Details

analyze1.5s (21.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample58.0ms (0.8%)

Algorithm

1×

intervals

Results

31.0ms	90×	body	1024	valid
8.0ms	41×	body	512	valid
5.0ms	91×	body	128	valid
4.0ms	11×	body	2048	valid
3.0ms	23×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

667×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
380×	`fma-def_binary64`
279×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	25	13
2	34	13
3	59	13
4	123	11
5	318	8
6	1056	8
7	4350	8
8	4987	8

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 30 to 24 computations (20% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
4×	`sqrt-prod_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 38

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
3.0ms	(+.f64 1 (exp.f64 x))

series8.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.0ms	(+.f64 1 (exp.f64 x))

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
283×	`fma-neg_binary64`
235×	`fma-def_binary64`
177×	`associate-/r/_binary64`
165×	`associate-+l+_binary64`

Counts

46 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	538
1	218	494
2	595	470
3	2140	454
4	4978	454
5	4938	454
6	5008	454

prune45.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Error

0.2b

Counts

64 → 3

Alt Table

Status	Error	Program
▶	20.4b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	20.7b	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 793 to 597 computations (24.7% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(pow.f64 (sqrt.f64 2) 5)
✓	9.8b	(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
✓	9.8b	(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
✓	11.9b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))

rewrite122.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`associate-*r/_binary64`
60×	`add-log-exp_binary64`
51×	`frac-add_binary64`
32×	`sum-log_binary64`
24×	`flip-+_binary64`

Counts

4 → 131

Calls

4 calls:

56.0ms	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
21.0ms	(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
20.0ms	(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
2.0ms	(pow.f64 (sqrt.f64 2) 5)

series87.0ms (1.2%)

Counts

4 → 25

Calls

4 calls:

55.0ms	(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3))))
23.0ms	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (sqrt.f64 2) 3)))))
9.0ms	(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))
0.0ms	(pow.f64 (sqrt.f64 2) 5)

simplify364.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

580×	`distribute-rgt-in_binary64`
557×	`distribute-lft-in_binary64`
436×	`fma-def_binary64`
165×	`cancel-sign-sub-inv_binary64`
144×	`*-commutative_binary64`

Counts

156 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	409	19128
1	1648	15556
2	5205	15556

prune736.0ms (10.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	285	1	286
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	286	3	289

Error

0.2b

Counts

289 → 3

Alt Table

Status	Error	Program
▶	20.5b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 2)) 1/16))
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	20.7b	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 28262 to 24973 computations (11.6% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))
✓	0.5b	(/.f64 x (sqrt.f64 2))
	1.6b	(pow.f64 (sqrt.f64 2) 5)
	9.8b	(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
111×	`unpow-prod-down_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Counts

2 → 205

Calls

2 calls:

7.0ms	(/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))
4.0ms	(/.f64 x (sqrt.f64 2))

series178.0ms (2.5%)

Counts

2 → 0

Calls

2 calls:

159.0ms	(/.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))
18.0ms	(/.f64 x (sqrt.f64 2))

simplify199.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

731×	`associate-*l/_binary64`
629×	`associate-l_binary64`
629×	`associate-*r/_binary64`
284×	`log-div_binary64`
260×	`associate-/l*_binary64`

Counts

205 → 354

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4220
1	326	4157
2	1603	3973
3	4718	3973
4	5117	3973

prune567.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	449	3	452

Error

0.2b

Counts

452 → 3

Alt Table

Status	Error	Program
▶	20.5b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (pow.f64 (cbrt.f64 x) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 2)) 1/16))
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	20.7b	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 15643 to 13254 computations (15.3% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 x) 3)
	1.0b	(pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)
✓	1.0b	(pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)
✓	9.8b	(+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (pow.f64 (cbrt.f64 x) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))

rewrite117.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-*r/_binary64`
15×	`unpow-prod-down_binary64`
14×	`frac-add_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

3 → 86

Calls

3 calls:

60.0ms

(pow.f64 (cbrt.f64 x) 3)

48.0ms

(+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (*.f64 (/.f64 (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (pow.f64 (cbrt.f64 x) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))

3.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)

series299.0ms (4.2%)

Counts

3 → 24

Calls

3 calls:

279.0ms

(pow.f64 (cbrt.f64 x) 3)

20.0ms

(+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (*.f64 1/16 (*.f64 (/.f64 (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)) (/.f64 (pow.f64 (cbrt.f64 x) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)))) (+.f64 (sqrt.f64 2) (*.f64 1/2 (/.f64 x (sqrt.f64 2))))))

0.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)

simplify159.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

514×	`unswap-sqr_binary64`
335×	`associate-l_binary64`
322×	`associate-r_binary64`
200×	`fma-def_binary64`
164×	`distribute-rgt-in_binary64`

Counts

110 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	3461
1	770	2919
2	3137	2911
3	4547	2911
4	4999	2911
5	4909	2911

prune374.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	238	3	241

Error

0.2b

Counts

241 → 3

Alt Table

Status	Error	Program
✓	0.3b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
	20.5b	(-.f64 (+.f64 (.f64 1/12 (/.f64 (pow.f64 x 3) (sqrt.f64 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 x 2) (sqrt.f64 2))) (+.f64 (.f64 1/16 (.f64 (/.f64 (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (.f64 (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) (cbrt.f64 (sqrt.f64 (sqrt.f64 2)))) 5) (pow.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 2))) 5))) (/.f64 (pow.f64 (cbrt.f64 x) 3) (pow.f64 (sqrt.f64 (sqrt.f64 2)) 5)))) (+.f64 (sqrt.f64 2) (.f64 1/2 (/.f64 x (sqrt.f64 2))))))) (.f64 (/.f64 (.f64 x x) (sqrt.f64 2)) 1/16))
	20.7b	(sqrt.f64 (+.f64 2 x))

Compiler

Compiled 12287 to 9992 computations (18.7% saved)

regimes91.0ms (1.3%)

Accuracy

Total 0.0b remaining (7.9%)

Threshold costs 0.0b (7.9%)

Compiler

Compiled 1954 to 1695 computations (13.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	9	8
2	8	8

end0.0ms (0%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

sample1.8s (26.2%)

Algorithm

1×

intervals

Results

880.0ms	2605×	body	1024	valid
265.0ms	1373×	body	512	valid
172.0ms	3060×	body	128	valid
116.0ms	291×	body	2048	valid
81.0ms	671×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 109 to 94 computations (13.8% saved)

Details

analyze1.5s (21.6%)

sample58.0ms (0.8%)

simplify52.0ms (0.7%)

prune3.0ms (0%)

localize4.0ms (0.1%)

rewrite8.0ms (0.1%)

series8.0ms (0.1%)

simplify100.0ms (1.4%)

prune45.0ms (0.6%)

localize27.0ms (0.4%)

rewrite122.0ms (1.7%)

series87.0ms (1.2%)

simplify364.0ms (5.2%)

prune736.0ms (10.4%)

localize23.0ms (0.3%)

rewrite24.0ms (0.3%)

series178.0ms (2.5%)

simplify199.0ms (2.8%)

prune567.0ms (8%)

localize33.0ms (0.5%)

rewrite117.0ms (1.7%)

series299.0ms (4.2%)

simplify159.0ms (2.2%)

prune374.0ms (5.3%)

regimes91.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (26.2%)

Profiling