Details

analyze1.8s (13%)

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)

sample9.6s (68.6%)

Results

6.2s	2093×	body	2048	valid
2.1s	3018×	body	1024	valid
623.0ms	1580×	body	512	valid
244.0ms	781×	body	256	valid
192.0ms	123×	body	4096	valid
116.0ms	661×	body	128	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify86.0ms (0.6%)

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

31.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.7b	(-.f64 x (tan.f64 x))
✓	1.7b	(-.f64 x (sin.f64 x))

series19.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

12.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
5.0ms	(-.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:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify107.0ms (0.8%)

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 → 152

Iterations

Useful iterations: 2 (0.0ms)

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

prune81.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	3	153

Error

Counts

153 → 3

Alt Table

Status	Error	Program
	31.4b	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
▶	31.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	32.2b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 3164 to 895 computations (71.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
✓	0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
	1.7b	(-.f64 x (tan.f64 x))
✓	1.7b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

series56.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

37.0ms	(/.f64 x (-.f64 x (tan.f64 x)))
11.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
8.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))

rewrite188.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

727×	`*-un-lft-identity_binary64`
717×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
421×	`add-cube-cbrt_binary64`

Counts

3 → 591

Calls

3 calls:

31.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

simplify780.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
412×	`unsub-neg_binary64`
312×	`fma-udef_binary64`
280×	`sub-neg_binary64`
250×	`associate-+r-_binary64`

Counts

627 → 574

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	622	41023
1	1422	27517
2	3251	20234
3	4263	20192
4	4884	20192
5	4829	20192

prune301.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	657	1	658
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	658	3	661

Error

Counts

661 → 3

Alt Table

Status	Error	Program
▶	31.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))
✓	31.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	32.2b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 33989 to 4862 computations (85.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))
✓	0.1b	(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))
	1.7b	(-.f64 x (tan.f64 x))
	1.7b	(-.f64 x (sin.f64 x))

series22.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

12.0ms	(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))
10.0ms	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`associate-l_binary64`
18×	`prod-diff_binary64`

Counts

2 → 88

Calls

2 calls:

13.0ms	(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))
0.0ms	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
338×	`associate-/r*_binary64`
308×	`distribute-rgt-in_binary64`
304×	`fma-neg_binary64`
288×	`distribute-lft-in_binary64`

Counts

112 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2931
1	441	2644
2	1513	2334
3	4531	2334
4	4940	2334

prune123.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Error

Counts

220 → 3

Alt Table

Status	Error	Program
✓	31.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))
✓	31.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
▶	32.2b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 5517 to 2122 computations (61.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	0.2b	(*.f64 27/112000 (pow.f64 x 6))
✓	19.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series14.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
4.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
3.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
0.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

445×	`fma-neg_binary64`
370×	`fma-def_binary64`
341×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
292×	`exp-prod_binary64`

Counts

115 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2086
1	260	1929
2	799	1728
3	2810	1715
4	4377	1706
5	4997	1706
6	4754	1706

prune107.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	125	3	128

Error

Counts

128 → 3

Alt Table

Status	Error	Program
✓	31.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (-.f64 x (sin.f64 x)))))
✓	31.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
✓	32.2b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 3418 to 2560 computations (25.1% saved)

regimes228.0ms (1.6%)

Accuracy

Total 0.0b remaining (30.6%)

Threshold costs 0.0b (30.6%)

Counts

75 → 3

Compiler

Compiled 2283 to 1587 computations (30.5% saved)

bsearch54.0ms (0.4%)

Steps

Iters	Range		Point
9	0.03049159675885598	226151.25760731447	0.09287712393157785
10	-825.1645469588282	-1.883810823971615e-10	-0.10457701635274878

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	78
1	31	78
2	41	78
3	47	78
4	51	78
5	52	78
6	52	78

end79.0ms (0.6%)

Compiler: Compiled 153 to 81 computations (47.1% saved)

Details

analyze1.8s (13%)

sample9.6s (68.6%)

simplify86.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

series19.0ms (0.1%)

rewrite21.0ms (0.2%)

simplify107.0ms (0.8%)

prune81.0ms (0.6%)

localize10.0ms (0.1%)

series56.0ms (0.4%)

rewrite188.0ms (1.3%)

simplify780.0ms (5.6%)

prune301.0ms (2.2%)

localize10.0ms (0.1%)

series22.0ms (0.2%)

rewrite21.0ms (0.1%)

simplify106.0ms (0.8%)

prune123.0ms (0.9%)

localize12.0ms (0.1%)

series14.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify125.0ms (0.9%)

prune107.0ms (0.8%)

regimes228.0ms (1.6%)

bsearch54.0ms (0.4%)

simplify4.0ms (0%)

end79.0ms (0.6%)

Profiling