Details

analyze1.4s (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample196.0ms (1.8%)

Algorithm

1×

intervals

Results

130.0ms	67×	body	2048	valid
40.0ms	98×	body	1024	valid
10.0ms	50×	body	512	valid
3.0ms	24×	body	256	valid
1.0ms	16×	body	128	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify248.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	990	14
1	990	14

prune4.0ms (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: 28.9b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 x (sin.f64 x))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

3 calls:

10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series275.0ms (2.5%)

Counts

3 → 9

Calls

3 calls:

127.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
95.0ms	(-.f64 x (tan.f64 x))
53.0ms	(-.f64 x (sin.f64 x))

simplify74.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4877	1847
1	4877	1847

prune145.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	87	6	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	6	94

Merged error: 0.0b

Counts

94 → 6

Compiler

Compiled 2660 to 970 computations (63.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 x (sin.f64 x))

rewrite44.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
32×	`log-pow_binary64`
31×	`exp-prod_binary64`
30×	`add-cube-cbrt_binary64`
24×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `pow1_binary64` `flip3--_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `div-sub_binary64` `div-inv_binary64`
1×	`cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64`

Counts

4 → 128

Calls

4 calls:

13.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
10.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series424.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
113.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
87.0ms	(-.f64 x (tan.f64 x))
39.0ms	(-.f64 x (sin.f64 x))

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4953	2756
1	4953	2756

prune118.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Merged error: 0.0b

Counts

146 → 6

Compiler

Compiled 2906 to 692 computations (76.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite61.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
21×	`distribute-lft-out--_binary64`
15×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 118

Calls

4 calls:

33.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
7.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series538.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

256.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
100.0ms	(-.f64 x (tan.f64 x))
99.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
83.0ms	(-.f64 x (tan.f64 x))

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5371	2681

prune125.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	131	5	136

Merged error: 0.0b

Counts

136 → 5

Compiler

Compiled 3195 to 707 computations (77.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x)))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 x (tan.f64 x))
1.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x))))

rewrite122.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

240×	`times-frac_binary64`
188×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
109×	`add-cube-cbrt_binary64`
68×	`cancel-sign-sub-inv_binary64`
33×	`difference-of-squares_binary64`
28×	`distribute-lft-out--_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
10×	`add-log-exp_binary64` `div-inv_binary64`
9×	`add-cbrt-cube_binary64`
7×	`div-exp_binary64`
5×	`pow1_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

4 → 220

Calls

4 calls:

75.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x))))
10.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series547.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x))))
104.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (sin.f64 x)))
98.0ms	(-.f64 x (tan.f64 x))
93.0ms	(-.f64 x (tan.f64 x))

simplify98.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5165	5625

prune195.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	232	5	237

Merged error: 0.0b

Counts

237 → 5

Compiler

Compiled 5604 to 986 computations (82.4% saved)

regimes45.0ms (0.4%)

Compiler: Compiled 192 to 108 computations (43.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	56
1	84	56

end0.0ms (0%)

sample6.2s (56.2%)

Algorithm

1×

intervals

Results

4.1s	1991×	body	2048	valid
1.2s	3045×	body	1024	valid
313.0ms	1492×	body	512	valid
120.0ms	96×	body	4096	valid
100.0ms	745×	body	256	valid
52.0ms	631×	body	128	valid

Compiler

Compiled 132 to 76 computations (42.4% saved)

Details

analyze1.4s (12.5%)

sample196.0ms (1.8%)

simplify248.0ms (2.2%)

prune4.0ms (0%)

localize18.0ms (0.2%)

rewrite29.0ms (0.3%)

series275.0ms (2.5%)

simplify74.0ms (0.7%)

prune145.0ms (1.3%)

localize14.0ms (0.1%)

rewrite44.0ms (0.4%)

series424.0ms (3.8%)

simplify66.0ms (0.6%)

prune118.0ms (1.1%)

localize10.0ms (0.1%)

rewrite61.0ms (0.5%)

series538.0ms (4.8%)

simplify69.0ms (0.6%)

prune125.0ms (1.1%)

localize12.0ms (0.1%)

rewrite122.0ms (1.1%)

series547.0ms (4.9%)

simplify98.0ms (0.9%)

prune195.0ms (1.8%)

regimes45.0ms (0.4%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.2s (56.2%)

Profiling