Details

analyze1.3s (14.1%)

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)

sample185.0ms (1.9%)

Algorithm

1×

intervals

Results

118.0ms	64×	body	2048	valid
38.0ms	105×	body	1024	valid
8.0ms	43×	body	512	valid
7.0ms	7×	body	4096	valid
2.0ms	20×	body	256	valid
1.0ms	17×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify174.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	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

Error

33.1b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.1b	(-.f64 x (tan.f64 x))
1.1b	(-.f64 x (sin.f64 x))

rewrite28.0ms (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:

9.0ms	(/.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))

series240.0ms (2.5%)

Counts

3 → 23

Calls

3 calls:

96.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
86.0ms	(-.f64 x (tan.f64 x))
57.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 466 to 377 computations (19.1% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5977	1953

prune94.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Error

0.0b

Counts

108 → 5

Compiler

Compiled 1769 to 463 computations (73.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 -1/2 (.f64 (.f64 x x) 9/40))
0.2b	(.f64 (.f64 x x) 9/40)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
1×	`flip3-+_binary64` `associate-l_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(.f64 (.f64 x x) 9/40)
3.0ms	(+.f64 -1/2 (.f64 (.f64 x x) 9/40))

series73.0ms (0.8%)

Counts

2 → 9

Calls

2 calls:

48.0ms	(+.f64 -1/2 (.f64 (.f64 x x) 9/40))
26.0ms	(.f64 (.f64 x x) 9/40)

Compiler

Compiled 95 to 96 computations (-1.1% saved)

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4820	387
1	4820	387

prune31.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Error

0.0b

Counts

44 → 5

Compiler

Compiled 454 to 299 computations (34.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
0.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
1.1b	(-.f64 x (tan.f64 x))
1.1b	(-.f64 x (tan.f64 x))

rewrite61.0ms (0.6%)

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:

35.0ms	(-.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))

series398.0ms (4.2%)

Counts

4 → 27

Calls

4 calls:

211.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
66.0ms	(-.f64 x (tan.f64 x))
64.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
56.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 699 to 544 computations (22.2% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4931	2729
1	4931	2729

prune109.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	145	5	150

Error

0.0b

Counts

150 → 5

Compiler

Compiled 2994 to 620 computations (79.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
1.1b	(-.f64 x (tan.f64 x))
1.1b	(-.f64 x (sin.f64 x))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
100×	`times-frac_binary64`
68×	`cbrt-prod_binary64`
62×	`unpow-prod-down_binary64` `cube-prod_binary64`
52×	`add-cube-cbrt_binary64`
42×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64` `associate-/r/_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`div-inv_binary64`
3×	`pow-unpow_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-exp_binary64`

Counts

4 → 192

Calls

4 calls:

21.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
12.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series378.0ms (3.9%)

Counts

4 → 31

Calls

4 calls:

165.0ms	(pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3)
91.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))) 3))
81.0ms	(-.f64 x (tan.f64 x))
40.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 773 to 652 computations (15.7% saved)

simplify105.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5198	5394

prune177.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	223	5	228

Error

0.0b

Counts

228 → 5

Compiler

Compiled 4255 to 1288 computations (69.7% saved)

regimes101.0ms (1.1%)

Accuracy

Total 0.0b remaining (40.5%)

Threshold costs 0.0b (40.5%)

Compiler

Compiled 643 to 353 computations (45.1% saved)

bsearch51.0ms (0.5%)

Steps

Iters	Range		Point
9	2.2170582684004132e-07	1.9804249795735036	0.005206135045402149
10	-0.3195383663525098	-9.909754041392325e-19	-0.06472604384936174

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	62
1	52	62

end0.0ms (0%)

sample5.7s (59.1%)

Algorithm

1×

intervals

Results

3.6s	1941×	body	2048	valid
994.0ms	2981×	body	1024	valid
279.0ms	1517×	body	512	valid
116.0ms	771×	body	256	valid
114.0ms	118×	body	4096	valid
57.0ms	672×	body	128	valid

Compiler

Compiled 341 to 184 computations (46% saved)

Details

analyze1.3s (14.1%)

sample185.0ms (1.9%)

simplify174.0ms (1.8%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite28.0ms (0.3%)

series240.0ms (2.5%)

simplify82.0ms (0.9%)

prune94.0ms (1%)

localize5.0ms (0.1%)

rewrite11.0ms (0.1%)

series73.0ms (0.8%)

simplify99.0ms (1%)

prune31.0ms (0.3%)

localize8.0ms (0.1%)

rewrite61.0ms (0.6%)

series398.0ms (4.2%)

simplify78.0ms (0.8%)

prune109.0ms (1.1%)

localize10.0ms (0.1%)

rewrite63.0ms (0.7%)

series378.0ms (3.9%)

simplify105.0ms (1.1%)

prune177.0ms (1.9%)

regimes101.0ms (1.1%)

bsearch51.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.7s (59.1%)

Profiling