Details

analyze695.0ms (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)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	65×	body	1024	valid
6.0ms	137×	body	128	valid
5.0ms	33×	body	512	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify285.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (106.0ms)

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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.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 (0.5%)

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 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series649.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
100.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
91.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
87.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune818.0ms (10.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	13	123

Merged error: 0.1b

Counts

123 → 13

Compiler

Compiled 13281 to 9454 computations (28.8% saved)

localize11.0ms (0.1%)

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

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

317×	`*-un-lft-identity_binary64`
264×	`times-frac_binary64`
179×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
69×	`distribute-lft-out_binary64`
50×	`difference-of-squares_binary64`
36×	`associate-/r*_binary64`
25×	`distribute-lft-out--_binary64`
13×	`associate-/r/_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `unpow-prod-down_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 251

Calls

4 calls:

22.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
13.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
4.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(+.f64 1 (tan.f64 x))

series752.0ms (10%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
235.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
79.0ms	(pow.f64 (tan.f64 x) 2)
47.0ms	(+.f64 1 (tan.f64 x))

simplify136.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4962	9358
1	4962	9358

prune651.0ms (8.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	263	13	276

Merged error: 0.0b

Counts

276 → 13

Compiler

Compiled 10558 to 7232 computations (31.5% saved)

localize14.0ms (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 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`pow1_binary64`
8×	`difference-of-squares_binary64`
7×	`associate-/l*_binary64`
6×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`associate-/l/_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-plus_binary64` `div-sub_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64`

Counts

4 → 113

Calls

4 calls:

12.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series705.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
154.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
77.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
73.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4946	2783
1	4946	2783

prune300.0ms (4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	124	14	138

Merged error: 0.0b

Counts

138 → 14

Compiler

Compiled 5787 to 3280 computations (43.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`exp-prod_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64` `add-exp-log_binary64`
4×	`log-prod_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `distribute-lft-out_binary64` `unpow-prod-down_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `rem-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 61

Calls

4 calls:

7.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
6.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
5.0ms	(+.f64 (tan.f64 x) 1)
3.0ms	(pow.f64 (tan.f64 x) 2)

series401.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
84.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
67.0ms	(pow.f64 (tan.f64 x) 2)
46.0ms	(+.f64 (tan.f64 x) 1)

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5132	695

prune101.0ms (1.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	72	15	87

Merged error: 0.0b

Counts

87 → 15

Compiler

Compiled 1938 to 1319 computations (31.9% saved)

regimes140.0ms (1.9%)

Compiler: Compiled 1494 to 1092 computations (26.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample1.3s (17.7%)

Algorithm

1×

intervals

Results

417.0ms	1975×	body	1024	valid
192.0ms	4512×	body	128	valid
136.0ms	991×	body	512	valid
48.0ms	516×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 393 to 284 computations (27.7% saved)

Details

analyze695.0ms (9.3%)

sample37.0ms (0.5%)

simplify285.0ms (3.8%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite36.0ms (0.5%)

series649.0ms (8.7%)

simplify102.0ms (1.4%)

prune818.0ms (10.9%)

localize11.0ms (0.1%)

rewrite76.0ms (1%)

series752.0ms (10%)

simplify136.0ms (1.8%)

prune651.0ms (8.7%)

localize14.0ms (0.2%)

rewrite41.0ms (0.5%)

series705.0ms (9.4%)

simplify85.0ms (1.1%)

prune300.0ms (4%)

localize15.0ms (0.2%)

rewrite26.0ms (0.3%)

series401.0ms (5.4%)

simplify77.0ms (1%)

prune101.0ms (1.4%)

regimes140.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (17.7%)

Profiling