Details

analyze948.0ms (7.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample10.0s (78%)

Results

4.6s	1612×	body	8192	exit
2.6s	4141×	body	1024	valid
903.0ms	1616×	body	1024	invalid
831.0ms	2032×	body	512	valid
291.0ms	813×	body	512	invalid
283.0ms	1021×	body	256	valid
144.0ms	166×	body	2048	valid
142.0ms	394×	body	256	invalid
141.0ms	896×	body	128	valid
56.0ms	381×	body	128	invalid
2.0ms	1×	body	2048	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
427×	`associate-/l*_binary64`
271×	`*-commutative_binary64`
263×	`associate-/r*_binary64`
222×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	26	15
3	39	15
4	63	15
5	120	15
6	276	15
7	708	15
8	1145	15
9	3095	15
10	4995	15

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

59.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	59.3b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	4.3b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series14.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

7.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
5.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
2.0ms	(sqrt.f64 (cos.f64 x))

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`log1p-expm1-u_binary64`
641×	`expm1-log1p-u_binary64`
345×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	139	30
2	1757	30

Stop Event

1×	node limit

Counts

3 → 83

Calls

3 calls:

42.0ms	(sqrt.f64 (cos.f64 x))
42.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
42.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

644×	`associate-l_binary64`
593×	`cancel-sign-sub-inv_binary64`
527×	`fma-def_binary64`
282×	`fma-neg_binary64`
166×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	194
1	107	194
2	298	158
3	1083	138
4	4830	138

Stop Event

1×	node limit

Counts

91 → 97

prune89.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	6	98

Error

36.2b

Counts

98 → 6

Alt Table

Status	Error	Program
	59.4b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.7b	(+.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 (.f64 (.f64 x x) (-.f64 1/2 (.f64 x 1/6))) x)))
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.3b	(/.f64 (fmod.f64 (exp.f64 x) (log1p.f64 (expm1.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	36.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 1663 to 553 computations (66.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
✓	0.9b	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
✓	1.4b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
✓	47.8b	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

series342.0ms (2.7%)

Counts

4 → 48

Calls

4 calls:

279.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
34.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
25.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
4.0ms	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`prod-diff_binary64`
267×	`fma-def_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`
176×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	237	42
2	2661	37

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

60.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
60.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
60.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
60.0ms	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

896×	`fma-def_binary64`
425×	`cancel-sign-sub-inv_binary64`
272×	`times-frac_binary64`
170×	`unswap-sqr_binary64`
166×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1593
1	489	1172
2	1924	962

Stop Event

1×	node limit

Counts

146 → 127

prune150.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	196	5	201

Error

36.2b

Counts

201 → 5

Alt Table

Status	Error	Program
	59.4b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.7b	(+.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 (.f64 (.f64 x x) (-.f64 1/2 (.f64 x 1/6))) x)))
▶	36.8b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 6441 to 2908 computations (54.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	1.4b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
✓	4.3b	(fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

series240.0ms (1.9%)

Counts

3 → 36

Calls

3 calls:

226.0ms

(log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

11.0ms

(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

2.0ms

(fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`log-prod_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
198×	`log-pow_binary64`
120×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	242	45
2	3011	41

Stop Event

1×	node limit

Counts

3 → 84

Calls

3 calls:

53.0ms

(log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))

53.0ms

(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))

53.0ms

(fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

simplify30.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-def_binary64`
278×	`associate-r_binary64`
259×	`associate-+l+_binary64`
247×	`associate--r+_binary64`
237×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1182
1	321	715
2	1186	629

Stop Event

1×	node limit

Counts

120 → 104

prune110.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

36.1b

Counts

143 → 6

Alt Table

Status	Error	Program
	59.4b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.7b	(+.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 (.f64 (.f64 x x) (-.f64 1/2 (.f64 x 1/6))) x)))
✓	36.8b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
▶	58.1b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3))) (exp.f64 x))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 3357 to 1987 computations (40.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x))))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3))) (exp.f64 x))
✓	0.9b	(pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)
✓	4.3b	(fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)))

series270.0ms (2.1%)

Counts

4 → 48

Calls

4 calls:

137.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)
122.0ms	(cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x))))
9.0ms	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3))) (exp.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)))

rewrite55.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
218×	`prod-diff_binary64`
208×	`log-pow_binary64`
157×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	293	51
2	3387	51

Stop Event

1×	node limit

Counts

4 → 105

Calls

4 calls:

54.0ms	(cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x))))
54.0ms	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3))) (exp.f64 x))
54.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)
54.0ms	(fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)))

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

566×	`fma-neg_binary64`
373×	`*-commutative_binary64`
321×	`distribute-rgt-neg-in_binary64`
294×	`distribute-lft-neg-in_binary64`
179×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	800
1	161	796
2	478	736
3	1902	710

Stop Event

1×	node limit

Counts

153 → 130

prune95.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	130	6	136

Error

36.1b

Counts

136 → 6

Alt Table

Status	Error	Program
	59.4b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	59.7b	(+.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (-.f64 (.f64 (.f64 x x) (-.f64 1/2 (.f64 x 1/6))) x)))
✓	36.8b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
✓	58.1b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3))) (exp.f64 x))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))

Compiler

Compiled 2635 to 1548 computations (41.3% saved)

regimes47.0ms (0.4%)

Accuracy

Total 0.6b remaining (1.6%)

Threshold costs 0.6b (1.6%)

Counts

26 → 1

Compiler

Compiled 942 to 604 computations (35.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	14	45

Stop Event

1×

saturated

end93.0ms (0.7%)

Compiler: Compiled 140 to 83 computations (40.7% saved)

Details

analyze948.0ms (7.4%)

sample10.0s (78%)

simplify29.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series14.0ms (0.1%)

rewrite44.0ms (0.3%)

simplify31.0ms (0.2%)

prune89.0ms (0.7%)

localize15.0ms (0.1%)

series342.0ms (2.7%)

rewrite61.0ms (0.5%)

simplify36.0ms (0.3%)

prune150.0ms (1.2%)

localize12.0ms (0.1%)

series240.0ms (1.9%)

rewrite55.0ms (0.4%)

simplify30.0ms (0.2%)

prune110.0ms (0.9%)

localize12.0ms (0.1%)

series270.0ms (2.1%)

rewrite55.0ms (0.4%)

simplify33.0ms (0.3%)

prune95.0ms (0.7%)

regimes47.0ms (0.4%)

simplify2.0ms (0%)

end93.0ms (0.7%)

Profiling