Details

analyze990.0ms (8.4%)

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)

sample267.0ms (2.3%)

Algorithm

1×

intervals

Results

127.0ms	48×	body	8192	exit
57.0ms	124×	body	1024	valid
20.0ms	47×	body	1024	nan
18.0ms	61×	body	512	valid
7.0ms	8×	body	2048	valid
6.0ms	34×	body	256	valid
5.0ms	21×	body	512	nan
3.0ms	29×	body	128	valid
3.0ms	17×	body	256	nan
1.0ms	12×	body	128	nan

Compiler

Compiled 24 to 18 computations (25% saved)

simplify83.0ms (0.7%)

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

60.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.3b	(/.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))
✓	4.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series14.0ms (0.1%)

Counts

3 → 8

Calls

3 calls:

9.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
4.0ms	(sqrt.f64 (cos.f64 x))
2.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 53

Calls

3 calls:

3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
1.0ms	(sqrt.f64 (cos.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

599×	`cancel-sign-sub-inv_binary64`
541×	`fma-def_binary64`
463×	`times-frac_binary64`
381×	`div-sub_binary64`
282×	`fma-neg_binary64`

Counts

61 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1190
1	212	1105
2	477	1069
3	1265	1049
4	3482	1048
5	4641	1048
6	5116	1048

prune62.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	3	74

Error

60.3b

Counts

74 → 3

Alt Table

Status	Error	Program
▶	60.3b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1279 to 353 computations (72.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
✓	0.1b	(cbrt.f64 (cos.f64 x))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	4.4b	(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

series394.0ms (3.3%)

Counts

4 → 48

Calls

4 calls:

190.0ms	(*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
184.0ms	(cbrt.f64 (cos.f64 x))
16.0ms	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
3.0ms	(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))
3.0ms	(/.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))) (exp.f64 x))
1.0ms	(cbrt.f64 (cos.f64 x))
0.0ms	(fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))

simplify137.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-neg_binary64`
441×	`associate-l_binary64`
433×	`distribute-rgt-neg-in_binary64`
390×	`associate-r_binary64`
390×	`distribute-lft-neg-in_binary64`

Counts

150 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	3639
1	362	2840
2	873	1982
3	2526	1969
4	4759	1969
5	4920	1969

prune216.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	199	2	201
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	200	4	204

Error

60.3b

Counts

204 → 4

Alt Table

Status	Error	Program
	60.3b	(/.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) (cbrt.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))) (/.f64 (exp.f64 x) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
▶	60.3b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 4539 to 1177 computations (74.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.1b	(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))
✓	0.7b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	49.0b	(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))

series13.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

8.0ms

(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

3.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))

2.0ms

(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms

(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

0.0ms

(expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))

0.0ms

(fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x)))))

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`cancel-sign-sub-inv_binary64`
541×	`fma-def_binary64`
463×	`times-frac_binary64`
381×	`div-sub_binary64`
282×	`fma-neg_binary64`

Counts

85 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	103	1453
1	209	1359
2	474	1323
3	1263	1303
4	3478	1302
5	4637	1302
6	5113	1302

prune105.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Error

60.3b

Counts

127 → 4

Alt Table

Status	Error	Program
	60.3b	(/.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) (cbrt.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))) (/.f64 (exp.f64 x) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
▶	60.3b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	60.3b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 2337 to 614 computations (73.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (cos.f64 x))
✓	0.7b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
✓	1.9b	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	4.4b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series10.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
20×	`log-pow_binary64`

Counts

2 → 62

Calls

2 calls:

4.0ms	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
1.0ms	(log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

simplify117.0ms (1%)

Algorithm

1×	egg-herbie

Rules

515×	`distribute-rgt-neg-in_binary64`
502×	`div-sub_binary64`
414×	`distribute-lft-neg-in_binary64`
312×	`associate-l_binary64`
299×	`cancel-sign-sub-inv_binary64`

Counts

86 → 106

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1888
1	175	1789
2	377	1755
3	915	1737
4	3008	1736
5	4292	1736
6	4959	1736

prune164.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	138	5	143

Error

60.3b

Counts

143 → 5

Alt Table

Status	Error	Program
✓	60.3b	(/.f64 (fmod.f64 (exp.f64 x) (expm1.f64 (log1p.f64 (sqrt.f64 (cos.f64 x))))) (exp.f64 x))
	60.3b	(.f64 (/.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (exp.f64 x))) (/.f64 (log.f64 (exp.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (sqrt.f64 (exp.f64 x))))
	60.3b	(*.f64 (/.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) (sqrt.f64 (exp.f64 x))) (/.f64 (log.f64 (exp.f64 (sqrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (sqrt.f64 (exp.f64 x))))
	60.3b	(/.f64 (.f64 (cbrt.f64 (fmod.f64 (exp.f64 x) (.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x)))))) (cbrt.f64 (fmod.f64 (exp.f64 x) (*.f64 (fabs.f64 (cbrt.f64 (cos.f64 x))) (sqrt.f64 (cbrt.f64 (cos.f64 x))))))) (/.f64 (exp.f64 x) (cbrt.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
	60.7b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 2802 to 612 computations (78.2% saved)

regimes96.0ms (0.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

55 → 1

Compiler

Compiled 2218 to 1084 computations (51.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	11	17
2	16	17
3	18	17
4	19	17
5	19	17

end1.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample8.8s (75%)

Algorithm

1×

intervals

Results

4.3s	1599×	body	8192	exit
2.0s	3910×	body	1024	valid
661.0ms	1590×	body	1024	nan
630.0ms	1974×	body	512	valid
200.0ms	762×	body	512	nan
189.0ms	1009×	body	256	valid
132.0ms	202×	body	2048	valid
97.0ms	905×	body	128	valid
64.0ms	377×	body	256	nan
33.0ms	374×	body	128	nan

Compiler

Compiled 142 to 71 computations (50% saved)

Details

analyze990.0ms (8.4%)

sample267.0ms (2.3%)

simplify83.0ms (0.7%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series14.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify93.0ms (0.8%)

prune62.0ms (0.5%)

localize11.0ms (0.1%)

series394.0ms (3.3%)

rewrite17.0ms (0.1%)

simplify137.0ms (1.2%)

prune216.0ms (1.8%)

localize10.0ms (0.1%)

series13.0ms (0.1%)

rewrite5.0ms (0%)

simplify101.0ms (0.9%)

prune105.0ms (0.9%)

localize9.0ms (0.1%)

series10.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify117.0ms (1%)

prune164.0ms (1.4%)

regimes96.0ms (0.8%)

simplify3.0ms (0%)

end1.0ms (0%)

sample8.8s (75%)

Profiling