Details

analyze37.0ms (0.7%)

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
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample32.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	45×	body	1024	valid
8.0ms	55×	body	512	valid
7.0ms	137×	body	128	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

9.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
✓	2.1b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite172.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

55.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

series14.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

simplify446.0ms (8%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-neg_binary64`
457×	`times-frac_binary64`
236×	`fma-def_binary64`
186×	`sub-neg_binary64`
176×	`exp-prod_binary64`

Counts

716 → 1385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	19278
1	989	13709
2	2519	9843
3	4349	9843
4	4815	9843

prune861.0ms (15.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1383	2	1385
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1383	3	1386

Error

0.1b

Counts

1386 → 3

Alt Table

Status	Error	Program
	30.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	26.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 33668 to 26196 computations (22.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	0.0b	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
✓	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	18.5b	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`associate-*l/_binary64`
39×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

4 → 181

Calls

4 calls:

18.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
12.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
12.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))

series25.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
9.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))
3.0ms	(-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2))
1.0ms	(+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (*.f64 (+.f64 x 1) x) 1))

simplify192.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

712×	`associate-r_binary64`
442×	`distribute-rgt-in_binary64`
409×	`distribute-lft-in_binary64`
342×	`*-commutative_binary64`
307×	`fma-def_binary64`

Counts

229 → 420

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6234
1	1064	4993
2	4286	4902
3	4952	4894
4	4946	4894

prune368.0ms (6.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	419	1	420
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	419	4	423

Error

0.1b

Counts

423 → 4

Alt Table

Status	Error	Program
	30.7b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
✓	9.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
▶	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
✓	26.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 1 x) (.f64 (+.f64 x 1) 2)) (-.f64 x 1)) (.f64 (.f64 (+.f64 x 1) x) 1)) (.f64 (*.f64 (+.f64 x 1) x) (-.f64 x 1)))

Compiler

Compiled 16786 to 12478 computations (25.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x 1) x)
	0.1b	(.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1))
✓	0.1b	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`associate-*l/_binary64`
8×	`associate-/r/_binary64`
8×	`*-un-lft-identity_binary64`

Counts

2 → 56

Calls

2 calls:

8.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))
4.0ms	(*.f64 (+.f64 x 1) x)

series11.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (+.f64 x 1) x)
5.0ms	(/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 x 1)))

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

520×	`associate-/r*_binary64`
506×	`distribute-rgt-in_binary64`
466×	`distribute-lft-in_binary64`
324×	`fma-def_binary64`
187×	`times-frac_binary64`

Counts

80 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1295
1	365	957
2	1226	936
3	4668	936
4	4964	936
5	4951	936

prune194.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	268	6	274
Fresh	1	0	1
Picked	1	0	1
Done	2	0	2
Total	272	6	278

Error

Counts

278 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
▶	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
	17.4b	(/.f64 2 (.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (sqrt.f64 (+.f64 x 1)) x)) (-.f64 x 1)))
	0.5b	(/.f64 (sqrt.f64 2) (/.f64 (fma.f64 x x -1) (/.f64 (sqrt.f64 2) x)))
	3.1b	(.f64 (/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 (.f64 x x) (*.f64 1 1)))) (+.f64 x 1))

Compiler

Compiled 3916 to 2878 computations (26.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
✓	0.5b	(/.f64 2 (fma.f64 x x x))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`times-frac_binary64`
136×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
80×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`

Counts

2 → 159

Calls

2 calls:

8.0ms	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
2.0ms	(/.f64 2 (fma.f64 x x x))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
4.0ms	(/.f64 2 (fma.f64 x x x))

simplify194.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-neg_binary64`
414×	`associate-/r*_binary64`
384×	`associate-/l/_binary64`
300×	`fma-def_binary64`
235×	`times-frac_binary64`

Counts

183 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4872
1	618	4739
2	1619	4586
3	4340	4553
4	4701	4553
5	4955	4553

prune270.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	321	6	327

Error

Counts

327 → 6

Alt Table

Status	Error	Program
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.1b	(*.f64 (/.f64 1 (fma.f64 x x x)) (/.f64 2 (-.f64 x 1)))
✓	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (-.f64 x 1))
	0.5b	(/.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 (-.f64 (pow.f64 x 3) x) (sqrt.f64 2)))
	2.8b	(*.f64 (/.f64 (/.f64 2 (fma.f64 x x x)) (fma.f64 x x -1)) (+.f64 x 1))
	3.1b	(.f64 (/.f64 2 (.f64 (.f64 (+.f64 x 1) x) (-.f64 (.f64 x x) (*.f64 1 1)))) (+.f64 x 1))

Compiler

Compiled 4705 to 2761 computations (41.3% saved)

regimes428.0ms (7.7%)

Accuracy

Total 0.1b remaining (91.1%)

Threshold costs 0.1b (91.1%)

Compiler

Compiled 4188 to 3132 computations (25.2% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	13	14
2	14	14
3	12	14

end1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample2.1s (36.8%)

Algorithm

1×

intervals

Results

503.0ms	1279×	body	1024	valid
458.0ms	1531×	body	512	valid
432.0ms	4448×	body	128	valid
143.0ms	742×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 111 to 81 computations (27% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze37.0ms (0.7%)

sample32.0ms (0.6%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite172.0ms (3.1%)

series14.0ms (0.3%)

simplify446.0ms (8%)

prune861.0ms (15.4%)

localize13.0ms (0.2%)

rewrite69.0ms (1.2%)

series25.0ms (0.5%)

simplify192.0ms (3.4%)

prune368.0ms (6.6%)

localize8.0ms (0.1%)

rewrite16.0ms (0.3%)

series11.0ms (0.2%)

simplify95.0ms (1.7%)

prune194.0ms (3.5%)

localize6.0ms (0.1%)

rewrite26.0ms (0.5%)

series10.0ms (0.2%)

simplify194.0ms (3.5%)

prune270.0ms (4.8%)

regimes428.0ms (7.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample2.1s (36.8%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22