Details

analyze327.0ms (6.6%)

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 (59%)

Results

1.5s	2089×	body	2048	valid
463.0ms	1149×	body	1024	valid
453.0ms	1574×	body	512	valid
296.0ms	2594×	body	128	valid
142.0ms	739×	body	256	valid
77.0ms	111×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess34.0ms (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)

simplify18.0ms (0.4%)

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)

localize14.0ms (0.3%)

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

rewrite55.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
259×	`prod-diff_binary64`
102×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	153	18
2	2128	18

Stop Event

1×	node limit

Counts

2 → 102

simplify34.0ms (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

118 → 119

prune142.0ms (2.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

0.0b

Counts

120 → 8

Alt Table

Status	Error	Program
	33.4b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (pow.f64 x -2)) (cbrt.f64 (pow.f64 x -2))) (cbrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (pow.f64 x -2) (cos.f64 x)))) (fma.f64 (neg.f64 (pow.f64 x -2)) (cos.f64 x) (*.f64 (pow.f64 x -2) (cos.f64 x))))
▶	15.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	33.2b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x) (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 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)))
	15.2b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	33.1b	(log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
	40.8b	(+.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (.f64 (cos.f64 x) (pow.f64 x -2)))) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 x) (pow.f64 x -2)))) (sqrt.f64 (.f64 (cos.f64 x) (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)

Compiler

Compiled 3287 to 1912 computations (41.8% saved)

localize8.0ms (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))

series30.0ms (0.6%)

Counts

4 → 40

Calls

12 calls:

8.0ms	(/.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
5.0ms	(/.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

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
145×	`egg-rr`
114×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	229	30
2	3474	30

Stop Event

1×	node limit

Counts

4 → 145

simplify39.0ms (0.8%)

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

prune120.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	181	6	187

Error

Counts

187 → 6

Alt Table

Status	Error	Program
	33.2b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x) (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 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)))
	15.3b	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (/.f64 (sin.f64 x) (+.f64 1 (cos.f64 x))))
	33.1b	(log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
▶	14.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	33.5b	(pow.f64 (/.f64 (*.f64 x x) (-.f64 1 (cos.f64 x))) -1)

Compiler

Compiled 3165 to 1724 computations (45.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 x) 2)
✓	0.3b	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
	0.3b	(+.f64 1 (cos.f64 x))
✓	14.1b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

series26.0ms (0.5%)

Counts

3 → 12

Calls

9 calls:

7.0ms	(pow.f64 (sin.f64 x) 2)	x	inf
6.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))	x	inf
6.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))	x	-inf
2.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))	x	-inf
1.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))	x	inf

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
191×	`fma-def_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	233	30
2	2938	30

Stop Event

1×	node limit

Counts

3 → 117

simplify38.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
649×	`cancel-sign-sub-inv_binary64`
390×	`fma-neg_binary64`
211×	`*-commutative_binary64`
145×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	192
1	121	184
2	355	176
3	1276	174
4	4863	174

Stop Event

1×	node limit

Counts

129 → 140

prune137.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	180	5	185

Error

Counts

185 → 5

Alt Table

Status	Error	Program
	33.2b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x) (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 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)))
▶	15.1b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
	33.1b	(log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
✓	14.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 3301 to 1922 computations (41.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
✓	14.1b	(/.f64 (sin.f64 x) (*.f64 x x))

series13.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

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

rewrite47.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

491×	`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	26
1	198	26
2	2648	26

Stop Event

1×	node limit

Counts

2 → 81

simplify34.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-l_binary64`
417×	`associate-r_binary64`
392×	`fma-def_binary64`
355×	`times-frac_binary64`
352×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	383
1	119	379
2	315	371
3	1067	367
4	4496	367

Stop Event

1×	node limit

Counts

105 → 99

prune129.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	99	5	104

Error

Counts

104 → 5

Alt Table

Status	Error	Program
	33.2b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 x)))) (fma.f64 (neg.f64 (/.f64 (cos.f64 x) x)) (/.f64 1 x) (.f64 (/.f64 (cos.f64 x) x) (/.f64 1 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)))
✓	15.1b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
	33.1b	(log1p.f64 (expm1.f64 (*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))))
✓	14.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

Compiler

Compiled 1601 to 1039 computations (35.1% saved)

regimes557.0ms (11.2%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

Counts

233 → 1

Compiler

Compiled 8562 to 6041 computations (29.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	11	17

Stop Event

1×

saturated

end95.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 115 to 79 computations (31.3% saved)

Details

analyze327.0ms (6.6%)

sample2.9s (59%)

preprocess34.0ms (0.7%)

simplify18.0ms (0.4%)

prune1.0ms (0%)

localize14.0ms (0.3%)

series5.0ms (0.1%)

rewrite55.0ms (1.1%)

simplify34.0ms (0.7%)

prune142.0ms (2.9%)

localize8.0ms (0.2%)

series30.0ms (0.6%)

rewrite61.0ms (1.2%)

simplify39.0ms (0.8%)

prune120.0ms (2.4%)

localize8.0ms (0.2%)

series26.0ms (0.5%)

rewrite50.0ms (1%)

simplify38.0ms (0.8%)

prune137.0ms (2.8%)

localize9.0ms (0.2%)

series13.0ms (0.3%)

rewrite47.0ms (1%)

simplify34.0ms (0.7%)

prune129.0ms (2.6%)

regimes557.0ms (11.2%)

simplify2.0ms (0%)

end95.0ms (1.9%)

Profiling