Details

analyze1.1s (21%)

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

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample58.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	74×	body	1024	valid
10.0ms	120×	body	128	valid
8.0ms	42×	body	512	valid
3.0ms	19×	body	256	valid
1.0ms	1×	body	2048	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune7.0ms (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

0.2b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

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-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

3 calls:

17.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
5.0ms	(/.f64 1 (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))

series287.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

127.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
127.0ms	(/.f64 x (tan.f64 B))
32.0ms	(/.f64 1 (sin.f64 B))

simplify86.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4891	1413
1	4891	1413

prune106.0ms (2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	90	13	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	92	13	105

Error

0.0b

Counts

105 → 13

Compiler

Compiled 1664 to 711 computations (57.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

8.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(/.f64 x (sin.f64 B))

series276.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B)))
93.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
56.0ms	(/.f64 x (sin.f64 B))
21.0ms	(/.f64 1 (sin.f64 B))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4965	1578
1	4965	1578

prune106.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	121	8	129

Error

0.0b

Counts

129 → 8

Compiler

Compiled 2130 to 788 computations (63% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 60

Calls

3 calls:

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

series138.0ms (2.6%)

Counts

3 → 9

Calls

3 calls:

71.0ms	(/.f64 (-.f64 1 (*.f64 x (cos.f64 B))) (sin.f64 B))
35.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))
32.0ms	(*.f64 x (cos.f64 B))

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5705	1080

prune63.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	68	9	77

Error

0.0b

Counts

77 → 9

Compiler

Compiled 1173 to 530 computations (54.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
19×	`add-exp-log_binary64`
16×	`associate-l_binary64`
13×	`add-cbrt-cube_binary64`
9×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
5×	`prod-exp_binary64`
4×	`unswap-sqr_binary64` `div-exp_binary64`
3×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cancel-sign-sub-inv_binary64` `associate-/l_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `div-inv_binary64` `frac-times_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `associate-*l/_binary64`

Counts

4 → 104

Calls

4 calls:

10.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))
4.0ms	(*.f64 x (cos.f64 B))
4.0ms	(/.f64 1 (sin.f64 B))
3.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))

series163.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

85.0ms	(.f64 (/.f64 1 (sin.f64 B)) (-.f64 1 (.f64 x (cos.f64 B))))
31.0ms	(-.f64 1 (*.f64 x (cos.f64 B)))
27.0ms	(*.f64 x (cos.f64 B))
20.0ms	(/.f64 1 (sin.f64 B))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4941	1576
1	4941	1576

prune96.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	116	9	125

Error

0.0b

Counts

125 → 9

Compiler

Compiled 1807 to 855 computations (52.7% saved)

regimes207.0ms (3.9%)

Accuracy

Total 0.2b remaining (97.4%)

Threshold costs 0.2b (97.4%)

Compiler

Compiled 1843 to 1332 computations (27.7% 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

end0.0ms (0%)

sample2.3s (42.5%)

Algorithm

1×

intervals

Results

688.0ms	2342×	body	1024	valid
307.0ms	3928×	body	128	valid
235.0ms	1144×	body	512	valid
88.0ms	574×	body	256	valid
13.0ms	172×	body	128	invalid
6.0ms	12×	body	2048	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 627 to 456 computations (27.3% saved)

Details

analyze1.1s (21%)

sample58.0ms (1.1%)

simplify14.0ms (0.3%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite33.0ms (0.6%)

series287.0ms (5.4%)

simplify86.0ms (1.6%)

prune106.0ms (2%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series276.0ms (5.2%)

simplify69.0ms (1.3%)

prune106.0ms (2%)

localize9.0ms (0.2%)

rewrite16.0ms (0.3%)

series138.0ms (2.6%)

simplify60.0ms (1.1%)

prune63.0ms (1.2%)

localize10.0ms (0.2%)

rewrite27.0ms (0.5%)

series163.0ms (3.1%)

simplify65.0ms (1.2%)

prune96.0ms (1.8%)

regimes207.0ms (3.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (42.5%)

Profiling