Details

analyze703.0ms (11.1%)

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)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	65×	body	1024	valid
7.0ms	144×	body	128	valid
3.0ms	22×	body	512	valid
2.0ms	25×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify201.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite41.0ms (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:

15.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.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)))

series346.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
56.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
45.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
40.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4956	2005
1	4956	2005

prune171.0ms (2.7%)

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 2652 to 1541 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite38.0ms (0.6%)

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:

10.0ms	(/.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 (tan.f64 x) (tan.f64 x))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series400.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
73.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
46.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
43.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify106.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4975	2783
1	4975	2783

prune149.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	125	11	136

Merged error: 0.0b

Counts

136 → 11

Compiler

Compiled 3334 to 1469 computations (55.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(/.f64 (cos.f64 x) (sin.f64 x))
0.2b	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
73×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64`
19×	`associate-/r*_binary64`
16×	`associate-/l*_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
7×	`div-inv_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64` `tan-quot_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
3×	`associate-/l/_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-/r/_binary64` `associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 186

Calls

4 calls:

28.0ms	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
7.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(/.f64 (cos.f64 x) (sin.f64 x))

series373.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 (-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
75.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
40.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
33.0ms	(/.f64 (cos.f64 x) (sin.f64 x))

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5098	5605

prune216.0ms (3.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	198	11	209

Merged error: 0.0b

Counts

209 → 11

Compiler

Compiled 5763 to 1933 computations (66.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite68.0ms (1.1%)

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:

19.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
12.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(+.f64 1 (tan.f64 x))

series402.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(/.f64 (+.f64 1 (tan.f64 x)) (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x))))
113.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
46.0ms	(pow.f64 (tan.f64 x) 2)
24.0ms	(+.f64 1 (tan.f64 x))

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4962	9358
1	4962	9358

prune434.0ms (6.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	263	11	274

Merged error: 0.0b

Counts

274 → 11

Compiler

Compiled 7395 to 4860 computations (34.3% saved)

regimes349.0ms (5.5%)

Compiler: Compiled 4110 to 3056 computations (25.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	20
1	19	20

end0.0ms (0%)

sample1.8s (29.3%)

Algorithm

1×

intervals

Results

331.0ms	2008×	body	1024	valid
190.0ms	4521×	body	128	valid
114.0ms	956×	body	512	valid
43.0ms	509×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 1045 to 778 computations (25.6% saved)

Details

analyze703.0ms (11.1%)

sample32.0ms (0.5%)

simplify201.0ms (3.2%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite41.0ms (0.7%)

series346.0ms (5.5%)

simplify84.0ms (1.3%)

prune171.0ms (2.7%)

localize12.0ms (0.2%)

rewrite38.0ms (0.6%)

series400.0ms (6.3%)

simplify106.0ms (1.7%)

prune149.0ms (2.4%)

localize12.0ms (0.2%)

rewrite64.0ms (1%)

series373.0ms (5.9%)

simplify97.0ms (1.5%)

prune216.0ms (3.4%)

localize13.0ms (0.2%)

rewrite68.0ms (1.1%)

series402.0ms (6.4%)

simplify131.0ms (2.1%)

prune434.0ms (6.9%)

regimes349.0ms (5.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (29.3%)

Profiling