Details

analyze2.6s (11.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample408.0ms (1.8%)

Algorithm

1×

intervals

Results

98.0ms	18×	body	5120	invalid
87.0ms	106×	body	1280	valid
59.0ms	29×	body	2560	invalid
47.0ms	27×	body	2560	valid
35.0ms	63×	body	640	valid
20.0ms	28×	body	1280	invalid
15.0ms	6×	body	5120	valid
9.0ms	22×	body	320	valid
5.0ms	9×	body	640	invalid
5.0ms	34×	body	80	invalid
4.0ms	12×	body	320	invalid
3.0ms	22×	body	80	valid
3.0ms	10×	body	160	valid
2.0ms	8×	body	160	invalid

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify39.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5186	32

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 42.3b

Counts

2 → 1

Compiler

Compiled 42 to 34 computations (19% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
0.6b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
19.6b	(/.f64 (pow.f64 t 3) (*.f64 l l))
26.6b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite80.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

228×	`add-exp-log_binary64`
139×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
51×	`div-exp_binary64`
37×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
32×	`pow-exp_binary64`
26×	`cbrt-unprod_binary64`
24×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
23×	`pow-to-exp_binary64` `unpow-prod-down_binary64`
18×	`associate-l_binary64`
12×	`associate-/l*_binary64`
11×	`pow1_binary64`
10×	`cube-prod_binary64` `associate-*l/_binary64`
8×	`cbrt-undiv_binary64`
5×	`sqr-pow_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `insert-posit16` `tan-quot_binary64`
3×	`div-inv_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
2×	`associate-*r/_binary64` `frac-times_binary64`
1×	`associate-/r*_binary64` `unpow2_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 191

Calls

4 calls:

28.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
16.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
13.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
9.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (4.9%)

Counts

4 → 12

Calls

4 calls:

609.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
315.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
127.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
52.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify106.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5164	4347

prune294.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	190	13	203
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	13	204

Merged error: 15.7b

Counts

204 → 13

Compiler

Compiled 5397 to 2773 computations (48.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.9b	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
23.5b	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))

rewrite52.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

163×	`add-exp-log_binary64`
102×	`prod-exp_binary64`
87×	`add-cbrt-cube_binary64`
48×	`cbrt-unprod_binary64`
27×	`div-exp_binary64`
15×	`cbrt-undiv_binary64` `add-sqr-sqrt_binary64`
10×	`pow-to-exp_binary64` `pow1_binary64` `pow-exp_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`*-commutative_binary64`
1×	`associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 128

Calls

4 calls:

21.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
11.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
8.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(pow.f64 (sin.f64 k) 2)

series519.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

285.0ms	(/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (*.f64 l l) (cos.f64 k)))
119.0ms	(.f64 (.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
80.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
34.0ms	(pow.f64 (sin.f64 k) 2)

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5276	2647

prune182.0ms (0.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	132	8	140
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	133	20	153

Merged error: 12.9b

Counts

153 → 20

Compiler

Compiled 3637 to 1681 computations (53.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.2b	(.f64 (/.f64 (.f64 k k) (.f64 l l)) (.f64 t (pow.f64 (sin.f64 k) 2)))
19.5b	(/.f64 (.f64 k k) (.f64 l l))

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
59×	`add-cbrt-cube_binary64`
58×	`prod-exp_binary64`
28×	`cbrt-unprod_binary64`
20×	`div-exp_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`cbrt-undiv_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64`
8×	`associate-l_binary64`
7×	`pow-to-exp_binary64` `pow1_binary64` `unpow-prod-down_binary64` `pow-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64`
2×	`times-frac_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `associate-*l/_binary64`

Counts

4 → 116

Calls

4 calls:

15.0ms	(.f64 (/.f64 (.f64 k k) (.f64 l l)) (.f64 t (pow.f64 (sin.f64 k) 2)))
8.0ms	(/.f64 (.f64 k k) (.f64 l l))
7.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(pow.f64 (sin.f64 k) 2)

series351.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(.f64 (/.f64 (.f64 k k) (.f64 l l)) (.f64 t (pow.f64 (sin.f64 k) 2)))
82.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
41.0ms	(/.f64 (.f64 k k) (.f64 l l))
28.0ms	(pow.f64 (sin.f64 k) 2)

simplify97.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5011	1790

prune163.0ms (0.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	7	12	19
Picked	1	0	1
Done	0	0	0
Total	131	17	148

Merged error: 2.0b

Counts

148 → 17

Compiler

Compiled 3165 to 1445 computations (54.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(pow.f64 (sin.f64 k) 2)
0.9b	(.f64 (/.f64 k l) (.f64 (/.f64 k l) (*.f64 t (pow.f64 (sin.f64 k) 2))))
1.4b	(*.f64 t (pow.f64 (sin.f64 k) 2))
5.4b	(.f64 (/.f64 k l) (.f64 t (pow.f64 (sin.f64 k) 2)))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`add-exp-log_binary64`
63×	`prod-exp_binary64`
59×	`add-cbrt-cube_binary64`
29×	`cbrt-unprod_binary64` `associate-l_binary64` `add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`div-exp_binary64`
18×	`times-frac_binary64`
12×	`pow1_binary64`
11×	`cbrt-undiv_binary64`
10×	`associate-r_binary64`
8×	`pow-to-exp_binary64` `pow-exp_binary64`
7×	`unpow-prod-down_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16` `associate-*l/_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `*-commutative_binary64`
2×	`div-inv_binary64`
1×	`associate-*r/_binary64` `pow-pow_binary64` `frac-times_binary64`

Counts

4 → 140

Calls

4 calls:

17.0ms	(.f64 (/.f64 k l) (.f64 (/.f64 k l) (*.f64 t (pow.f64 (sin.f64 k) 2))))
12.0ms	(.f64 (/.f64 k l) (.f64 t (pow.f64 (sin.f64 k) 2)))
8.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms	(pow.f64 (sin.f64 k) 2)

series529.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(.f64 (/.f64 k l) (.f64 (/.f64 k l) (*.f64 t (pow.f64 (sin.f64 k) 2))))
206.0ms	(.f64 (/.f64 k l) (.f64 t (pow.f64 (sin.f64 k) 2)))
82.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
35.0ms	(pow.f64 (sin.f64 k) 2)

simplify137.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5034	2441

prune183.0ms (0.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	141	11	152
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	149	20	169

Merged error: 0.4b

Counts

169 → 20

Compiler

Compiled 3427 to 1532 computations (55.3% saved)

regimes194.0ms (0.9%)

Compiler: Compiled 2104 to 1529 computations (27.3% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	31
1	18	31

end0.0ms (0%)

sample15.2s (67.6%)

Algorithm

1×

intervals

Results

3.4s	723×	body	5120	invalid
3.2s	1272×	body	2560	invalid
2.8s	3283×	body	1280	valid
1.4s	998×	body	2560	valid
1.1s	1944×	body	640	valid
686.0ms	208×	body	5120	valid
597.0ms	699×	body	1280	invalid
275.0ms	525×	body	640	invalid
254.0ms	613×	body	320	valid
130.0ms	896×	body	80	invalid
129.0ms	344×	body	320	invalid
102.0ms	686×	body	80	valid
74.0ms	268×	body	160	valid
48.0ms	186×	body	160	invalid

Compiler

Compiled 546 to 395 computations (27.7% saved)

Details

analyze2.6s (11.6%)

sample408.0ms (1.8%)

simplify39.0ms (0.2%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite80.0ms (0.4%)

series1.1s (4.9%)

simplify106.0ms (0.5%)

prune294.0ms (1.3%)

localize16.0ms (0.1%)

rewrite52.0ms (0.2%)

series519.0ms (2.3%)

simplify83.0ms (0.4%)

prune182.0ms (0.8%)

localize17.0ms (0.1%)

rewrite41.0ms (0.2%)

series351.0ms (1.6%)

simplify97.0ms (0.4%)

prune163.0ms (0.7%)

localize16.0ms (0.1%)

rewrite49.0ms (0.2%)

series529.0ms (2.4%)

simplify137.0ms (0.6%)

prune183.0ms (0.8%)

regimes194.0ms (0.9%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample15.2s (67.6%)

Profiling