Details

analyze1.0s (21.6%)

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%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	206×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	36×	body	80	invalid
1.0ms	12×	body	320	valid
1.0ms	12×	body	160	valid

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

prune7.0ms (0.2%)

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: 15.7b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
4.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.9b	(* (- y z) (/ (- t x) (- a z)))

rewrite36.0ms (0.7%)

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:

16.0ms	(* (- y z) (/ (- t x) (- a z)))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
7.0ms	(/ (- t x) (- a z))

series101.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

53.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
35.0ms	(* (- y z) (/ (- t x) (- a z)))
13.0ms	(/ (- t x) (- a z))

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5183	1602

prune195.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 3.2b

Counts

129 → 10

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.7b	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
9.8b	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log`
14×	`add-sqr-sqrt` `add-cbrt-cube`
13×	`*-un-lft-identity`
10×	`cbrt-prod`
9×	`pow1` `frac-times` `prod-exp` `cbrt-unprod`
7×	`add-cube-cbrt`
6×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`associate-l` `associate-*l/`
4×	`cbrt-undiv` `cbrt-div` `div-exp`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

26.0ms	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
4.0ms	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series227.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))))
54.0ms	(+ x (* (* (- y z) (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))
27.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5032	1489

prune222.0ms (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	90	11	101

Merged error: 3.2b

Counts

101 → 11

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.6b	(* (cbrt (- a z)) (cbrt (- a z)))
2.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite61.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(cbrt (- a z))

series167.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ (- 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)))))
31.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
26.0ms	(cbrt (- a z))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5636	2900

prune279.0ms (5.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	187	11	198

Merged error: 3.2b

Counts

198 → 11

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
5.9b	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
5.9b	(* (- y z) (/ 1 (/ (- a z) (- t x))))

rewrite78.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 344

Calls

4 calls:

35.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))
11.0ms	(/ 1 (/ (- a z) (- t x)))
8.0ms	(/ (- a z) (- t x))
4.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))

series160.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (- y z) (/ 1 (/ (- a z) (- t x))))
54.0ms	(+ x (* (- y z) (/ 1 (/ (- a z) (- t x)))))
31.0ms	(/ 1 (/ (- a z) (- t x)))
13.0ms	(/ (- a z) (- t x))

simplify77.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5155	4965

prune415.0ms (8.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	353	3	356
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	356	11	367

Merged error: 3.2b

Counts

367 → 11

regimes562.0ms (11.7%)

Accuracy

Total 6.5b remaining (64.3%)

Threshold costs 0b (0%)

bsearch42.0ms (0.9%)

Steps

Iters	Range		Point
7	1.3013603304751068e+130	3.192561180074034e+132	1.9136028607171334e+132
6	-1.8493631218427484e+209	-2.728273253059235e+208	-3.491633338612442e+208

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	55
1	69	55

end0.0ms (0%)

sample855.0ms (17.8%)

Algorithm

1×

intervals

Results

274.0ms	6549×	body	80	valid
69.0ms	466×	body	640	valid
55.0ms	1292×	body	80	invalid
52.0ms	440×	body	320	valid
51.0ms	279×	body	1280	valid
31.0ms	254×	body	160	valid
3.0ms	12×	body	2560	valid

Details

analyze1.0s (21.6%)

sample30.0ms (0.6%)

simplify64.0ms (1.3%)

prune7.0ms (0.2%)

localize9.0ms (0.2%)

rewrite36.0ms (0.7%)

series101.0ms (2.1%)

simplify41.0ms (0.8%)

prune195.0ms (4%)

localize15.0ms (0.3%)

rewrite38.0ms (0.8%)

series227.0ms (4.7%)

simplify28.0ms (0.6%)

prune222.0ms (4.6%)

localize13.0ms (0.3%)

rewrite61.0ms (1.3%)

series167.0ms (3.5%)

simplify44.0ms (0.9%)

prune279.0ms (5.8%)

localize10.0ms (0.2%)

rewrite78.0ms (1.6%)

series160.0ms (3.3%)

simplify77.0ms (1.6%)

prune415.0ms (8.6%)

regimes562.0ms (11.7%)

bsearch42.0ms (0.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample855.0ms (17.8%)

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