Details

analyze168.0ms (5.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample32.0ms (1.1%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify64.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	47.2b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 82 to 58 computations (29.3% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.8b	(/.f64 1 (*.f64 i i))

rewrite141.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

42×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 146

Calls

3 calls:

18.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
16.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
15.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 2722 to 1879 computations (31% saved)

series30.0ms (1.1%)

Error

0.0b

Counts

3 → 21

Calls

3 calls:

10.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
5.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 430 to 377 computations (12.3% saved)

simplify113.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

530×	`associate-l_binary64`
444×	`fma-neg_binary64`
416×	`fma-def_binary64`
300×	`times-frac_binary64`
249×	`associate-*l/_binary64`

Counts

167 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2028
1	417	1826
2	1221	1448
3	4397	1448
4	4785	1448

prune58.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	31.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
	47.2b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 1166 to 962 computations (17.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 4 (pow.f64 i -2))
0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

rewrite90.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-cube-cbrt_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`flip3--_binary64`
8×	`add-log-exp_binary64`

Counts

2 → 94

Calls

2 calls:

15.0ms	(-.f64 4 (pow.f64 i -2))
14.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 1658 to 1323 computations (20.2% saved)

series24.0ms (0.8%)

Error

Counts

2 → 18

Calls

2 calls:

10.0ms	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
9.0ms	(-.f64 4 (pow.f64 i -2))

Compiler

Compiled 370 to 323 computations (12.7% saved)

simplify105.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-neg_binary64`
356×	`associate-l_binary64`
314×	`fma-def_binary64`
305×	`associate-r_binary64`
163×	`distribute-rgt-in_binary64`

Counts

112 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1777
1	365	1558
2	1017	1345
3	3473	1297
4	4864	1297
5	4787	1297

prune34.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	55	3	58

Error

Counts

58 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
▶	31.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
	47.2b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 763 to 590 computations (22.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.2b	(.f64 (.f64 i i) -1/4)

rewrite77.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-cube-cbrt_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-log-exp_binary64`

Counts

2 → 82

Calls

2 calls:

18.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
14.0ms	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 1533 to 903 computations (41.1% saved)

series18.0ms (0.6%)

Error

Counts

2 → 9

Calls

2 calls:

11.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
5.0ms	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 174 to 141 computations (19% saved)

simplify116.0ms (4%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
310×	`prod-exp_binary64`
233×	`cancel-sign-sub-inv_binary64`
209×	`*-commutative_binary64`
207×	`exp-prod_binary64`

Counts

91 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1203
1	272	1083
2	887	997
3	3010	970
4	3628	970
5	4918	970
6	4811	970

prune23.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	56	3	59

Error

Counts

59 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
✓	31.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
▶	47.2b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 713 to 458 computations (35.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
0.1b	(.f64 (.f64 i i) (*.f64 i i))
17.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
43.0b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

rewrite203.0ms (7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

54×	`add-exp-log_binary64`
33×	`prod-exp_binary64`
33×	`add-cube-cbrt_binary64`
22×	`add-cbrt-cube_binary64`
18×	`pow2_binary64`

Counts

4 → 184

Calls

4 calls:

32.0ms	(.f64 (.f64 i i) (*.f64 i i))
22.0ms	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
20.0ms	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
19.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

Compiler

Compiled 5618 to 3455 computations (38.5% saved)

series40.0ms (1.4%)

Error

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
9.0ms	(-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1)
6.0ms	(.f64 (.f64 i i) (*.f64 i i))
5.0ms	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

Compiler

Compiled 806 to 614 computations (23.8% saved)

simplify118.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
520×	`fma-neg_binary64`
333×	`times-frac_binary64`
295×	`log-prod_binary64`
264×	`unswap-sqr_binary64`

Counts

208 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	2951
1	515	2152
2	2801	2016
3	4418	2016
4	4874	2016

prune76.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))
	31.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
	47.2b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 2345 to 1462 computations (37.7% saved)

regimes270.0ms (9.4%)

Accuracy

Total 0.3b remaining (99.2%)

Threshold costs 0.3b (99.2%)

Compiler

Compiled 4038 to 3113 computations (22.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	20	13

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.0s (36.4%)

Algorithm

1×

intervals

Results

607.0ms	8000×	body	128	valid
118.0ms	8000×	pre	128	true

Compiler

Compiled 85 to 60 computations (29.4% saved)

Details

analyze168.0ms (5.8%)

sample32.0ms (1.1%)

simplify64.0ms (2.2%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

rewrite141.0ms (4.9%)

series30.0ms (1.1%)

simplify113.0ms (3.9%)

prune58.0ms (2%)

localize5.0ms (0.2%)

rewrite90.0ms (3.1%)

series24.0ms (0.8%)

simplify105.0ms (3.6%)

prune34.0ms (1.2%)

localize5.0ms (0.2%)

rewrite77.0ms (2.7%)

series18.0ms (0.6%)

simplify116.0ms (4%)

prune23.0ms (0.8%)

localize9.0ms (0.3%)

rewrite203.0ms (7%)

series40.0ms (1.4%)

simplify118.0ms (4.1%)

prune76.0ms (2.6%)

regimes270.0ms (9.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (36.4%)

Profiling