Details

analyze342.0ms (6.9%)

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)

sample66.0ms (1.3%)

Algorithm

1×

intervals

Results

32.0ms	67×	body	2048	valid
9.0ms	57×	body	512	valid
7.0ms	32×	body	1024	valid
4.0ms	75×	body	128	valid
3.0ms	7×	body	4096	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 20 to 14 computations (30% 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

32.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.4b	(/.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
✓	1.2b	(-.f64 1 (cos.f64 x))
✓	17.1b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite14.0ms (0.3%)

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))

series11.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))

simplify113.0ms (2.3%)

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 → 129

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

prune81.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Error

0.0b

Counts

130 → 9

Alt Table

Status	Error	Program
▶	17.8b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	30.7b	(fma.f64 (*.f64 x x) -1/24 (fma.f64 1/720 (pow.f64 x 4) 1/2))
	32.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (*.f64 x (fma.f64 x (cos.f64 x) x)))
	32.5b	(/.f64 (-.f64 (.f64 1 1) (.f64 (cos.f64 x) (cos.f64 x))) (.f64 (.f64 x x) (+.f64 1 (cos.f64 x))))
	32.4b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 (.f64 1 1) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
	32.7b	(/.f64 (+.f64 1 (.f64 (neg.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x)))) (cbrt.f64 (cos.f64 x)))) (*.f64 x x))
	31.8b	(/.f64 (/.f64 (-.f64 1 (cos.f64 x)) x) x)
	31.9b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	32.4b	(/.f64 (exp.f64 (log.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))

Compiler

Compiled 1774 to 899 computations (49.3% 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))
✓	0.3b	(+.f64 1 (cos.f64 x))
✓	17.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite29.0ms (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:

8.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
6.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
3.0ms	(+.f64 1 (cos.f64 x))

series56.0ms (1.1%)

Counts

4 → 40

Calls

4 calls:

29.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
20.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
2.0ms	(+.f64 1 (cos.f64 x))

simplify112.0ms (2.2%)

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 → 287

Iterations

Useful iterations: 2 (0.0ms)

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

prune171.0ms (3.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	283	4	287
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	291	5	296

Error

Counts

296 → 5

Alt Table

Status	Error	Program
	17.8b	(/.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) (+.f64 1 (cos.f64 x))) (*.f64 x x))
	32.4b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 (.f64 1 1) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	0.3b	(/.f64 1 (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))))
	32.3b	(-.f64 (/.f64 1/2 (.f64 x (fma.f64 x (cos.f64 x) x))) (.f64 (/.f64 1/2 (*.f64 x (fma.f64 x (cos.f64 x) x))) (cos.f64 (+.f64 x x))))

Compiler

Compiled 4371 to 1953 computations (55.3% saved)

localize9.0ms (0.2%)

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)))

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

series65.0ms (1.3%)

Counts

3 → 28

Calls

3 calls:

31.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
27.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
7.0ms	(/.f64 (sin.f64 x) x)

simplify118.0ms (2.4%)

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 → 191

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

prune119.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	191	5	196

Error

Counts

196 → 5

Alt Table

Status	Error	Program
	17.8b	(/.f64 (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) (+.f64 1 (cos.f64 x))) (*.f64 x x))
	32.4b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 (.f64 1 1) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
✓	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))))
	32.3b	(-.f64 (/.f64 1/2 (.f64 x (fma.f64 x (cos.f64 x) x))) (.f64 (/.f64 1/2 (*.f64 x (fma.f64 x (cos.f64 x) x))) (cos.f64 (+.f64 x x))))

Compiler

Compiled 2764 to 1384 computations (49.9% saved)

localize9.0ms (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 x (tan.f64 (/.f64 x 2)))
	0.1b	(/.f64 (sin.f64 x) x)

rewrite40.0ms (0.8%)

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:

10.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
3.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))

series61.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

34.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))
27.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))

simplify353.0ms (7.1%)

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 → 501

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

prune363.0ms (7.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	545	1	546
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	547	4	551

Error

Counts

551 → 4

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
	0.1b	(*.f64 (/.f64 (sin.f64 (/.f64 x 2)) x) (/.f64 (/.f64 (sin.f64 x) x) (cos.f64 (/.f64 x 2))))
	32.4b	(/.f64 (-.f64 (pow.f64 1 3) (pow.f64 (cos.f64 x) 3)) (.f64 (.f64 x x) (+.f64 (.f64 1 1) (+.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 1 (cos.f64 x))))))
	32.3b	(-.f64 (/.f64 1/2 (.f64 x (fma.f64 x (cos.f64 x) x))) (.f64 (/.f64 1/2 (*.f64 x (fma.f64 x (cos.f64 x) x))) (cos.f64 (+.f64 x x))))

Compiler

Compiled 11073 to 5295 computations (52.2% saved)

regimes752.0ms (15.1%)

Accuracy

Total 0.1b remaining (76.7%)

Threshold costs 0.1b (76.7%)

Compiler

Compiled 14201 to 9091 computations (36% saved)

simplify3.0ms (0.1%)

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

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.0s (40.7%)

Algorithm

1×

intervals

Results

955.0ms	1959×	body	2048	valid
279.0ms	1094×	body	1024	valid
233.0ms	1512×	body	512	valid
141.0ms	2562×	body	128	valid
80.0ms	755×	body	256	valid
52.0ms	118×	body	4096	valid

Compiler

Compiled 105 to 67 computations (36.2% 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

analyze342.0ms (6.9%)

sample66.0ms (1.3%)

simplify27.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite14.0ms (0.3%)

series11.0ms (0.2%)

simplify113.0ms (2.3%)

prune81.0ms (1.6%)

localize10.0ms (0.2%)

rewrite29.0ms (0.6%)

series56.0ms (1.1%)

simplify112.0ms (2.2%)

prune171.0ms (3.4%)

localize9.0ms (0.2%)

rewrite21.0ms (0.4%)

series65.0ms (1.3%)

simplify118.0ms (2.4%)

prune119.0ms (2.4%)

localize9.0ms (0.2%)

rewrite40.0ms (0.8%)

series61.0ms (1.2%)

simplify353.0ms (7.1%)

prune363.0ms (7.3%)

regimes752.0ms (15.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.0s (40.7%)

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