Details

analyze1.8s (14.7%)

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 11 to 7 computations (36.4% saved)

sample9.3s (77.8%)

Results

5.4s	1987×	body	2048	valid
2.5s	3146×	body	1024	valid
726.0ms	1567×	body	512	valid
259.0ms	750×	body	256	valid
169.0ms	109×	body	4096	valid
119.0ms	697×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

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

Error

29.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.8b	(-.f64 x (sin.f64 x))
✓	0.8b	(-.f64 x (tan.f64 x))

series16.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

7.0ms	(-.f64 x (tan.f64 x))
7.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.0ms	(-.f64 x (sin.f64 x))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

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

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune122.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
✓	29.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	29.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
	34.6b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 3153 to 883 computations (72% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.0b	(log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
	0.8b	(-.f64 x (sin.f64 x))
	0.8b	(-.f64 x (tan.f64 x))

series14.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

14.0ms

(log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

938×	`times-frac_binary64`
472×	`associate-/l*_binary64`
322×	`fma-neg_binary64`
315×	`associate-/r*_binary64`
283×	`fma-def_binary64`

Counts

23 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	863
1	249	822
2	917	744
3	4936	744
4	5187	744

prune86.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	180	3	183

Error

Counts

183 → 3

Alt Table

Status	Error	Program
✓	29.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
▶	34.6b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 4120 to 1492 computations (63.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.3b	(.f64 9/40 (.f64 x x))
✓	17.5b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series10.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
2.0ms	(.f64 9/40 (.f64 x x))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 52

Calls

3 calls:

5.0ms	(.f64 9/40 (.f64 x x))
5.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-neg_binary64`
399×	`associate-+r+_binary64`
379×	`associate-+l+_binary64`
320×	`fma-def_binary64`
300×	`times-frac_binary64`

Counts

88 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1147
1	199	1072
2	668	980
3	2038	980
4	4543	969
5	4942	969

prune57.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	29.1b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	29.1b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))))
✓	34.6b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 1543 to 1127 computations (27% saved)

regimes71.0ms (0.6%)

Accuracy

Total 0.0b remaining (11.6%)

Threshold costs 0.0b (11.6%)

Counts

24 → 3

Compiler

Compiled 520 to 400 computations (23.1% saved)

bsearch59.0ms (0.5%)

Steps

Iters	Range		Point
9	0.0005096067154228253	10464.159382846341	0.02803816352959124
11	-1.8837587084822929	-1.003984892091254e-28	-0.03244483507352827

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	59
1	28	59
2	36	59
3	40	59
4	42	59
5	42	59

end67.0ms (0.6%)

Compiler: Compiled 115 to 68 computations (40.9% saved)

Details

analyze1.8s (14.7%)

sample9.3s (77.8%)

simplify84.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series16.0ms (0.1%)

rewrite21.0ms (0.2%)

simplify110.0ms (0.9%)

prune122.0ms (1%)

localize11.0ms (0.1%)

series14.0ms (0.1%)

rewrite1.0ms (0%)

simplify63.0ms (0.5%)

prune86.0ms (0.7%)

localize7.0ms (0.1%)

series10.0ms (0.1%)

rewrite12.0ms (0.1%)

simplify74.0ms (0.6%)

prune57.0ms (0.5%)

regimes71.0ms (0.6%)

bsearch59.0ms (0.5%)

simplify3.0ms (0%)

end67.0ms (0.6%)

Profiling