Details

analyze672.0ms (9.3%)

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)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	62×	body	1024	valid
6.0ms	142×	body	128	valid
4.0ms	29×	body	512	valid
2.0ms	23×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify278.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune4.0ms (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)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.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))

rewrite36.0ms (0.5%)

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)))

series627.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

359.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
92.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
91.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
85.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune948.0ms (13.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	104	18	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	19	123

Merged error: 0.1b

Counts

123 → 19

Compiler

Compiled 15501 to 10955 computations (29.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`add-sqr-sqrt_binary64`
64×	`*-un-lft-identity_binary64` `times-frac_binary64`
40×	`difference-of-sqr--1_binary64`
36×	`difference-of-squares_binary64`
26×	`add-cube-cbrt_binary64`
25×	`unpow-prod-down_binary64`
21×	`unpow2_binary64` `sqr-pow_binary64`
10×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
8×	`associate-/r_binary64` `add-exp-log_binary64` `associate-/l_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 148

Calls

4 calls:

16.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
6.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series626.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
79.0ms	(pow.f64 (tan.f64 x) 2)
78.0ms	(pow.f64 (tan.f64 x) 2)
76.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4968	3785
1	4968	3785

prune602.0ms (8.3%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	8	9	17
Picked	0	1	1
Done	0	1	1
Total	160	19	179

Merged error: 0.1b

Counts

179 → 19

Compiler

Compiled 10195 to 7542 computations (26% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
12×	`pow1_binary64` `difference-of-squares_binary64`
9×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out_binary64`
5×	`associate-/l*_binary64`
4×	`associate-/r*_binary64` `tan-quot_binary64`
3×	`pow-unpow_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

10.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)

series568.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

332.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
82.0ms	(pow.f64 (tan.f64 x) 2)
80.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
74.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4928	2105
1	4928	2105

prune248.0ms (3.4%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	2	14	16
Picked	0	1	1
Done	0	2	2
Total	118	19	137

Merged error: 0.1b

Counts

137 → 19

Compiler

Compiled 4296 to 3076 computations (28.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`flip3-+_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `flip-+_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `frac-times_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`associate-r/_binary64` `difference-of-sqr--1_binary64` `+-commutative_binary64` `associate-l/_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

12.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (+.f64 (tan.f64 x) -1))
5.0ms	(+.f64 (tan.f64 x) 1)
4.0ms	(+.f64 (tan.f64 x) -1)
3.0ms	(pow.f64 (tan.f64 x) 2)

series301.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (+.f64 (tan.f64 x) -1))
79.0ms	(pow.f64 (tan.f64 x) 2)
45.0ms	(+.f64 (tan.f64 x) -1)
44.0ms	(+.f64 (tan.f64 x) 1)

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5406	1110

prune241.0ms (3.3%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	3	12	15
Picked	1	0	1
Done	0	3	3
Total	86	19	105

Merged error: 0.0b

Counts

105 → 19

Compiler

Compiled 4218 to 3067 computations (27.3% saved)

regimes166.0ms (2.3%)

Compiler: Compiled 1746 to 1352 computations (22.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample1.4s (19.3%)

Algorithm

1×

intervals

Results

416.0ms	1997×	body	1024	valid
185.0ms	4469×	body	128	valid
140.0ms	1037×	body	512	valid
45.0ms	492×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 454 to 352 computations (22.5% saved)

Details

analyze672.0ms (9.3%)

sample38.0ms (0.5%)

simplify278.0ms (3.8%)

prune4.0ms (0.1%)

localize17.0ms (0.2%)

rewrite36.0ms (0.5%)

series627.0ms (8.7%)

simplify101.0ms (1.4%)

prune948.0ms (13.1%)

localize9.0ms (0.1%)

rewrite45.0ms (0.6%)

series626.0ms (8.7%)

simplify67.0ms (0.9%)

prune602.0ms (8.3%)

localize9.0ms (0.1%)

rewrite31.0ms (0.4%)

series568.0ms (7.9%)

simplify78.0ms (1.1%)

prune248.0ms (3.4%)

localize11.0ms (0.1%)

rewrite30.0ms (0.4%)

series301.0ms (4.2%)

simplify73.0ms (1%)

prune241.0ms (3.3%)

regimes166.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (19.3%)

Profiling