add-cube-cbrt`
30×	`add-cbrt-cube`
27×	`associate-*l/`
22×	`prod-exp` `cbrt-unprod`
17×	`distribute-lft-out--` `difference-of-squares`
13×	`cbrt-undiv` `div-exp`
10×	`add-log-exp`
6×	`pow1`
4×	`unswap-sqr`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 219

Calls

4 calls:

115.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z)))))
6.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
5.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
5.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series219.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z)))))
56.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
53.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))
51.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (* (cbrt (- a z)) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4995	7598
1	4995	7598

prune710.0ms (12.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	231	14	245

Merged error: 2.4b

Counts

245 → 14

regimes753.0ms (13.2%)

Accuracy

Total 6.7b remaining (66.2%)

Threshold costs 0b (0%)

bsearch45.0ms (0.8%)

Steps

Iters	Range		Point
7	1.3013603304751068e+130	3.192561180074034e+132	1.5608717846500168e+132
8	-5.218678212404121e+211	-2.728273253059235e+208	-4.412580790819901e+208

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	46
1	66	46

end0.0ms (0%)

sample811.0ms (14.2%)

Algorithm

1×

intervals

Results

262.0ms	6575×	body	80	valid
70.0ms	463×	body	640	valid
51.0ms	413×	body	320	valid
50.0ms	1245×	body	80	invalid
49.0ms	257×	body	1280	valid
20.0ms	273×	body	160	valid
4.0ms	19×	body	2560	valid

Details

analyze1.1s (18.6%)

sample30.0ms (0.5%)

simplify56.0ms (1%)

prune18.0ms (0.3%)

localize9.0ms (0.2%)

rewrite35.0ms (0.6%)

series102.0ms (1.8%)

simplify48.0ms (0.8%)

prune209.0ms (3.7%)

localize14.0ms (0.2%)

rewrite56.0ms (1%)

series167.0ms (2.9%)

simplify42.0ms (0.7%)

prune218.0ms (3.8%)

localize18.0ms (0.3%)

rewrite154.0ms (2.7%)

series169.0ms (3%)

simplify53.0ms (0.9%)

prune451.0ms (7.9%)

localize31.0ms (0.5%)

rewrite156.0ms (2.7%)

series219.0ms (3.8%)

simplify70.0ms (1.2%)

prune710.0ms (12.4%)

regimes753.0ms (13.2%)

bsearch45.0ms (0.8%)

simplify2.0ms (0%)

end0.0ms (0%)

sample811.0ms (14.2%)

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