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)

sample13.7s (89.2%)

Results

11.0s	4284×	body	2048	valid
2.0s	2109×	body	1024	valid
479.0ms	1044×	body	512	valid
139.0ms	504×	body	256	valid
50.0ms	315×	body	128	valid

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify40.0ms (0.3%)

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

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

31.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.1b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
✓	2.8b	(-.f64 x (sin.f64 x))

series16.0ms (0.1%)

Counts

2 → 18

Calls

2 calls:

13.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite115.0ms (0.7%)

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

Calls

2 calls:

106.0ms	(/.f64 (-.f64 x (sin.f64 x)) (tan.f64 x))
106.0ms	(-.f64 x (sin.f64 x))

simplify37.0ms (0.2%)

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

prune207.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	270	4	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	271	4	275

Error

0.1b

Counts

275 → 4

Alt Table

Status	Error	Program
	47.5b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (sqrt.f64 (tan.f64 x))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (tan.f64 x))))
▶	0.5b	(-.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	10.4b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (fma.f64 (pow.f64 x 9) -1/362880 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))))) (tan.f64 x))
	31.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 x (sin.f64 x)))) (tan.f64 x))

Compiler

Compiled 10511 to 2880 computations (72.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6)))
✓	0.1b	(*.f64 11/15120 (pow.f64 x 6))
✓	0.1b	(*.f64 23/360 (pow.f64 x 4))
✓	0.2b	(*.f64 1/6 (pow.f64 x 2))

series16.0ms (0.1%)

Counts

4 → 3

Calls

4 calls:

7.0ms	(*.f64 23/360 (pow.f64 x 4))
4.0ms	(+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6)))
3.0ms	(*.f64 11/15120 (pow.f64 x 6))
2.0ms	(*.f64 1/6 (pow.f64 x 2))

rewrite52.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

320×	`fma-def_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
200×	`log-pow_binary64`
161×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	324	35
2	3562	35

Stop Event

1×	node limit

Counts

4 → 96

Calls

4 calls:

50.0ms	(+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6)))
50.0ms	(*.f64 11/15120 (pow.f64 x 6))
50.0ms	(*.f64 23/360 (pow.f64 x 4))
50.0ms	(*.f64 1/6 (pow.f64 x 2))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

672×	`sqr-pow_binary64`
492×	`associate-l_binary64`
467×	`unswap-sqr_binary64`
325×	`*-commutative_binary64`
314×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	20	21
2	42	21
3	105	21
4	355	21
5	1368	21
6	2416	21
7	2573	21
8	2837	21
9	3101	21
10	3447	21
11	3896	21
12	4416	21

Stop Event

1×	node limit

Counts

99 → 98

prune146.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Error

0.0b

Counts

102 → 8

Alt Table

Status	Error	Program
	47.5b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (sqrt.f64 (tan.f64 x))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (tan.f64 x))))
✓	0.5b	(-.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	10.4b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (fma.f64 (pow.f64 x 9) -1/362880 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))))) (tan.f64 x))
	34.6b	(-.f64 (exp.f64 (fma.f64 2 (log.f64 x) (log1p.f64 -5/6))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6))))
	15.7b	(-.f64 (sqrt.f64 (.f64 (pow.f64 x 4) 1/36)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
▶	0.6b	(-.f64 (pow.f64 (.f64 x (sqrt.f64 1/6)) 2) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	1.1b	(-.f64 (pow.f64 (cbrt.f64 (.f64 1/6 (.f64 x x))) 3) (+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6))))
	31.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 x (sin.f64 x)))) (tan.f64 x))

Compiler

Compiled 2444 to 1982 computations (18.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (sqrt.f64 1/6))
	0.1b	(*.f64 11/15120 (pow.f64 x 6))
	0.1b	(*.f64 23/360 (pow.f64 x 4))
✓	0.2b	(pow.f64 (*.f64 x (sqrt.f64 1/6)) 2)

series11.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(pow.f64 (*.f64 x (sqrt.f64 1/6)) 2)
3.0ms	(*.f64 x (sqrt.f64 1/6))

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`log1p-expm1-u_binary64`
522×	`expm1-log1p-u_binary64`
371×	`unpow-prod-down_binary64`
267×	`log-prod_binary64`
155×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	146	13
2	1523	13

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

41.0ms	(*.f64 x (sqrt.f64 1/6))
41.0ms	(pow.f64 (*.f64 x (sqrt.f64 1/6)) 2)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-l_binary64`
538×	`sqr-pow_binary64`
462×	`*-commutative_binary64`
456×	`associate-r_binary64`
328×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	216
1	19	156
2	38	156
3	95	156
4	386	156
5	2078	156
6	2191	156
7	2388	156
8	2584	156
9	2817	156
10	3120	156
11	3761	156
12	4236	156
13	4856	156

Stop Event

1×	node limit

Counts

93 → 72

prune177.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Status	Error	Program
	47.5b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (sqrt.f64 (tan.f64 x))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (tan.f64 x))))
	0.5b	(-.f64 (.f64 (sqrt.f64 1/6) (.f64 x (.f64 x (sqrt.f64 1/6)))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
✓	0.5b	(-.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
▶	0.5b	(-.f64 (.f64 x (.f64 (sqrt.f64 1/6) (.f64 x (sqrt.f64 1/6)))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	10.4b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (fma.f64 (pow.f64 x 9) -1/362880 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))))) (tan.f64 x))
✓	0.6b	(-.f64 (pow.f64 (.f64 x (sqrt.f64 1/6)) 2) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	31.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 x (sin.f64 x)))) (tan.f64 x))
	0.8b	(-.f64 (.f64 (sqrt.f64 1/6) (pow.f64 (.f64 (pow.f64 1/6 1/4) x) 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6))))

Compiler

Compiled 2502 to 2011 computations (19.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 1/6) (.f64 x (sqrt.f64 1/6)))
7.0ms	(.f64 x (.f64 (sqrt.f64 1/6) (*.f64 x (sqrt.f64 1/6))))

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
500×	`unpow-prod-down_binary64`
331×	`log-prod_binary64`
162×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	25
1	142	11
2	1593	11

Stop Event

1×	node limit

Counts

2 → 34

Calls

2 calls:

48.0ms	(.f64 x (.f64 (sqrt.f64 1/6) (*.f64 x (sqrt.f64 1/6))))
48.0ms	(.f64 (sqrt.f64 1/6) (.f64 x (sqrt.f64 1/6)))

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-l_binary64`
538×	`sqr-pow_binary64`
508×	`associate-r_binary64`
475×	`*-commutative_binary64`
256×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	252
1	19	132
2	41	132
3	105	132
4	435	132
5	2432	132
6	2541	132
7	2736	132
8	2932	132
9	3161	132
10	3466	132
11	4107	132
12	4582	132

Stop Event

1×	node limit

Counts

58 → 38

prune107.0ms (0.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	62	10	72

Error

0.0b

Counts

72 → 10

Alt Table

Status	Error	Program
	47.5b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) 2) (sqrt.f64 (tan.f64 x))) (/.f64 (cbrt.f64 (-.f64 x (sin.f64 x))) (sqrt.f64 (tan.f64 x))))
	0.5b	(-.f64 (.f64 (sqrt.f64 1/6) (.f64 x (.f64 x (sqrt.f64 1/6)))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
✓	0.5b	(-.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
✓	0.5b	(-.f64 (.f64 x (.f64 (sqrt.f64 1/6) (.f64 x (sqrt.f64 1/6)))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	10.4b	(/.f64 (fma.f64 (pow.f64 x 5) -1/120 (fma.f64 (pow.f64 x 9) -1/362880 (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/5040 (pow.f64 x 7))))) (tan.f64 x))
	18.0b	(-.f64 (.f64 x (sqrt.f64 (.f64 1/36 (.f64 x x)))) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
✓	0.6b	(-.f64 (pow.f64 (.f64 x (sqrt.f64 1/6)) 2) (+.f64 (.f64 23/360 (pow.f64 x 4)) (*.f64 11/15120 (pow.f64 x 6))))
	1.2b	(-.f64 (.f64 x (pow.f64 (cbrt.f64 (.f64 1/6 x)) 3)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6))))
	31.1b	(/.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 (sin.f64 x) 2)) (/.f64 1 (+.f64 x (sin.f64 x)))) (tan.f64 x))
	0.8b	(-.f64 (.f64 (sqrt.f64 1/6) (pow.f64 (.f64 (pow.f64 1/6 1/4) x) 2)) (+.f64 (.f64 23/360 (pow.f64 x 4)) (.f64 11/15120 (pow.f64 x 6))))

Compiler

Compiled 1612 to 1282 computations (20.5% saved)

regimes173.0ms (1.1%)

Accuracy

Total 0.3b remaining (89.1%)

Threshold costs 0.3b (89.1%)

Counts

71 → 1

Compiler

Compiled 2482 to 1852 computations (25.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	16	28

Stop Event

1×

saturated

end208.0ms (1.4%)

Compiler: Compiled 253 to 190 computations (24.9% saved)

Details

analyze4.0ms (0%)

sample13.7s (89.2%)

simplify40.0ms (0.3%)

prune2.0ms (0%)

localize4.0ms (0%)

series16.0ms (0.1%)

rewrite115.0ms (0.7%)

simplify37.0ms (0.2%)

prune207.0ms (1.3%)

localize9.0ms (0.1%)

series16.0ms (0.1%)

rewrite52.0ms (0.3%)

simplify56.0ms (0.4%)

prune146.0ms (0.9%)

localize10.0ms (0.1%)

series11.0ms (0.1%)

rewrite43.0ms (0.3%)

simplify80.0ms (0.5%)

prune177.0ms (1.2%)

localize13.0ms (0.1%)

series14.0ms (0.1%)

rewrite49.0ms (0.3%)

simplify66.0ms (0.4%)

prune107.0ms (0.7%)

regimes173.0ms (1.1%)

simplify2.0ms (0%)

end208.0ms (1.4%)

Profiling