Details

analyze1.1s (14.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	546	28
1	546	28
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Symmetry

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample55.0ms (0.7%)

Algorithm

1×

intervals

Results

21.0ms	67×	body	1024	valid
10.0ms	140×	body	128	valid
6.0ms	27×	body	512	valid
3.0ms	20×	body	256	valid
1.0ms	2×	body	2048	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune6.0ms (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

Error

0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite127.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/l_binary64` `associate-/r_binary64` `difference-of-squares_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`div-exp_binary64` `distribute-lft-out--_binary64`
2×	`cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `tan-quot_binary64` `associate-/r/_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `diff-log_binary64` `frac-sub_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64`

Counts

3 → 94

Calls

3 calls:

16.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1561 to 635 computations (59.3% saved)

series526.0ms (7.2%)

Error

0.1b

Counts

3 → 27

Calls

3 calls:

275.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
196.0ms	(/.f64 x (tan.f64 B))
32.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 926 to 610 computations (34.1% saved)

simplify94.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4929	1754
1	4929	1754

prune110.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Error

0.0b

Counts

123 → 9

Compiler

Compiled 1860 to 797 computations (57.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
0.1b	(*.f64 x (cos.f64 B))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite113.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64` `times-frac_binary64`
15×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-inv_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `associate-/r*_binary64`
4×	`div-exp_binary64` `associate-/l*_binary64`
3×	`cbrt-undiv_binary64` `associate-l_binary64` `associate-r_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `distribute-lft-out--_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-prod-down_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `diff-log_binary64` `frac-sub_binary64` `sub-div_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
5.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
4.0ms	(*.f64 x (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1848 to 644 computations (65.2% saved)

series507.0ms (6.9%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

228.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B)))
152.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
70.0ms	(*.f64 x (cos.f64 B))
32.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1316 to 841 computations (36.1% saved)

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5059	1925

prune110.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

Counts

143 → 8

Compiler

Compiled 2299 to 916 computations (60.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (tan.f64 B) x)
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))

rewrite282.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

193×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
120×	`*-un-lft-identity_binary64`
99×	`add-cube-cbrt_binary64`
44×	`cancel-sign-sub-inv_binary64`
21×	`add-exp-log_binary64`
19×	`associate-/r*_binary64`
15×	`div-inv_binary64` `difference-of-squares_binary64`
13×	`add-cbrt-cube_binary64`
10×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `add-log-exp_binary64`
5×	`cbrt-undiv_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `frac-2neg_binary64` `clear-num_binary64`
2×	`inv-pow_binary64` `pow-flip_binary64` `associate-/r/_binary64`
1×	`tan-quot_binary64` `associate-/l/_binary64` `diff-log_binary64` `frac-sub_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64`

Counts

4 → 213

Calls

4 calls:

35.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
4.0ms	(/.f64 (tan.f64 B) x)
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 4456 to 2172 computations (51.3% saved)

series690.0ms (9.4%)

Error

Counts

4 → 36

Calls

4 calls:

274.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 1 (/.f64 (tan.f64 B) x)))
194.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
161.0ms	(/.f64 (tan.f64 B) x)
34.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1340 to 903 computations (32.6% saved)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4966	3958
1	4966	3958

prune199.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	249	8	257

Error

Counts

257 → 8

Compiler

Compiled 4148 to 1732 computations (58.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`add-exp-log_binary64` `swap-sqr_binary64` `associate-l_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1524 to 464 computations (69.6% saved)

series354.0ms (4.8%)

Error

Counts

4 → 12

Calls

4 calls:

99.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
87.0ms	(cbrt.f64 x)
83.0ms	(cbrt.f64 x)
75.0ms	(cbrt.f64 x)

Compiler

Compiled 663 to 472 computations (28.8% saved)

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune68.0ms (0.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 1573 to 554 computations (64.8% saved)

regimes277.0ms (3.8%)

Accuracy

Total 0.1b remaining (96%)

Threshold costs 0.1b (96%)

Compiler

Compiled 2668 to 1932 computations (27.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

Removed

()

end0.0ms (0%)

sample2.4s (32.6%)

Algorithm

1×

intervals

Results

620.0ms	2318×	body	1024	valid
290.0ms	4003×	body	128	valid
210.0ms	1106×	body	512	valid
79.0ms	562×	body	256	valid
11.0ms	173×	body	128	invalid
5.0ms	11×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 902 to 656 computations (27.3% saved)

Details

analyze1.1s (14.3%)

sample55.0ms (0.7%)

simplify16.0ms (0.2%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite127.0ms (1.7%)

series526.0ms (7.2%)

simplify94.0ms (1.3%)

prune110.0ms (1.5%)

localize9.0ms (0.1%)

rewrite113.0ms (1.5%)

series507.0ms (6.9%)

simplify81.0ms (1.1%)

prune110.0ms (1.5%)

localize11.0ms (0.2%)

rewrite282.0ms (3.8%)

series690.0ms (9.4%)

simplify91.0ms (1.2%)

prune199.0ms (2.7%)

localize14.0ms (0.2%)

rewrite76.0ms (1%)

series354.0ms (4.8%)

simplify75.0ms (1%)

prune68.0ms (0.9%)

regimes277.0ms (3.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (32.6%)

Profiling