Details

analyze695.0ms (7.5%)

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)

sample37.0ms (0.4%)

Algorithm

1×

intervals

Results

15.0ms	65×	body	1024	valid
6.0ms	130×	body	128	valid
5.0ms	40×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify283.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune4.0ms (0%)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.4%)

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` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series629.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
96.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
94.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
86.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune173.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	13	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 0.0b

Counts

123 → 13

Compiler

Compiled 2714 to 1582 computations (41.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`associate-r_binary64` `add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`distribute-lft-out--_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r_binary64` `associate-/r/_binary64` `associate-l*_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `unpow2_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

25.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
15.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
4.0ms	(+.f64 (tan.f64 x) 1)
3.0ms	(pow.f64 (tan.f64 x) 2)

series828.0ms (9%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
292.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
75.0ms	(pow.f64 (tan.f64 x) 2)
46.0ms	(+.f64 (tan.f64 x) 1)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5268	3347

prune211.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	149	11	160

Merged error: 0.0b

Counts

160 → 11

Compiler

Compiled 3823 to 2502 computations (34.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite77.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64`
72×	`difference-of-squares_binary64`
55×	`log-pow_binary64`
54×	`exp-prod_binary64`
44×	`add-cube-cbrt_binary64`
25×	`distribute-lft-out_binary64`
24×	`unpow-prod-down_binary64`
20×	`unpow2_binary64` `sqr-pow_binary64`
12×	`associate-/l*_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `div-sub_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 184

Calls

4 calls:

24.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
17.0ms	(/.f64 (-.f64 1 (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)

series1.2s (13.5%)

Counts

4 → 12

Calls

4 calls:

767.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
335.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
74.0ms	(pow.f64 (tan.f64 x) 2)
73.0ms	(pow.f64 (tan.f64 x) 2)

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5235	4308

prune279.0ms (3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	196	11	207

Merged error: 0.0b

Counts

207 → 11

Compiler

Compiled 4836 to 3460 computations (28.5% saved)

localize12.0ms (0.1%)

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	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3))
0.4b	(pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3)

rewrite113.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

270×	`*-un-lft-identity_binary64`
206×	`add-sqr-sqrt_binary64`
192×	`times-frac_binary64`
146×	`unpow-prod-down_binary64`
128×	`difference-of-squares_binary64`
114×	`cbrt-prod_binary64`
108×	`cube-prod_binary64`
78×	`add-cube-cbrt_binary64`
48×	`distribute-lft-out_binary64`
36×	`sqr-pow_binary64`
34×	`unpow2_binary64`
16×	`distribute-lft-out--_binary64`
9×	`pow-unpow_binary64` `add-exp-log_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64`
2×	`cube-div_binary64` `rem-cube-cbrt_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `div-exp_binary64`

Counts

4 → 288

Calls

4 calls:

28.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3))
23.0ms	(pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series1.1s (11.9%)

Counts

4 → 12

Calls

4 calls:

604.0ms	(pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3)
348.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 3))
73.0ms	(pow.f64 (tan.f64 x) 2)
72.0ms	(pow.f64 (tan.f64 x) 2)

simplify139.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4959	9256
1	4959	9256

prune507.0ms (5.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	300	11	311

Merged error: 0.0b

Counts

311 → 11

Compiler

Compiled 7117 to 5151 computations (27.6% saved)

regimes412.0ms (4.5%)

Compiler: Compiled 4610 to 3476 computations (24.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	22
1	29	22

end0.0ms (0%)

sample2.1s (22.5%)

Algorithm

1×

intervals

Results

407.0ms	1974×	body	1024	valid
193.0ms	4503×	body	128	valid
137.0ms	1000×	body	512	valid
47.0ms	514×	body	256	valid
3.0ms	9×	body	2048	valid

Compiler

Compiled 1171 to 882 computations (24.7% saved)

Details

analyze695.0ms (7.5%)

sample37.0ms (0.4%)

simplify283.0ms (3.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite36.0ms (0.4%)

series629.0ms (6.8%)

simplify97.0ms (1.1%)

prune173.0ms (1.9%)

localize11.0ms (0.1%)

rewrite63.0ms (0.7%)

series828.0ms (9%)

simplify76.0ms (0.8%)

prune211.0ms (2.3%)

localize12.0ms (0.1%)

rewrite77.0ms (0.8%)

series1.2s (13.5%)

simplify96.0ms (1%)

prune279.0ms (3%)

localize12.0ms (0.1%)

rewrite113.0ms (1.2%)

series1.1s (11.9%)

simplify139.0ms (1.5%)

prune507.0ms (5.5%)

regimes412.0ms (4.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (22.5%)

Profiling