Details

analyze880.0ms (25.8%)

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
0%	99.8%	0.2%	10
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
2.0ms	68×	body	80	invalid

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	718	9
1	718	9

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: 6.2b

Counts

2 → 1

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(* y (- z t))
0.0b	(+ x (/ (* y (- z t)) a))
7.1b	(/ (* y (- z t)) a)

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

11.0ms	(/ (* y (- z t)) a)
6.0ms	(* y (- z t))
4.0ms	(+ x (/ (* y (- z t)) a))

series33.0ms (1%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ x (/ (* y (- z t)) a))
11.0ms	(/ (* y (- z t)) a)
7.0ms	(* y (- z t))

simplify37.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5072	574

prune109.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Merged error: 0.0b

Counts

69 → 8

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.5b	(/ (* (/ y (* (cbrt a) (cbrt a))) (- z t)) (cbrt a))
4.8b	(* (/ y (* (cbrt a) (cbrt a))) (- z t))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log`
19×	`add-sqr-sqrt` `add-cbrt-cube`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`cbrt-prod`
10×	`times-frac`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-l`
6×	`pow1` `associate-/r*`
5×	`associate-r` `associate-/l/`
4×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
2×	`sub-neg` `pow1/3` `associate-*l/` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 94

Calls

4 calls:

12.0ms	(/ (* (/ y (* (cbrt a) (cbrt a))) (- z t)) (cbrt a))
11.0ms	(* (/ y (* (cbrt a) (cbrt a))) (- z t))
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series122.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ y (* (cbrt a) (cbrt a))) (- z t))
23.0ms	(cbrt a)
21.0ms	(cbrt a)
18.0ms	(/ (* (/ y (* (cbrt a) (cbrt a))) (- z t)) (cbrt a))

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4938	987
1	4938	987

prune159.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	107	7	114

Merged error: 0.0b

Counts

114 → 7

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
1.5b	(/ (* (/ (* (cbrt y) (cbrt y)) (cbrt a)) (* (- z t) (/ (cbrt y) (cbrt a)))) (cbrt a))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log`
23×	`add-cbrt-cube`
19×	`cbrt-undiv` `div-exp`
18×	`prod-exp` `cbrt-unprod`
15×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate-/l/`
9×	`frac-times`
7×	`associate-*r/`
6×	`times-frac` `associate-/r*`
5×	`associate-*l/`
4×	`pow1` `flip3--` `flip--` `add-log-exp`
3×	`pow1/3`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

18.0ms	(/ (* (/ (* (cbrt y) (cbrt y)) (cbrt a)) (* (- z t) (/ (cbrt y) (cbrt a)))) (cbrt a))
1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series77.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt a)
20.0ms	(cbrt a)
20.0ms	(cbrt a)
15.0ms	(/ (* (/ (* (cbrt y) (cbrt y)) (cbrt a)) (* (- z t) (/ (cbrt y) (cbrt a)))) (cbrt a))

simplify50.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4988	855
1	4988	855

prune123.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	99	7	106

Merged error: 0.0b

Counts

106 → 7

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ y (/ a (- z t))))
0.0b	(/ a (- z t))
6.6b	(/ y (/ a (- z t)))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac`
105×	`*-un-lft-identity`
103×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
5×	`flip3--` `flip--` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 151

Calls

3 calls:

18.0ms	(+ x (/ y (/ a (- z t))))
8.0ms	(/ y (/ a (- z t)))
5.0ms	(/ a (- z t))

series37.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ x (/ y (/ a (- z t))))
12.0ms	(/ y (/ a (- z t)))
7.0ms	(/ a (- z t))

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4997	2025
1	4997	2025

prune160.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	2	2	4
Picked	0	1	1
Done	2	0	2
Total	162	5	167

Merged error: 0.0b

Counts

167 → 5

regimes576.0ms (16.9%)

Accuracy

Total 0.8b remaining (97.2%)

Threshold costs 0.8b (97.2%)

bsearch39.0ms (1.2%)

Steps

Iters	Range		Point
4	1.0963315291225472e-21	1.6667713538188546e-21	1.506335153123018e-21
10	-6.445191084779187e-38	-9.875119927324217e-48	-7.687636000289944e-43

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms (0%)

sample664.0ms (19.5%)

Algorithm

1×

intervals

Results

268.0ms	8000×	body	80	valid
87.0ms	2389×	body	80	invalid

Details

analyze880.0ms (25.8%)

sample25.0ms (0.7%)

simplify37.0ms (1.1%)

prune7.0ms (0.2%)

localize7.0ms (0.2%)

rewrite22.0ms (0.7%)

series33.0ms (1%)

simplify37.0ms (1.1%)

prune109.0ms (3.2%)

localize11.0ms (0.3%)

rewrite28.0ms (0.8%)

series122.0ms (3.6%)

simplify71.0ms (2.1%)

prune159.0ms (4.7%)

localize15.0ms (0.4%)

rewrite24.0ms (0.7%)

series77.0ms (2.3%)

simplify50.0ms (1.5%)

prune123.0ms (3.6%)

localize7.0ms (0.2%)

rewrite37.0ms (1.1%)

series37.0ms (1.1%)

simplify48.0ms (1.4%)

prune160.0ms (4.7%)

regimes576.0ms (16.9%)

bsearch39.0ms (1.2%)

simplify1.0ms (0%)

end0.0ms (0%)

sample664.0ms (19.5%)

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