Details

analyze2.3s (20.3%)

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)

sample203.0ms (1.8%)

Algorithm

1×

intervals

Results

132.0ms	68×	body	2048	valid
42.0ms	94×	body	1024	valid
12.0ms	50×	body	512	valid
3.0ms	18×	body	256	valid
2.0ms	24×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

simplify89.0ms (0.8%)

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 → 0

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

32.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 20 to 12 computations (40% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.4b	(-.f64 x (sin.f64 x))
1.6b	(-.f64 x (tan.f64 x))

rewrite122.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

47×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`flip3--_binary64`
14×	`add-log-exp_binary64`
13×	`add-cbrt-cube_binary64`

Counts

3 → 146

Calls

3 calls:

17.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
16.0ms	(-.f64 x (tan.f64 x))
15.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 2984 to 493 computations (83.5% saved)

series55.0ms (0.5%)

Error

0.0b

Counts

3 → 27

Calls

3 calls:

21.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
12.0ms	(-.f64 x (tan.f64 x))
7.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 904 to 582 computations (35.6% saved)

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

532×	`cancel-sign-sub-inv_binary64`
511×	`fma-neg_binary64`
172×	`sub-neg_binary64`
137×	`times-frac_binary64`
130×	`associate-r_binary64`

Counts

173 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	2737
1	688	2611
2	2712	2450
3	4643	2439
4	4887	2439

prune35.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	3	72

Error

0.0b

Counts

72 → 3

Alt Table

Status	Error	Program
▶	31.0b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	32.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	33.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (*.f64 x (cos.f64 x))))))

Compiler

Compiled 1308 to 486 computations (62.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 9/40 (.f64 x x))
0.5b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
16.1b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

rewrite122.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`

Counts

3 → 117

Calls

3 calls:

18.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
15.0ms	(.f64 9/40 (.f64 x x))
10.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

Compiler

Compiled 2597 to 1963 computations (24.4% saved)

series29.0ms (0.3%)

Error

0.0b

Counts

3 → 14

Calls

3 calls:

10.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
9.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
5.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 338 to 273 computations (19.2% saved)

simplify142.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

471×	`unswap-sqr_binary64`
405×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
248×	`*-commutative_binary64`
242×	`distribute-lft-in_binary64`

Counts

131 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	137	1687
1	323	1633
2	1045	1533
3	3509	1509
4	4241	1499
5	4944	1499
6	4814	1499

prune35.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
✓	31.0b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
▶	31.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
✓	32.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	33.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (*.f64 x (cos.f64 x))))))

Compiler

Compiled 1050 to 753 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
0.6b	(*.f64 (pow.f64 x 4) -27/2800)
16.1b	(fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800))

rewrite117.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

26×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 117

Calls

3 calls:

14.0ms	(*.f64 (pow.f64 x 4) -27/2800)
13.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
9.0ms	(fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800))

Compiler

Compiled 2618 to 1927 computations (26.4% saved)

series98.0ms (0.9%)

Error

Counts

3 → 14

Calls

3 calls:

81.0ms	(fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800))
7.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
6.0ms	(*.f64 (pow.f64 x 4) -27/2800)

Compiler

Compiled 319 to 265 computations (16.9% saved)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

690×	`associate-l_binary64`
547×	`associate-r_binary64`
496×	`unswap-sqr_binary64`
289×	`fma-def_binary64`
166×	`distribute-rgt-in_binary64`

Counts

131 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1935
1	337	1848
2	941	1727
3	3661	1679
4	5015	1679

prune38.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	66	4	70

Error

Counts

70 → 4

Alt Table

Status	Error	Program
✓	31.0b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
✓	31.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
✓	32.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	33.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (*.f64 x (cos.f64 x))))))

Compiler

Compiled 1152 to 790 computations (31.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
15.8b	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))
15.8b	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))

rewrite200.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
16×	`unpow-prod-down_binary64`
16×	`pow-to-exp_binary64`

Counts

4 → 174

Calls

4 calls:

19.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))
17.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))
14.0ms	(pow.f64 (sin.f64 x) 2)
13.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 6281 to 2426 computations (61.4% saved)

series95.0ms (0.9%)

Error

Counts

4 → 13

Calls

4 calls:

58.0ms	(pow.f64 (sin.f64 x) 2)
14.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2)))
12.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (.f64 x (cos.f64 x))))
6.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 1314 to 697 computations (47% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

438×	`associate-*l/_binary64`
421×	`associate-/l/_binary64`
346×	`associate-*r/_binary64`
328×	`fma-def_binary64`
304×	`prod-exp_binary64`

Counts

187 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	2248
1	300	1918
2	1095	1886
3	3489	1710
4	5228	1710

prune60.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	4	108

Error

Counts

108 → 4

Alt Table

Status	Error	Program
	31.0b	(-.f64 (.f64 9/40 (.f64 x x)) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
	31.0b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 (pow.f64 x 4) -27/2800)) 1/2)
	32.2b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
	33.0b	(-.f64 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 (.f64 x x) (pow.f64 (cos.f64 x) 2))))) (+.f64 (/.f64 (sin.f64 x) x) (/.f64 (pow.f64 (sin.f64 x) 2) (.f64 x (*.f64 x (cos.f64 x))))))

Compiler

Compiled 3018 to 1182 computations (60.8% saved)

regimes302.0ms (2.7%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Compiler

Compiled 3905 to 2160 computations (44.7% saved)

bsearch49.0ms (0.4%)

Steps

Iters	Range		Point
7	0.005433699804174966	1.291795540654184	0.02665164670869842
10	-9060.48826805608	-2.2037094697895102e-7	-2.420166958477668

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	106
1	54	106
2	68	106
3	83	106
4	92	106
5	96	106
6	97	106
7	96	106

end1.0ms (0%)

Compiler: Compiled 70 to 41 computations (41.4% saved)

sample6.7s (60.2%)

Algorithm

1×

intervals

Results

4.2s	1991×	body	2048	valid
1.4s	3034×	body	1024	valid
386.0ms	1477×	body	512	valid
150.0ms	134×	body	4096	valid
125.0ms	714×	body	256	valid
76.0ms	650×	body	128	valid

Compiler

Compiled 159 to 97 computations (39% saved)

Details

analyze2.3s (20.3%)

sample203.0ms (1.8%)

simplify89.0ms (0.8%)

prune1.0ms (0%)

localize8.0ms (0.1%)

rewrite122.0ms (1.1%)

series55.0ms (0.5%)

simplify133.0ms (1.2%)

prune35.0ms (0.3%)

localize9.0ms (0.1%)

rewrite122.0ms (1.1%)

series29.0ms (0.3%)

simplify142.0ms (1.3%)

prune35.0ms (0.3%)

localize9.0ms (0.1%)

rewrite117.0ms (1.1%)

series98.0ms (0.9%)

simplify96.0ms (0.9%)

prune38.0ms (0.3%)

localize23.0ms (0.2%)

rewrite200.0ms (1.8%)

series95.0ms (0.9%)

simplify94.0ms (0.8%)

prune60.0ms (0.5%)

regimes302.0ms (2.7%)

bsearch49.0ms (0.4%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample6.7s (60.2%)

Profiling