Details

analyze332.0ms (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample2.9s (66%)

Results

1.5s	2089×	body	2048	valid
455.0ms	1149×	body	1024	valid
437.0ms	1574×	body	512	valid
274.0ms	2594×	body	128	valid
137.0ms	739×	body	256	valid
79.0ms	111×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess32.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

424×	`fma-def_binary64`
293×	`fma-neg_binary64`
86×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	73	12
5	127	12
6	192	12
7	317	12
8	621	12
9	1140	12
10	1700	12
11	1829	12
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-def_binary64`
293×	`fma-neg_binary64`
86×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	73	12
5	127	12
6	192	12
7	317	12
8	621	12
9	1140	12
10	1700	12
11	1829	12

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

33.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.3b	(-.f64 1 (cos.f64 x))
✓	14.6b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series5.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

1.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))	x	-inf
1.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))	x	inf
1.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))	x	0
1.0ms	(-.f64 1 (cos.f64 x))	x	0
0.0ms	(-.f64 1 (cos.f64 x))	x	inf

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
75×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	152	18
2	2130	18

Stop Event

1×	node limit

Counts

2 → 66

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-l_binary64`
468×	`fma-def_binary64`
434×	`associate-r_binary64`
413×	`unswap-sqr_binary64`
387×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	224
1	97	220
2	266	214
3	901	212
4	4446	212

Stop Event

1×	node limit

Counts

82 → 83

prune67.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Error

0.0b

Counts

84 → 9

Alt Table

Status	Error	Program
	15.2b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	33.1b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
	32.7b	(-.f64 (pow.f64 x -2) (*.f64 (cos.f64 x) (pow.f64 x -2)))
	33.5b	(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
	33.3b	(pow.f64 (cbrt.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))) 3)
	30.0b	(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 6) -1/40320 (fma.f64 1/720 (pow.f64 x 4) 1/2)))
	42.6b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 x 4))) (/.f64 (-.f64 1 (cos.f64 x)) (pow.f64 (cbrt.f64 x) 2)))
	33.5b	(.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (.f64 x x)))
▶	15.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

Compiler

Compiled 1363 to 856 computations (37.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.3b	(+.f64 1 (cos.f64 x))
✓	14.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series27.0ms (0.6%)

Counts

4 → 40

Calls

12 calls:

6.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))	x	-inf
6.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))	x	inf
5.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))	x	-inf
4.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))	x	inf
1.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))	x	0

rewrite62.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`
116×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	228	30
2	3521	30

Stop Event

1×	node limit

Counts

4 → 145

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
452×	`fma-neg_binary64`
209×	`*-commutative_binary64`
187×	`fma-def_binary64`
167×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	564
1	155	556
2	460	496
3	1638	496
4	4511	496

Stop Event

1×	node limit

Counts

185 → 179

prune117.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	15.7b	(.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
	33.5b	(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)
▶	15.2b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
	30.0b	(fma.f64 x (*.f64 x -1/24) (fma.f64 (pow.f64 x 6) -1/40320 (fma.f64 1/720 (pow.f64 x 4) 1/2)))
	33.1b	(pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)
	32.6b	(*.f64 (/.f64 1 x) (/.f64 (-.f64 1 (cos.f64 x)) x))
	15.3b	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))))

Compiler

Compiled 3149 to 1739 computations (44.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	14.1b	(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))

series18.0ms (0.4%)

Counts

2 → 24

Calls

6 calls:

4.0ms	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))	x	-inf
4.0ms	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))	x	inf
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))	x	-inf
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) (*.f64 x x))	x	inf
1.0ms	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))	x	0

rewrite45.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`log-prod_binary64`
180×	`pow1/3_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
163×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	198	29
2	2619	29

Stop Event

1×	node limit

Counts

2 → 71

simplify37.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

492×	`unswap-sqr_binary64`
463×	`associate-l_binary64`
423×	`associate-r_binary64`
417×	`fma-def_binary64`
350×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	467
1	115	465
2	289	457
3	927	455
4	4038	455

Stop Event

1×	node limit

Counts

95 → 89

prune71.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	91	5	96

Error

Counts

96 → 5

Alt Table

Status	Error	Program
	0.2b	(.f64 (sin.f64 x) (.f64 (/.f64 (tan.f64 (*.f64 x 1/2)) x) (/.f64 1 x)))
▶	0.1b	(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x)) x)
	33.1b	(pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)
	0.3b	(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
	15.7b	(.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))

Compiler

Compiled 1502 to 1025 computations (31.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x)) x)
✓	0.1b	(/.f64 (tan.f64 (*.f64 x 1/2)) x)
✓	0.1b	(.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x))

series36.0ms (0.8%)

Counts

3 → 36

Calls

9 calls:

10.0ms	(/.f64 (tan.f64 (*.f64 x 1/2)) x)	x	inf
5.0ms	(.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x))	x	-inf
5.0ms	(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x)) x)	x	-inf
4.0ms	(/.f64 (tan.f64 (*.f64 x 1/2)) x)	x	-inf
4.0ms	(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x)) x)	x	inf

rewrite59.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
180×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`
156×	`log-div_binary64`
150×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	40
1	195	40
2	2710	40

Stop Event

1×	node limit

Counts

3 → 114

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
429×	`cancel-sign-sub-inv_binary64`
259×	`fma-neg_binary64`
241×	`times-frac_binary64`
210×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	680
1	152	672
2	415	664
3	1393	662
4	4523	662

Stop Event

1×	node limit

Counts

150 → 140

prune103.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

Counts

145 → 5

Alt Table

Status	Error	Program
	33.1b	(pow.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2)) 1)
	0.3b	(/.f64 (sin.f64 x) (/.f64 x (/.f64 (tan.f64 (*.f64 x 1/2)) x)))
	15.7b	(.f64 (pow.f64 (sin.f64 x) 2) (/.f64 1 (.f64 (+.f64 1 (cos.f64 x)) (*.f64 x x))))
	0.2b	(.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (*.f64 (sin.f64 x) (/.f64 1 x)))
✓	0.1b	(/.f64 (.f64 (/.f64 (tan.f64 (.f64 x 1/2)) x) (sin.f64 x)) x)

Compiler

Compiled 2360 to 1456 computations (38.3% saved)

regimes181.0ms (4.2%)

Accuracy

Total 0.1b remaining (79.2%)

Threshold costs 0.1b (79.2%)

Counts

107 → 1

Compiler

Compiled 2899 to 2104 computations (27.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17

Stop Event

1×

saturated

end72.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 89 to 63 computations (29.2% saved)

Details

analyze332.0ms (7.6%)

sample2.9s (66%)

preprocess32.0ms (0.7%)

simplify22.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite42.0ms (1%)

simplify32.0ms (0.7%)

prune67.0ms (1.5%)

localize10.0ms (0.2%)

series27.0ms (0.6%)

rewrite62.0ms (1.4%)

simplify41.0ms (1%)

prune117.0ms (2.7%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite45.0ms (1%)

simplify37.0ms (0.9%)

prune71.0ms (1.6%)

localize7.0ms (0.2%)

series36.0ms (0.8%)

rewrite59.0ms (1.4%)

simplify46.0ms (1%)

prune103.0ms (2.4%)

regimes181.0ms (4.2%)

simplify2.0ms (0%)

end72.0ms (1.7%)

Profiling