Details

analyze496.0ms (8.7%)

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)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	67×	body	1024	valid
6.0ms	135×	body	128	valid
5.0ms	37×	body	512	valid
2.0ms	17×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify195.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

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

Merged 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))

rewrite29.0ms (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

4 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)))

series328.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
50.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
44.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
40.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune170.0ms (3%)

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

Merged error: 0.1b

Counts

123 → 12

Compiler

Compiled 2695 to 1565 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.6%)

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:

11.0ms	(*.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))

series162.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
43.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
29.0ms	(+.f64 (tan.f64 x) 1)
26.0ms	(-.f64 1 (tan.f64 x))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5281	1370

prune128.0ms (2.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	105	14	119

Merged error: 0.0b

Counts

119 → 14

Compiler

Compiled 2610 to 1449 computations (44.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1 (pow.f64 (tan.f64 x) 2))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64_760`
68×	`add-sqr-sqrt_binary64_782`
55×	`log-pow_binary64_849`
54×	`exp-prod_binary64_812`
48×	`times-frac_binary64_766`
40×	`difference-of-squares_binary64_729`
28×	`add-cube-cbrt_binary64_795`
19×	`unpow-prod-down_binary64_839`
13×	`unpow2_binary64_825` `sqr-pow_binary64_732`
12×	`distribute-lft-out_binary64_711`
8×	`cancel-sign-sub-inv_binary64_726`
7×	`pow1_binary64_821`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `pow-unpow_binary64_837`
5×	`distribute-lft-out--_binary64_712`
4×	`add-cbrt-cube_binary64_796`
3×	`log-prod_binary64_846`
2×	`associate-/r/_binary64_706` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `pow-pow_binary64_832`
1×	`diff-log_binary64_852` `log-div_binary64_847` `flip3-+_binary64_763` `exp-diff_binary64_808` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `rem-log-exp_binary64_801` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 131

Calls

4 calls:

22.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
6.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series556.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

438.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
42.0ms	(-.f64 1 (pow.f64 (tan.f64 x) 2))
38.0ms	(pow.f64 (tan.f64 x) 2)
37.0ms	(pow.f64 (tan.f64 x) 2)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5352	2120

prune195.0ms (3.4%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	142	15	157

Merged error: 0.0b

Counts

157 → 15

Compiler

Compiled 3393 to 2425 computations (28.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

4 calls:

7.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
5.0ms	(/.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))

series241.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
75.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
44.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
41.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4930	1378
1	4930	1378

prune93.0ms (1.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	11	12
Picked	1	0	1
Done	0	2	2
Total	102	15	117

Merged error: 0.0b

Counts

117 → 15

Compiler

Compiled 2233 to 829 computations (62.9% saved)

regimes450.0ms (7.9%)

Compiler: Compiled 5302 to 3872 computations (27% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	25
1	24	25

end0.0ms (0%)

sample2.2s (37.8%)

Algorithm

1×

intervals

Results

339.0ms	1920×	body	1024	valid
198.0ms	4573×	body	128	valid
132.0ms	989×	body	512	valid
46.0ms	512×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 1346 to 983 computations (27% saved)

Details

analyze496.0ms (8.7%)

sample31.0ms (0.5%)

simplify195.0ms (3.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite29.0ms (0.5%)

series328.0ms (5.8%)

simplify78.0ms (1.4%)

prune170.0ms (3%)

localize12.0ms (0.2%)

rewrite32.0ms (0.6%)

series162.0ms (2.8%)

simplify74.0ms (1.3%)

prune128.0ms (2.2%)

localize11.0ms (0.2%)

rewrite48.0ms (0.8%)

series556.0ms (9.7%)

simplify83.0ms (1.5%)

prune195.0ms (3.4%)

localize12.0ms (0.2%)

rewrite30.0ms (0.5%)

series241.0ms (4.2%)

simplify86.0ms (1.5%)

prune93.0ms (1.6%)

regimes450.0ms (7.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (37.8%)

Profiling