Details

analyze361.0ms (6.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample3.1s (57.5%)

Results

1.6s	2100×	body	2048	valid
472.0ms	1148×	body	1024	valid
458.0ms	1537×	body	512	valid
288.0ms	2603×	body	128	valid
160.0ms	770×	body	256	valid
74.0ms	98×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-def_binary64`
293×	`fma-neg_binary64`
85×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

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

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.9b	(-.f64 1 (cos.f64 x))
✓	14.0b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series9.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

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

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
7×	`add-cbrt-cube_binary64`

Counts

2 → 63

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
3.0ms	(-.f64 1 (cos.f64 x))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
411×	`associate-l_binary64`
405×	`times-frac_binary64`
353×	`associate-r_binary64`
344×	`fma-def_binary64`

Counts

79 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1152
1	283	1017
2	853	961
3	3327	961
4	4699	961
5	4954	961
6	4828	961

prune77.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Error

0.0b

Counts

92 → 8

Alt Table

Status	Error	Program
	30.9b	(/.f64 (+.f64 1 (.f64 (neg.f64 1) (cos.f64 x))) (.f64 x x))
	31.0b	(/.f64 (.f64 (cbrt.f64 (-.f64 1 (cos.f64 x))) (cbrt.f64 (-.f64 1 (cos.f64 x)))) (/.f64 (.f64 x x) (cbrt.f64 (-.f64 1 (cos.f64 x)))))
▶	14.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.9b	(/.f64 (.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (sqrt.f64 (-.f64 1 (cos.f64 x)))) (.f64 x x))
	31.0b	(/.f64 (log.f64 (/.f64 (exp.f64 1) (exp.f64 (cos.f64 x)))) (*.f64 x x))
	31.0b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	30.1b	(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
	32.1b	(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))

Compiler

Compiled 1712 to 867 computations (49.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.5b	(+.f64 1 (cos.f64 x))
✓	13.9b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series34.0ms (0.6%)

Counts

4 → 40

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
12.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
25×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
3.0ms	(+.f64 1 (cos.f64 x))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-*l/_binary64`
540×	`associate-/r/_binary64`
423×	`fma-def_binary64`
335×	`fma-neg_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

162 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2904
1	504	2230
2	1767	2192
3	4643	2192
4	4935	2192

prune150.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	209	5	214

Error

Counts

214 → 5

Alt Table

Status	Error	Program
	31.0b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	14.5b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
	0.4b	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))

Compiler

Compiled 4328 to 1921 computations (55.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
✓	0.1b	(/.f64 (sin.f64 x) x)
✓	0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

series26.0ms (0.5%)

Counts

3 → 28

Calls

3 calls:

12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
11.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
3.0ms	(/.f64 (sin.f64 x) x)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
19×	`add-cbrt-cube_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
6.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
2.0ms	(/.f64 (sin.f64 x) x)

simplify104.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
593×	`associate-/l/_binary64`
549×	`associate-*l/_binary64`
440×	`associate-l_binary64`
391×	`associate-/r*_binary64`

Counts

121 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	2266
1	433	2003
2	1333	1993
3	4088	1989
4	4749	1989
5	5173	1989

prune111.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Error

Counts

152 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
▶	0.1b	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
	31.0b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	14.5b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 x (fma.f64 x (cos.f64 x) x)))
	0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))

Compiler

Compiled 2730 to 1356 computations (50.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
	0.1b	(/.f64 (sin.f64 x) x)
✓	0.1b	(/.f64 x (tan.f64 (/.f64 x 2)))

series30.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))
10.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))

rewrite54.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

452×	`times-frac_binary64`
213×	`*-un-lft-identity_binary64`
213×	`add-sqr-sqrt_binary64`
213×	`add-cube-cbrt_binary64`
31×	`div-inv_binary64`

Counts

2 → 261

Calls

2 calls:

12.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
3.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))

simplify298.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-neg_binary64`
437×	`associate-/r/_binary64`
403×	`associate-*l/_binary64`
303×	`*-commutative_binary64`
301×	`associate-/r*_binary64`

Counts

285 → 408

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	475	10149
1	1300	9660
2	3230	9486
3	3597	9408
4	4811	9406
5	5197	9406

prune429.0ms (8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	450	4	454

Error

Counts

454 → 4

Alt Table

Status	Error	Program
	0.2b	(*.f64 (sin.f64 x) (/.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) x))
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.4b	(/.f64 (/.f64 (sin.f64 x) 1) (/.f64 x (/.f64 (tan.f64 (/.f64 x 2)) x)))
	31.0b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))

Compiler

Compiled 11064 to 5287 computations (52.2% saved)

regimes195.0ms (3.6%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

85 → 1

Compiler

Compiled 2736 to 1777 computations (35.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
2	10	17

end64.0ms (1.2%)

Compiler: Compiled 75 to 49 computations (34.7% saved)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Details

analyze361.0ms (6.8%)

sample3.1s (57.5%)

simplify27.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify103.0ms (1.9%)

prune77.0ms (1.4%)

localize10.0ms (0.2%)

series34.0ms (0.6%)

rewrite31.0ms (0.6%)

simplify97.0ms (1.8%)

prune150.0ms (2.8%)

localize8.0ms (0.1%)

series26.0ms (0.5%)

rewrite21.0ms (0.4%)

simplify104.0ms (1.9%)

prune111.0ms (2.1%)

localize10.0ms (0.2%)

series30.0ms (0.6%)

rewrite54.0ms (1%)

simplify298.0ms (5.6%)

prune429.0ms (8%)

regimes195.0ms (3.6%)

simplify2.0ms (0%)

end64.0ms (1.2%)

Profiling

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12