Details

analyze493.0ms (8.2%)

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)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	68×	body	1024	valid
9.0ms	135×	body	128	valid
3.0ms	27×	body	512	valid
2.0ms	26×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify199.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune2.0ms (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

Error

0.4b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize7.0ms (0.1%)

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))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_782`
27×	`*-un-lft-identity_binary64_760`
22×	`add-cube-cbrt_binary64_795`
18×	`pow1_binary64_821`
15×	`times-frac_binary64_766`
10×	`add-exp-log_binary64_798` `difference-of-squares_binary64_729` `add-cbrt-cube_binary64_796`
8×	`tan-quot_binary64_919`
6×	`add-log-exp_binary64_799` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
5×	`associate-/l*_binary64_705`
3×	`associate-/r*_binary64_704`
2×	`pow2_binary64_841` `unswap-sqr_binary64_728` `associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow-sqr_binary64_733` `pow-plus_binary64_823` `frac-times_binary64_770` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 110

Calls

4 calls:

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

series338.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
48.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
42.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune170.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	12	123

Error

0.0b

Counts

123 → 12

Compiler

Compiled 2709 to 1578 computations (41.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_760` `add-sqr-sqrt_binary64_782`
13×	`add-cube-cbrt_binary64_795` `pow1_binary64_821`
9×	`cancel-sign-sub-inv_binary64_726` `associate-r_binary64_700`
8×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
7×	`associate-l_binary64_701`
5×	`frac-times_binary64_770`
4×	`flip3-+_binary64_763` `distribute-lft-in_binary64_709` `difference-of-squares_binary64_729` `distribute-rgt-in_binary64_710` `flip-+_binary64_734` `tan-quot_binary64_919` `flip--_binary64_735` `flip3--_binary64_764`
3×	`associate-l/_binary64_703` `swap-sqr_binary64_727` `associate-r/_binary64_702` `sub-neg_binary64_753`
2×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `diff-log_binary64_852` `pow-sqr_binary64_733` `pow-plus_binary64_823` `+-commutative_binary64_690` `sum-log_binary64_851` `pow-prod-up_binary64_830`

Counts

4 → 95

Calls

4 calls:

12.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(+.f64 (tan.f64 x) 1)
4.0ms	(-.f64 1 (tan.f64 x))

series165.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
26.0ms	(-.f64 1 (tan.f64 x))
26.0ms	(+.f64 (tan.f64 x) 1)

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5281	1370

prune124.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Error

0.0b

Counts

119 → 12

Compiler

Compiled 2582 to 1429 computations (44.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
17×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-log-exp_binary64_799` `associate-r_binary64_700` `associate-l_binary64_701` `tan-quot_binary64_919` `times-frac_binary64_766`
3×	`associate-l/_binary64_703` `prod-exp_binary64_809` `associate-/r_binary64_704` `swap-sqr_binary64_727` `cbrt-unprod_binary64_793`
2×	`unswap-sqr_binary64_728` `cbrt-undiv_binary64_794` `div-inv_binary64_757` `difference-of-squares_binary64_729` `div-exp_binary64_811` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `diff-log_binary64_852` `frac-2neg_binary64_771` `associate-/l/_binary64_707` `pow-sqr_binary64_733` `pow-plus_binary64_823` `associate-/l_binary64_705` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-up_binary64_830` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 90

Calls

4 calls:

6.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series236.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
73.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
44.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
43.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify95.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4930	1378
1	4930	1378

prune109.0ms (1.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	102	12	114

Error

0.0b

Counts

114 → 12

Compiler

Compiled 2489 to 1019 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite71.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

317×	`*-un-lft-identity_binary64_760`
264×	`times-frac_binary64_766`
179×	`add-sqr-sqrt_binary64_782`
104×	`add-cube-cbrt_binary64_795`
69×	`distribute-lft-out_binary64_711`
50×	`difference-of-squares_binary64_729`
36×	`associate-/r*_binary64_704`
25×	`distribute-lft-out--_binary64_712`
13×	`associate-/r/_binary64_706`
12×	`add-exp-log_binary64_798`
11×	`add-cbrt-cube_binary64_796`
8×	`associate-/l*_binary64_705`
7×	`div-inv_binary64_757`
6×	`add-log-exp_binary64_799` `flip--_binary64_735` `flip3--_binary64_764`
5×	`pow1_binary64_821`
4×	`cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `div-exp_binary64_811`
3×	`flip3-+_binary64_763` `flip-+_binary64_734` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`unpow2_binary64_825` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `sum-log_binary64_851` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 251

Calls

4 calls:

23.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
11.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(+.f64 1 (tan.f64 x))

series419.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

222.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
128.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
41.0ms	(pow.f64 (tan.f64 x) 2)
27.0ms	(+.f64 1 (tan.f64 x))

simplify142.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4962	9358
1	4962	9358

prune414.0ms (6.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	9	10
Picked	0	1	1
Done	1	0	1
Total	263	12	275

Error

0.0b

Counts

275 → 12

Compiler

Compiled 7395 to 4860 computations (34.3% saved)

regimes463.0ms (7.7%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Compiler

Compiled 5582 to 4096 computations (26.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample2.2s (37%)

Algorithm

1×

intervals

Results

332.0ms	1946×	body	1024	valid
183.0ms	4504×	body	128	valid
124.0ms	1025×	body	512	valid
47.0ms	520×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 1415 to 1035 computations (26.9% saved)

Details

analyze493.0ms (8.2%)

sample32.0ms (0.5%)

simplify199.0ms (3.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite35.0ms (0.6%)

series338.0ms (5.6%)

simplify103.0ms (1.7%)

prune170.0ms (2.8%)

localize9.0ms (0.2%)

rewrite33.0ms (0.5%)

series165.0ms (2.7%)

simplify82.0ms (1.4%)

prune124.0ms (2.1%)

localize12.0ms (0.2%)

rewrite29.0ms (0.5%)

series236.0ms (3.9%)

simplify95.0ms (1.6%)

prune109.0ms (1.8%)

localize10.0ms (0.2%)

rewrite71.0ms (1.2%)

series419.0ms (6.9%)

simplify142.0ms (2.4%)

prune414.0ms (6.9%)

regimes463.0ms (7.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (37%)

Profiling