Details

analyze696.0ms (12.2%)

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)

sample33.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	57×	body	1024	valid
7.0ms	161×	body	128	valid
4.0ms	26×	body	512	valid
2.0ms	12×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify286.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

prune12.0ms (0.2%)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize10.0ms (0.2%)

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))))
0.1b	(-.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))

rewrite38.0ms (0.7%)

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:

9.0ms	(*.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)))

series638.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

364.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
98.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
97.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
78.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4912	2005
1	4912	2005

prune662.0ms (11.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	11	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

Compiler

Compiled 10624 to 7365 computations (30.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`pow1_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64` `cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
5×	`frac-times_binary64`
4×	`flip3-+_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64` `tan-quot_binary64`
3×	`sub-neg_binary64` `swap-sqr_binary64` `associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 95

Calls

4 calls:

12.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(-.f64 1 (tan.f64 x))
4.0ms	(+.f64 (tan.f64 x) 1)

series330.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
92.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
52.0ms	(+.f64 (tan.f64 x) 1)
49.0ms	(-.f64 1 (tan.f64 x))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5219	1370

prune179.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 3441 to 2059 computations (40.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
0.2b	(+.f64 (tan.f64 x) 1)
0.2b	(exp.f64 (+.f64 (tan.f64 x) 1))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
8×	`exp-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`log-prod_binary64` `tan-quot_binary64`
3×	`swap-sqr_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 71

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
5.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
5.0ms	(+.f64 (tan.f64 x) 1)

series402.0ms (7%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
81.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
78.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
46.0ms	(+.f64 (tan.f64 x) 1)

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5033	736

prune126.0ms (2.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	11	11
Picked	1	0	1
Done	0	1	1
Total	83	13	96

Merged error: 0.0b

Counts

96 → 13

Compiler

Compiled 2404 to 1477 computations (38.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
0.2b	(+.f64 (tan.f64 x) 1)
0.2b	(exp.f64 (+.f64 (tan.f64 x) 1))
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite24.0ms (0.4%)

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:

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

series400.0ms (7%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
82.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
78.0ms	(pow.f64 (tan.f64 x) 2)
42.0ms	(+.f64 (tan.f64 x) 1)

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5132	695

prune81.0ms (1.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	73	13	86

Merged error: 0.0b

Counts

86 → 13

Compiler

Compiled 1576 to 1053 computations (33.2% saved)

regimes63.0ms (1.1%)

Compiler: Compiled 574 to 424 computations (26.1% 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%)

sample1.3s (22.3%)

Algorithm

1×

intervals

Results

423.0ms	1973×	body	1024	valid
193.0ms	4532×	body	128	valid
135.0ms	958×	body	512	valid
51.0ms	525×	body	256	valid
4.0ms	12×	body	2048	valid

Compiler

Compiled 313 to 230 computations (26.5% saved)

Details

analyze696.0ms (12.2%)

sample33.0ms (0.6%)

simplify286.0ms (5%)

prune12.0ms (0.2%)

localize10.0ms (0.2%)

rewrite38.0ms (0.7%)

series638.0ms (11.2%)

simplify104.0ms (1.8%)

prune662.0ms (11.6%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series330.0ms (5.8%)

simplify78.0ms (1.4%)

prune179.0ms (3.1%)

localize16.0ms (0.3%)

rewrite28.0ms (0.5%)

series402.0ms (7%)

simplify87.0ms (1.5%)

prune126.0ms (2.2%)

localize14.0ms (0.3%)

rewrite24.0ms (0.4%)

series400.0ms (7%)

simplify80.0ms (1.4%)

prune81.0ms (1.4%)

regimes63.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (22.3%)

Profiling