Details

analyze1.9s (11.5%)

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)

sample11.2s (68.9%)

Results

5.0s	1569×	body	8192	exit
2.9s	4074×	body	1024	valid
991.0ms	1616×	body	1024	invalid
928.0ms	2067×	body	512	valid
328.0ms	1050×	body	256	valid
317.0ms	811×	body	512	invalid
209.0ms	178×	body	2048	valid
155.0ms	887×	body	128	valid
116.0ms	398×	body	256	invalid
62.0ms	411×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
493×	`fma-neg_binary64`
430×	`associate-/l*_binary64`
379×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	25	15
3	36	15
4	59	15
5	103	15
6	204	15
7	435	15
8	703	15
9	1995	15
10	2934	15
11	3478	15
12	4158	15
13	4980	15
14	4913	15

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

60.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.7b	(/.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	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	5.6b	(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))
3.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite52.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 83

Calls

3 calls:

50.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
50.0ms	(sqrt.f64 (cos.f64 x))
50.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	30
1	138	30
2	1678	30
3	5217	30
0	0	0
1	0	0

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

801×	`distribute-rgt-neg-in_binary64`
665×	`associate-l_binary64`
593×	`cancel-sign-sub-inv_binary64`
527×	`fma-def_binary64`
442×	`unswap-sqr_binary64`

Counts

91 → 97

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	39	194
1	106	194
2	281	158
3	903	138
4	3054	137
5	4717	137
6	4953	137

prune82.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Error

37.1b

Counts

98 → 4

Alt Table

Status	Error	Program
	60.7b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	37.5b	(/.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))
	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.7b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Compiler

Compiled 1610 to 522 computations (67.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
✓	0.9b	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
✓	1.3b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
✓	47.1b	(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)))))))

series1.3s (7.9%)

Counts

4 → 48

Calls

4 calls:

715.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
279.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
276.0ms	(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)))))))

rewrite66.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

635×	`prod-diff_binary64`
467×	`log-prod_binary64`
267×	`fma-def_binary64`
179×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Counts

4 → 113

Calls

4 calls:

64.0ms	(*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))
64.0ms	(log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))
64.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
64.0ms	(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)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	214	40
2	2435	37
3	5356	37
0	0	0
1	0	0

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-neg_binary64`
380×	`distribute-rgt-neg-in_binary64`
359×	`distribute-lft-neg-in_binary64`
239×	`neg-mul-1_binary64`
222×	`associate-r_binary64`

Counts

161 → 141

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	980
1	194	807
2	541	650
3	1857	600
4	4728	564
5	4922	564

prune248.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	213	4	217

Error

37.1b

Counts

217 → 4

Alt Table

Status	Error	Program
	60.7b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	37.5b	(/.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))
▶	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.7b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Compiler

Compiled 6000 to 2171 computations (63.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
✓	0.1b	(pow.f64 (cbrt.f64 (cos.f64 x)) 2)
✓	0.1b	(cbrt.f64 (cos.f64 x))
✓	5.6b	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

series354.0ms (2.2%)

Counts

4 → 48

Calls

4 calls:

176.0ms	(pow.f64 (cbrt.f64 (cos.f64 x)) 2)
172.0ms	(cbrt.f64 (cos.f64 x))
4.0ms	(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
2.0ms	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

rewrite82.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

685×	`log1p-expm1-u_binary64`
685×	`expm1-log1p-u_binary64`
146×	`expm1-udef_binary64`
146×	`log1p-udef_binary64`
144×	`log-pow_binary64`

Counts

4 → 81

Calls

4 calls:

81.0ms	(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
81.0ms	(pow.f64 (cbrt.f64 (cos.f64 x)) 2)
81.0ms	(cbrt.f64 (cos.f64 x))
81.0ms	(fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	189	26
2	1849	26
3	4937	26
4	4939	26
0	0	0
1	0	0

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

658×	`fma-def_binary64`
628×	`cancel-sign-sub-inv_binary64`
625×	`sub-neg_binary64`
516×	`distribute-rgt-neg-in_binary64`
407×	`distribute-lft-neg-in_binary64`

Counts

129 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	420
1	150	420
2	370	414
3	1130	408
4	2920	408
5	4440	408
6	4987	408
7	4997	408
8	4922	408

prune90.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Error

37.1b

Counts

144 → 4

Alt Table

Status	Error	Program
	60.7b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	37.5b	(/.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))
✓	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	60.7b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Compiler

Compiled 2792 to 1307 computations (53.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
	0.0b	(sqrt.f64 (cos.f64 x))
✓	2.9b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))
	5.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series10.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

rewrite74.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
140×	`expm1-udef_binary64`
140×	`log1p-udef_binary64`
78×	`add-sqr-sqrt_binary64`

Counts

1 → 45

Calls

1 calls:

72.0ms

(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	154	15
2	1849	15
3	4961	15
4	4969	15
0	0	0
1	0	0

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

530×	`distribute-rgt-neg-in_binary64`
427×	`distribute-lft-neg-in_binary64`
374×	`sub-neg_binary64`
294×	`associate-l_binary64`
293×	`cancel-sign-sub-inv_binary64`

Counts

57 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	262
1	61	262
2	159	228
3	496	210
4	1935	199
5	4322	199
6	4999	199
7	4949	199

prune83.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	149	4	153

Error

37.1b

Counts

153 → 4

Alt Table

Status	Error	Program
	60.7b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	37.5b	(/.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))
✓	60.6b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2)) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	60.7b	(log.f64 (exp.f64 (/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))))

Compiler

Compiled 2561 to 820 computations (68% saved)

regimes189.0ms (1.2%)

Accuracy

Total 0.5b remaining (1.2%)

Threshold costs 0.5b (1.2%)

Counts

105 → 1

Compiler

Compiled 3670 to 2384 computations (35% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	18	36
2	18	36

end82.0ms (0.5%)

Compiler: Compiled 112 to 69 computations (38.4% saved)

Details

analyze1.9s (11.5%)

sample11.2s (68.9%)

simplify97.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series12.0ms (0.1%)

rewrite52.0ms (0.3%)

simplify68.0ms (0.4%)

prune82.0ms (0.5%)

localize15.0ms (0.1%)

series1.3s (7.9%)

rewrite66.0ms (0.4%)

simplify69.0ms (0.4%)

prune248.0ms (1.5%)

localize11.0ms (0.1%)

series354.0ms (2.2%)

rewrite82.0ms (0.5%)

simplify111.0ms (0.7%)

prune90.0ms (0.6%)

localize9.0ms (0.1%)

series10.0ms (0.1%)

rewrite74.0ms (0.5%)

simplify82.0ms (0.5%)

prune83.0ms (0.5%)

regimes189.0ms (1.2%)

simplify2.0ms (0%)

end82.0ms (0.5%)

Profiling