Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample103.0ms (1.6%)

Algorithm

1×

intervals

Results

45.0ms	70×	body	2048	valid
39.0ms	113×	body	1024	valid
8.0ms	45×	body	512	valid
3.0ms	20×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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: 37.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.8b	(cos.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `cos-sum_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `associate--l-_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-cos_binary64`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series108.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

80.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
27.0ms	(cos.f64 (+.f64 x eps))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5101	444

prune118.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	25	7	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	7	33

Merged error: 0.5b

Counts

33 → 7

Compiler

Compiled 1691 to 945 computations (44.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.9b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`distribute-lft-out_binary64` `sum-log_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

4 → 60

Calls

4 calls:

13.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.0ms	(+.f64 x (+.f64 x eps))

series282.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
99.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
39.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
31.0ms	(+.f64 x (+.f64 x eps))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4950	1369
1	4950	1369

prune308.0ms (4.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	8	72
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Merged error: 0.5b

Counts

79 → 12

Compiler

Compiled 5243 to 3652 computations (30.3% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
4.8b	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`sin-sum_binary64`
6×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
3×	`add-log-exp_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`associate-*r/_binary64` `unswap-sqr_binary64`

Counts

3 → 52

Calls

3 calls:

10.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
9.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
5.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

series232.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

101.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (*.f64 eps 1/2)))))
96.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (+.f64 x (.f64 eps 1/2))))
34.0ms	(sin.f64 (+.f64 x (*.f64 eps 1/2)))

simplify101.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4867	1328
1	4867	1328

prune292.0ms (4.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	53	8	61
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	61	12	73

Merged error: 0.1b

Counts

73 → 12

Compiler

Compiled 4745 to 3684 computations (22.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
0.1b	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
0.1b	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
7.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
5.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))
5.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))

series528.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (*.f64 eps 1/2)))))
152.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2))))
74.0ms	(.f64 (cos.f64 x) (sin.f64 (.f64 eps 1/2)))
70.0ms	(.f64 (sin.f64 x) (cos.f64 (.f64 eps 1/2)))

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	1986
1	4979	1986

prune470.0ms (7.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	80	14	94

Merged error: 0.0b

Counts

94 → 14

Compiler

Compiled 7917 to 6099 computations (23% saved)

regimes84.0ms (1.3%)

Compiler: Compiled 914 to 732 computations (19.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	35
1	24	35

end0.0ms (0%)

sample3.5s (53.8%)

Algorithm

1×

intervals

Results

1.3s	2059×	body	2048	valid
1.2s	3819×	body	1024	valid
253.0ms	1356×	body	512	valid
62.0ms	520×	body	256	valid
16.0ms	244×	body	128	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 485 to 390 computations (19.6% saved)

Details

analyze2.0ms (0%)

sample103.0ms (1.6%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.2%)

series108.0ms (1.7%)

simplify58.0ms (0.9%)

prune118.0ms (1.8%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series282.0ms (4.3%)

simplify60.0ms (0.9%)

prune308.0ms (4.7%)

localize12.0ms (0.2%)

rewrite28.0ms (0.4%)

series232.0ms (3.6%)

simplify101.0ms (1.6%)

prune292.0ms (4.5%)

localize19.0ms (0.3%)

rewrite37.0ms (0.6%)

series528.0ms (8.1%)

simplify79.0ms (1.2%)

prune470.0ms (7.2%)

regimes84.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.5s (53.8%)

Profiling