Details

analyze514.0ms (8.4%)

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)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	75×	body	1024	valid
6.0ms	137×	body	128	valid
4.0ms	28×	body	512	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify205.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

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

0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize8.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite30.0ms (0.5%)

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

8 calls:

7.0ms	(/.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)))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series384.0ms (6.3%)

Counts

4 → 18

Calls

4 calls:

203.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
65.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
62.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
54.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Compiler

Compiled 540 to 432 computations (20% saved)

simplify105.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4908	2014
1	4908	2014

prune306.0ms (5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	115	13	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Error

0.0b

Counts

129 → 13

Compiler

Compiled 2782 to 1619 computations (41.8% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite30.0ms (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

8 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))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series278.0ms (4.6%)

Counts

4 → 17

Calls

4 calls:

95.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
76.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
56.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
51.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

Compiler

Compiled 575 to 442 computations (23.1% saved)

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4927	1371
1	4927	1371

prune147.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	107	13	120

Error

0.0b

Counts

120 → 13

Compiler

Compiled 2598 to 1062 computations (59.1% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
16×	`add-sqr-sqrt_binary64_782`
12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
8×	`pow1_binary64_821`
6×	`associate-/r_binary64_704` `associate-r_binary64_700` `associate-l*_binary64_701` `times-frac_binary64_766`
4×	`cbrt-undiv_binary64_794` `associate-*l/_binary64_703` `prod-exp_binary64_809` `add-log-exp_binary64_799` `tan-quot_binary64_919` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
2×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-/l/_binary64_707` `div-inv_binary64_757` `associate-/l_binary64_705` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 82

Calls

8 calls:

6.0ms	(/.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) (sin.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
0.0ms	(+.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))

series262.0ms (4.3%)

Counts

4 → 16

Calls

4 calls:

80.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
76.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
53.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
52.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

Compiler

Compiled 642 to 470 computations (26.8% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4998	1240
1	4998	1240

prune105.0ms (1.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	98	13	111

Error

0.0b

Counts

111 → 13

Compiler

Compiled 2705 to 925 computations (65.8% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
0.1b	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
0.1b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
0.1b	(+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `pow-unpow_binary64_837` `unpow-prod-down_binary64_839` `add-sqr-sqrt_binary64_782`
8×	`add-exp-log_binary64_798` `pow1_binary64_821`
4×	`unpow2_binary64_825` `add-log-exp_binary64_799` `pow-exp_binary64_828` `add-cbrt-cube_binary64_796` `pow-to-exp_binary64_829` `sqr-pow_binary64_732` `pow-pow_binary64_832`

Counts

4 → 72

Calls

8 calls:

5.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
0.0ms	(+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))

series100.0ms (1.6%)

Counts

4 → 16

Calls

4 calls:

26.0ms	(pow.f64 (sin.f64 x) 2)
26.0ms	(pow.f64 (cos.f64 x) 2)
24.0ms	(pow.f64 (sin.f64 x) 2)
23.0ms	(pow.f64 (cos.f64 x) 2)

Compiler

Compiled 684 to 550 computations (19.6% saved)

simplify59.0ms (1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4947	634
1	4947	634

prune113.0ms (1.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	88	13	101

Error

0.0b

Counts

101 → 13

Compiler

Compiled 2236 to 1442 computations (35.5% saved)

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	555	2104
1	555	2104

regimes555.0ms (9.1%)

Compiler: Compiled 6291 to 4612 computations (26.7% saved)

bsearch0.0ms (0%)

regimes246.0ms (4%)

Compiler: Compiled 2179 to 1633 computations (25.1% saved)

bsearch0.0ms (0%)

regimes57.0ms (0.9%)

Compiler: Compiled 151 to 129 computations (14.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

regimes10.0ms (0.2%)

Accuracy

Total 0.3b remaining (88.4%)

Threshold costs 0.3b (88.4%)

Compiler

Compiled 25 to 25 computations (0% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 56 to 39 computations (30.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	87
1	74	87

end0.0ms (0%)

sample2.2s (36.9%)

Algorithm

1×

intervals

Results

355.0ms	2054×	body	1024	valid
201.0ms	4460×	body	128	valid
130.0ms	1016×	body	512	valid
42.0ms	465×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 1376 to 1003 computations (27.1% saved)

Pareto

0.038645269845598455

Details

analyze514.0ms (8.4%)

sample34.0ms (0.6%)

simplify205.0ms (3.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite30.0ms (0.5%)

series384.0ms (6.3%)

simplify105.0ms (1.7%)

prune306.0ms (5%)

localize13.0ms (0.2%)

rewrite30.0ms (0.5%)

series278.0ms (4.6%)

simplify90.0ms (1.5%)

prune147.0ms (2.4%)

localize15.0ms (0.2%)

rewrite28.0ms (0.5%)

series262.0ms (4.3%)

simplify78.0ms (1.3%)

prune105.0ms (1.7%)

localize12.0ms (0.2%)

rewrite18.0ms (0.3%)

series100.0ms (1.6%)

simplify59.0ms (1%)

prune113.0ms (1.9%)

simplify34.0ms (0.6%)

regimes555.0ms (9.1%)

bsearch0.0ms (0%)

regimes246.0ms (4%)

bsearch0.0ms (0%)

regimes57.0ms (0.9%)

bsearch1.0ms (0%)

regimes10.0ms (0.2%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (36.9%)

Profiling