Details

analyze754.0ms (13.4%)

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%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.1%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample2.8s (50.3%)

Results

1.4s	2846×	body	1024	valid
680.0ms	1388×	body	512	valid
330.0ms	3042×	body	128	valid
163.0ms	289×	body	2048	valid
144.0ms	691×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 41 to 35 computations (14.6% saved)

simplify45.0ms (0.8%)

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 (0.1%)

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(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)))

series7.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

5.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite6.0ms (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)))
2.0ms	(+.f64 1 (exp.f64 x))

simplify162.0ms (2.9%)

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 → 55

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

prune58.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	2	56

Error

0.2b

Counts

56 → 2

Alt Table

Status	Error	Program
✓	0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	19.9b	(-.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)))))

Status

Error

Program

✓

0.2b

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

▶

19.9b

(-.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)))))

Compiler

Compiled 785 to 591 computations (24.7% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(pow.f64 (sqrt.f64 2) 5)
✓	9.3b	(+.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))))))
✓	9.3b	(+.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))))
✓	12.3b	(-.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)))))

series82.0ms (1.5%)

Counts

4 → 25

Calls

4 calls:

44.0ms	(+.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))))
27.0ms	(-.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)))))
11.0ms	(+.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)

rewrite133.0ms (2.4%)

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:

57.0ms	(-.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)))))
26.0ms	(+.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))))))
18.0ms	(+.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)

simplify232.0ms (4.1%)

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 → 229

Iterations

Useful iterations: 1 (0.0ms)

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

prune723.0ms (12.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	229	2	231

Error

0.2b

Counts

231 → 2

Alt Table

Status	Error	Program
▶	19.9b	(-.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 (.f64 x x) (sqrt.f64 2)) 1/16))
✓	0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Status

Error

Program

▶

19.9b

(-.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 (*.f64 x x) (sqrt.f64 2)) 1/16))

✓

0.2b

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

Compiler

Compiled 28307 to 25014 computations (11.6% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 x x) (sqrt.f64 2))
✓	0.4b	(/.f64 x (sqrt.f64 2))
	1.6b	(pow.f64 (sqrt.f64 2) 5)
	9.3b	(+.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))))))

series39.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

33.0ms	(/.f64 (*.f64 x x) (sqrt.f64 2))
6.0ms	(/.f64 x (sqrt.f64 2))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
18×	`sqrt-prod_binary64`

Counts

2 → 70

Calls

2 calls:

4.0ms	(/.f64 (*.f64 x x) (sqrt.f64 2))
3.0ms	(/.f64 x (sqrt.f64 2))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

646×	`div-sub_binary64`
337×	`fma-neg_binary64`
312×	`sub-neg_binary64`
255×	`*-commutative_binary64`
209×	`fma-def_binary64`

Counts

82 → 81

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	1042
1	176	959
2	424	959
3	1113	959
4	1463	959
5	2059	959
6	3727	959
7	4909	959

prune258.0ms (4.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	154	2	156

Error

0.2b

Counts

156 → 2

Alt Table

Status	Error	Program
✓	19.9b	(-.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 (.f64 x x) (sqrt.f64 2)) 1/16))
✓	0.2b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Status

Error

Program

✓

19.9b

(-.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 (*.f64 x x) (sqrt.f64 2)) 1/16))

✓

0.2b

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

Compiler

Compiled 8975 to 7644 computations (14.8% saved)

regimes83.0ms (1.5%)

Accuracy

Total 0.0b remaining (7.1%)

Threshold costs 0.0b (7.1%)

Counts

17 → 1

Compiler

Compiled 1738 to 1497 computations (13.9% saved)

simplify2.0ms (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

end65.0ms (1.1%)

Compiler: Compiled 66 to 57 computations (13.6% saved)

Details

analyze754.0ms (13.4%)

sample2.8s (50.3%)

simplify45.0ms (0.8%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite6.0ms (0.1%)

simplify162.0ms (2.9%)

prune58.0ms (1%)

localize28.0ms (0.5%)

series82.0ms (1.5%)

rewrite133.0ms (2.4%)

simplify232.0ms (4.1%)

prune723.0ms (12.8%)

localize25.0ms (0.4%)

series39.0ms (0.7%)

rewrite10.0ms (0.2%)

simplify86.0ms (1.5%)

prune258.0ms (4.6%)

regimes83.0ms (1.5%)

simplify2.0ms (0%)

end65.0ms (1.1%)

Profiling