Details

analyze931.0ms (22.7%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
26.2%	73.6%	0.2%	14

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	24×	body	80	invalid

simplify192.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (191.0ms)

Iter	Nodes	Cost
0	5600	11

prune16.0ms (0.4%)

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: 0.0b

Counts

2 → 2

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
1.2b	(* y (/ (- z t) (- a t)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `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 → 113

Calls

3 calls:

13.0ms	(* y (/ (- z t) (- a t)))
7.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* y (/ (- z t) (- a t))))

series57.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ x (* y (/ (- z t) (- a t))))
16.0ms	(* y (/ (- z t) (- a t)))
9.0ms	(/ (- z t) (- a t))

simplify43.0ms (1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4984	1366
1	4984	1366

prune166.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Merged error: 0b

Counts

124 → 6

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
6.6b	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
50×	`times-frac`
46×	`associate-r`
42×	`cbrt-prod`
28×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`cbrt-div`
18×	`add-cbrt-cube`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`pow1/3` `associate-r/` `associate-l/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 136

Calls

4 calls:

32.0ms	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))
5.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))

series109.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(cbrt (- a t))
27.0ms	(* (/ y (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))
27.0ms	(cbrt (- a t))
26.0ms	(cbrt (- a t))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4947	2200
1	4947	2200

prune181.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Merged error: 0b

Counts

154 → 6

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
3.0b	(cbrt (/ (- z t) (- a t)))
3.0b	(cbrt (/ (- z t) (- a t)))
3.0b	(cbrt (/ (- z t) (- a t)))

rewrite77.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

333×	`*-un-lft-identity`
277×	`cbrt-prod`
273×	`add-sqr-sqrt`
229×	`times-frac`
106×	`distribute-lft-out--`
93×	`add-cube-cbrt`
78×	`difference-of-squares`
58×	`swap-sqr`
34×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3--` `flip--` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 276

Calls

4 calls:

33.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
7.0ms	(cbrt (/ (- z t) (- a t)))
7.0ms	(cbrt (/ (- z t) (- a t)))
7.0ms	(cbrt (/ (- z t) (- a t)))

series267.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (cbrt (/ (- z t) (- a t))) (cbrt (/ (- z t) (- a t))))
63.0ms	(cbrt (/ (- z t) (- a t)))
62.0ms	(cbrt (/ (- z t) (- a t)))
60.0ms	(cbrt (/ (- z t) (- a t)))

simplify118.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

288 → 288

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5428	5460

prune354.0ms (8.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	288	6	294

Merged error: 0b

Counts

294 → 6

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b	(* y (/ (- z t) (- a t)))
5.0b	(cbrt (* y (/ (- z t) (- a t))))
5.0b	(cbrt (* y (/ (- z t) (- a t))))
5.0b	(cbrt (* y (/ (- z t) (- a t))))

rewrite40.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
31×	`associate-r`
26×	`times-frac`
16×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`associate-*r/` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-l`
2×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`

Counts

4 → 80

Calls

4 calls:

13.0ms	(* y (/ (- z t) (- a t)))
8.0ms	(cbrt (* y (/ (- z t) (- a t))))
8.0ms	(cbrt (* y (/ (- z t) (- a t))))
8.0ms	(cbrt (* y (/ (- z t) (- a t))))

series186.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (* y (/ (- z t) (- a t))))
56.0ms	(cbrt (* y (/ (- z t) (- a t))))
55.0ms	(cbrt (* y (/ (- z t) (- a t))))
17.0ms	(* y (/ (- z t) (- a t)))

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5071	935

prune110.0ms (2.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	92	6	98

Merged error: 0b

Counts

98 → 6

regimes367.0ms (9%)

Accuracy

Total 1.2b remaining (97.9%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	11
1	24	11

end0.0ms (0%)

sample634.0ms (15.5%)

Algorithm

1×

intervals

Results

316.0ms	7997×	body	80	valid
28.0ms	763×	body	80	invalid
0.0ms	1×	body	1280	valid
0.0ms	2×	body	160	valid

Details

analyze931.0ms (22.7%)

sample24.0ms (0.6%)

simplify192.0ms (4.7%)

prune16.0ms (0.4%)

localize8.0ms (0.2%)

rewrite28.0ms (0.7%)

series57.0ms (1.4%)

simplify43.0ms (1%)

prune166.0ms (4%)

localize13.0ms (0.3%)

rewrite49.0ms (1.2%)

series109.0ms (2.7%)

simplify62.0ms (1.5%)

prune181.0ms (4.4%)

localize16.0ms (0.4%)

rewrite77.0ms (1.9%)

series267.0ms (6.5%)

simplify118.0ms (2.9%)

prune354.0ms (8.6%)

localize15.0ms (0.4%)

rewrite40.0ms (1%)

series186.0ms (4.5%)

simplify37.0ms (0.9%)

prune110.0ms (2.7%)

regimes367.0ms (9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample634.0ms (15.5%)

Profiling