Details

analyze2.7s (23.4%)

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)

sample328.0ms (2.8%)

Algorithm

1×

intervals

Results

148.0ms	62×	body	2048	valid
44.0ms	96×	body	1024	valid
12.0ms	50×	body	512	valid
5.0ms	4×	body	4096	valid
4.0ms	23×	body	256	valid
2.0ms	21×	body	128	valid

Compiler

Compiled 22 to 14 computations (36.4% 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

28.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.8b	(/.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)))
✓	1.4b	(-.f64 x (tan.f64 x))
✓	1.4b	(-.f64 x (sin.f64 x))

series20.0ms (0.2%)

Counts

3 → 30

Calls

3 calls:

13.0ms	(/.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))

rewrite20.0ms (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)))
3.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

simplify103.0ms (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 → 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

prune61.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	2	153

Error

0.0b

Counts

153 → 2

Alt Table

Status	Error	Program
▶	34.3b	(-.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))
✓	28.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 3120 to 871 computations (72.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	0.1b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.2b	(*.f64 27/112000 (pow.f64 x 6))
✓	20.8b	(-.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))

series15.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(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 27/2800 (pow.f64 x 4) 1/2)
0.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))

simplify114.0ms (1%)

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

prune101.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
✓	28.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
▶	34.3b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))

Compiler

Compiled 3415 to 2561 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))
✓	0.1b	(fma.f64 (pow.f64 x 4) -27/2800 -1/2)
✓	21.0b	(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

series44.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

37.0ms

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

4.0ms

(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

3.0ms

(fma.f64 (pow.f64 x 4) -27/2800 -1/2)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 30

Calls

3 calls:

0.0ms

(fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2))

0.0ms

(fma.f64 (pow.f64 x 4) -27/2800 -1/2)

0.0ms

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

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-def_binary64`
493×	`fma-neg_binary64`
413×	`exp-prod_binary64`
318×	`unsub-neg_binary64`
301×	`exp-sum_binary64`

Counts

66 → 63

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	60	1087
1	110	942
2	241	942
3	1018	942
4	2657	942
5	4666	942
6	5018	942

prune41.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
✓	28.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	34.3b	(fma.f64 9/40 (*.f64 x x) (fma.f64 27/112000 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -27/2800 -1/2)))

Compiler

Compiled 1346 to 982 computations (27% saved)

regimes95.0ms (0.8%)

Accuracy

Total 0.0b remaining (3.3%)

Threshold costs 0.0b (3.3%)

Counts

22 → 3

Compiler

Compiled 630 to 484 computations (23.2% saved)

bsearch49.0ms (0.4%)

Steps

Iters	Range		Point
8	0.01545048000401875	9.855736188026997	0.09538815243467016
9	-209152.30561560838	-0.0025116415472123165	-0.09385386690406423

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	26	50
1	33	50
2	41	50
3	45	50
4	47	50
5	47	50

end1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

sample7.7s (66.3%)

Algorithm

1×

intervals

Results

4.4s	2014×	body	2048	valid
2.2s	2926×	body	1024	valid
423.0ms	1572×	body	512	valid
133.0ms	115×	body	4096	valid
126.0ms	725×	body	256	valid
68.0ms	648×	body	128	valid

Compiler

Compiled 74 to 52 computations (29.7% saved)

Details

analyze2.7s (23.4%)

sample328.0ms (2.8%)

simplify84.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series20.0ms (0.2%)

rewrite20.0ms (0.2%)

simplify103.0ms (0.9%)

prune61.0ms (0.5%)

localize10.0ms (0.1%)

series15.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify114.0ms (1%)

prune101.0ms (0.9%)

localize9.0ms (0.1%)

series44.0ms (0.4%)

rewrite2.0ms (0%)

simplify74.0ms (0.6%)

prune41.0ms (0.4%)

regimes95.0ms (0.8%)

bsearch49.0ms (0.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.7s (66.3%)

Profiling