Details

analyze967.0ms (7.1%)

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)

sample10.2s (74.9%)

Results

4.7s	1612×	body	8192	exit
2.6s	4141×	body	1024	valid
902.0ms	1616×	body	1024	invalid
866.0ms	2032×	body	512	valid
293.0ms	813×	body	512	invalid
293.0ms	1021×	body	256	valid
159.0ms	166×	body	2048	valid
147.0ms	896×	body	128	valid
103.0ms	394×	body	256	invalid
57.0ms	381×	body	128	invalid
1.0ms	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%)

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)))

series12.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

8.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite45.0ms (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:

44.0ms	(sqrt.f64 (cos.f64 x))
44.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
44.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify30.0ms (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

prune98.0ms (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
	59.3b	(/.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))
	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)))

Compiler

Compiled 1663 to 553 computations (66.7% saved)

localize32.0ms (0.2%)

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)))))))

series827.0ms (6.1%)

Counts

4 → 48

Calls

4 calls:

454.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
209.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
160.0ms	(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)))))))

rewrite52.0ms (0.4%)

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:

49.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
49.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
49.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
49.0ms	(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

658×	`fma-neg_binary64`
378×	`distribute-rgt-neg-in_binary64`
360×	`distribute-lft-neg-in_binary64`
222×	`associate-r_binary64`
210×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	980
1	199	807
2	589	650
3	2327	600

Stop Event

1×	node limit

Counts

146 → 126

prune132.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	193	5	198

Error

36.2b

Counts

198 → 5

Alt Table

Status	Error	Program
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 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))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
	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)))

Compiler

Compiled 5371 to 2053 computations (61.8% 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)))))))

series330.0ms (2.4%)

Counts

3 → 36

Calls

3 calls:

315.0ms

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

12.0ms

(/.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)))))))

rewrite53.0ms (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:

51.0ms

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

51.0ms

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

51.0ms

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

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
246×	`associate-+l+_binary64`
227×	`associate-+l-_binary64`
205×	`associate-+r+_binary64`
199×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	53	843
1	154	655
2	425	597
3	1719	559

Stop Event

1×	node limit

Counts

120 → 103

prune103.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	135	6	141

Error

36.1b

Counts

141 → 6

Alt Table

Status	Error	Program
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 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))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
	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)))
▶	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))

Compiler

Compiled 2872 to 1591 computations (44.6% saved)

localize11.0ms (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)))

series282.0ms (2.1%)

Counts

4 → 48

Calls

4 calls:

143.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)
127.0ms	(cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x))))
10.0ms	(/.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)))

rewrite61.0ms (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:

59.0ms	(cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x))))
59.0ms	(/.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))
59.0ms	(pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)
59.0ms	(fmod.f64 (exp.f64 x) (+.f64 2/3 (pow.f64 (cbrt.f64 (*.f64 1/3 (sqrt.f64 (cos.f64 x)))) 3)))

simplify34.0ms (0.2%)

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

prune97.0ms (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
	60.1b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 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))
	59.3b	(exp.f64 (-.f64 (log.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) x))
	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)))
✓	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))

Compiler

Compiled 2635 to 1548 computations (41.3% saved)

regimes42.0ms (0.3%)

Accuracy

Total 0.6b remaining (1.6%)

Threshold costs 0.6b (1.6%)

Counts

22 → 1

Compiler

Compiled 778 to 500 computations (35.7% 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

end97.0ms (0.7%)

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

Details

analyze967.0ms (7.1%)

sample10.2s (74.9%)

simplify29.0ms (0.2%)

prune3.0ms (0%)

localize7.0ms (0%)

series12.0ms (0.1%)

rewrite45.0ms (0.3%)

simplify30.0ms (0.2%)

prune98.0ms (0.7%)

localize32.0ms (0.2%)

series827.0ms (6.1%)

rewrite52.0ms (0.4%)

simplify36.0ms (0.3%)

prune132.0ms (1%)

localize12.0ms (0.1%)

series330.0ms (2.4%)

rewrite53.0ms (0.4%)

simplify31.0ms (0.2%)

prune103.0ms (0.8%)

localize11.0ms (0.1%)

series282.0ms (2.1%)

rewrite61.0ms (0.4%)

simplify34.0ms (0.2%)

prune97.0ms (0.7%)

regimes42.0ms (0.3%)

simplify2.0ms (0%)

end97.0ms (0.7%)

Profiling