Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
37.5%	12.5%	50%	3
43.7%	6.2%	50%	4
46.8%	3.1%	50%	5
48.4%	1.6%	50%	6
49.2%	0.8%	50%	7
49.6%	0.4%	50%	8
49.8%	0.2%	50%	9
49.9%	0.1%	50%	10
49.9%	0%	50%	11
49.9%	0%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample11.9s (89.7%)

Results

9.6s	4355×	body	2048	valid
1.6s	1989×	body	1024	valid
434.0ms	1079×	body	512	valid
164.0ms	544×	body	256	valid
66.0ms	289×	body	128	valid

Compiler

Compiled 30 to 20 computations (33.3% saved)

preprocess41.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

577×	`fma-def_binary64`
278×	`fma-neg_binary64`
235×	`times-frac_binary64`
176×	`div-sub_binary64`
119×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	56	11
5	86	11
6	150	11
7	238	11
8	380	11
9	714	11
10	1628	11
11	2249	11
12	2882	11
13	2945	11
14	2983	11
15	2993	11
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

577×	`fma-def_binary64`
278×	`fma-neg_binary64`
235×	`times-frac_binary64`
176×	`div-sub_binary64`
119×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	11	11
2	18	11
3	29	11
4	56	11
5	86	11
6	150	11
7	238	11
8	380	11
9	714	11
10	1628	11
11	2249	11
12	2882	11
13	2945	11
14	2983	11
15	2993	11

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

29.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.2b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
✓	3.4b	(-.f64 x (sin.f64 x))

series13.0ms (0.1%)

Counts

2 → 18

Calls

6 calls:

5.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))	x	-inf
5.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))	x	inf
1.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))	x	0
1.0ms	(-.f64 x (sin.f64 x))	x	0
0.0ms	(-.f64 x (sin.f64 x))	x	-inf

rewrite102.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log1p-expm1-u_binary64`
864×	`expm1-log1p-u_binary64`
591×	`prod-diff_binary64`
254×	`egg-rr`
75×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	140	17
2	2168	17

Stop Event

1×	node limit

Counts

2 → 254

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
478×	`cancel-sign-sub-inv_binary64`
387×	`unswap-sqr_binary64`
346×	`fma-neg_binary64`
272×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	272
1	133	266
2	344	262
3	1234	248
4	4380	248

Stop Event

1×	node limit

Counts

272 → 274

prune150.0ms (1.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	272	2	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	273	2	275

Error

0.1b

Counts

275 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	9.3b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120)) (tan.f64 x))

Compiler

Compiled 10405 to 2812 computations (73% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 x 6) -11/15120)
✓	0.1b	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
✓	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))

series11.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))	x	-inf
1.0ms	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))	x	inf
1.0ms	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))	x	inf
1.0ms	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))	x	-inf
1.0ms	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))	x	0

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

448×	`log-prod_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
181×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	274	42
2	2836	42

Stop Event

1×	node limit

Counts

3 → 75

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-neg_binary64`
774×	`cancel-sign-sub-inv_binary64`
366×	`associate-l_binary64`
285×	`unswap-sqr_binary64`
275×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	456
1	54	454
2	127	420
3	446	420
4	2464	420

Stop Event

1×	node limit

Counts

111 → 87

prune85.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Error

0.1b

Counts

89 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	18.9b	(cbrt.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 3))
▶	0.3b	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)
	0.7b	(pow.f64 (cbrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 3)
	9.3b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120)) (tan.f64 x))

Compiler

Compiled 1935 to 1417 computations (26.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (pow.f64 x 4) -23/360 (*.f64 (pow.f64 x 6) -11/15120))
	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
✓	0.3b	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)
✓	30.0b	(sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))

series33.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

10.0ms	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)	x	0
8.0ms	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)	x	inf
8.0ms	(pow.f64 (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))) 2)	x	-inf
2.0ms	(sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))	x	0
2.0ms	(sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))	x	-inf

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
196×	`log-pow_binary64`
152×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
1	335	44
2	3225	44

Stop Event

1×	node limit

Counts

2 → 71

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

939×	`fma-neg_binary64`
342×	`fma-def_binary64`
225×	`associate-/r*_binary64`
222×	`associate-r_binary64`
213×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	709
1	292	616
2	1007	576
3	4501	576

Stop Event

1×	node limit

Counts

95 → 105

prune193.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	172	4	176
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	175	6	181

Error

0.0b

Counts

181 → 6

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
	0.7b	(pow.f64 (*.f64 (sqrt.f64 1/6) x) 2)
✓	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	0.8b	(fma.f64 (.f64 (cbrt.f64 (.f64 1/6 (.f64 x x))) (cbrt.f64 (.f64 1/6 (.f64 x x)))) (cbrt.f64 (.f64 1/6 (.f64 x x))) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	0.4b	(.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
	9.3b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120)) (tan.f64 x))

Compiler

Compiled 4519 to 3456 computations (23.5% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
✓	0.1b	(.f64 x (.f64 x 1/6))
✓	0.4b	(*.f64 x 1/6)

series7.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))	x	-inf
1.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))	x	inf
1.0ms	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))	x	0
1.0ms	(.f64 x (.f64 x 1/6))	x	-inf
1.0ms	(.f64 x (.f64 x 1/6))	x	inf

rewrite49.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

734×	`log1p-expm1-u_binary64`
734×	`expm1-log1p-u_binary64`
153×	`log1p-udef_binary64`
149×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	189	25
2	2039	25

Stop Event

1×	node limit

Counts

3 → 51

simplify57.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
666×	`fma-neg_binary64`
395×	`distribute-rgt-neg-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
336×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	297
1	30	279
2	63	279
3	186	279
4	750	279
5	1829	279
6	3094	279
7	4840	279

Stop Event

1×	node limit

Counts

87 → 58

prune63.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Error

0.0b

Counts

64 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (.f64 (pow.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))) 1/4) (sqrt.f64 (fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120))))))
	14.7b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (sqrt.f64 (.f64 1/36 (*.f64 x x)))))
✓	0.2b	(fma.f64 (pow.f64 x 4) -23/360 (.f64 x (.f64 x 1/6)))
	0.7b	(pow.f64 (*.f64 (sqrt.f64 1/6) x) 2)
	12.8b	(fma.f64 (pow.f64 x 4) -23/360 (sqrt.f64 (*.f64 (pow.f64 x 4) 1/36)))
✓	0.2b	(fma.f64 1/6 (.f64 x x) (fma.f64 (pow.f64 x 4) -23/360 (.f64 (pow.f64 x 6) -11/15120)))
	9.3b	(/.f64 (fma.f64 1/6 (pow.f64 x 3) (*.f64 (pow.f64 x 5) -1/120)) (tan.f64 x))

Compiler

Compiled 925 to 709 computations (23.4% saved)

regimes138.0ms (1%)

Accuracy

Total 0.2b remaining (44.8%)

Threshold costs 0.2b (44.8%)

Counts

86 → 1

Compiler

Compiled 2432 to 1788 computations (26.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	14	21

Stop Event

1×

saturated

end141.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 159 to 120 computations (24.5% saved)

Details

analyze4.0ms (0%)

sample11.9s (89.7%)

preprocess41.0ms (0.3%)

simplify33.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0%)

series13.0ms (0.1%)

rewrite102.0ms (0.8%)

simplify37.0ms (0.3%)

prune150.0ms (1.1%)

localize8.0ms (0.1%)

series11.0ms (0.1%)

rewrite48.0ms (0.4%)

simplify33.0ms (0.2%)

prune85.0ms (0.6%)

localize10.0ms (0.1%)

series33.0ms (0.3%)

rewrite51.0ms (0.4%)

simplify40.0ms (0.3%)

prune193.0ms (1.5%)

localize6.0ms (0%)

series7.0ms (0.1%)

rewrite49.0ms (0.4%)

simplify57.0ms (0.4%)

prune63.0ms (0.5%)

regimes138.0ms (1%)

simplify2.0ms (0%)

end141.0ms (1.1%)

Profiling