Details

analyze700.0ms (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	61×	body	1024	valid
6.0ms	144×	body	128	valid
5.0ms	31×	body	512	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify316.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5717	24

prune5.0ms (0.1%)

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: 0.4b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series646.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

364.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
102.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
95.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
85.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5715	1997

prune171.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	110	11	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Merged error: 0.1b

Counts

122 → 11

Compiler

Compiled 2630 to 1529 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (cos.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)

series107.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow.f64 (cos.f64 x) 2)
27.0ms	(pow.f64 (sin.f64 x) 2)
27.0ms	(pow.f64 (cos.f64 x) 2)
26.0ms	(pow.f64 (sin.f64 x) 2)

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5233	660

prune124.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

Compiler

Compiled 2413 to 1587 computations (34.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))

rewrite68.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
15×	`difference-of-squares_binary64`
12×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
5×	`distribute-lft-out_binary64`
4×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 96

Calls

4 calls:

48.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series768.0ms (13.9%)

Counts

4 → 12

Calls

4 calls:

542.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
81.0ms	(pow.f64 (tan.f64 x) 2)
73.0ms	(pow.f64 (tan.f64 x) 2)
72.0ms	(pow.f64 (tan.f64 x) 2)

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4989	2346
1	4989	2346

prune172.0ms (3.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Merged error: 0.0b

Counts

119 → 12

Compiler

Compiled 3062 to 2170 computations (29.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (tan.f64 x))
0.2b	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
0.2b	(+.f64 (tan.f64 x) 1)
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
25×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `difference-of-squares_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
7×	`pow1_binary64`
5×	`distribute-lft-out--_binary64`
4×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

22.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
4.0ms	(+.f64 (tan.f64 x) 1)
4.0ms	(-.f64 1 (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)

series551.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

379.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
69.0ms	(pow.f64 (tan.f64 x) 2)
58.0ms	(-.f64 1 (tan.f64 x))
44.0ms	(+.f64 (tan.f64 x) 1)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5072	2081

prune134.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	111	11	122

Merged error: 0.0b

Counts

122 → 11

Compiler

Compiled 2554 to 1653 computations (35.3% saved)

regimes58.0ms (1%)

Compiler: Compiled 554 to 418 computations (24.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	31
1	28	31

end0.0ms (0%)

sample1.3s (22.9%)

Algorithm

1×

intervals

Results

423.0ms	2002×	body	1024	valid
195.0ms	4492×	body	128	valid
141.0ms	1001×	body	512	valid
47.0ms	500×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 310 to 232 computations (25.2% saved)

Details

analyze700.0ms (12.6%)

sample35.0ms (0.6%)

simplify316.0ms (5.7%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite33.0ms (0.6%)

series646.0ms (11.7%)

simplify76.0ms (1.4%)

prune171.0ms (3.1%)

localize12.0ms (0.2%)

rewrite16.0ms (0.3%)

series107.0ms (1.9%)

simplify52.0ms (0.9%)

prune124.0ms (2.2%)

localize9.0ms (0.2%)

rewrite68.0ms (1.2%)

series768.0ms (13.9%)

simplify98.0ms (1.8%)

prune172.0ms (3.1%)

localize10.0ms (0.2%)

rewrite43.0ms (0.8%)

series551.0ms (9.9%)

simplify60.0ms (1.1%)

prune134.0ms (2.4%)

regimes58.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (22.9%)

Profiling