Details

analyze63.0ms (2.8%)

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)

sample30.0ms (1.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify49.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	39	28
2	177	19
3	904	13
4	2320	13
5	4069	13
6	5047	13

prune4.0ms (0.2%)

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))))
	46.3b	(/.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))

Compiler

Compiled 82 to 58 computations (29.3% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.4b	(/.f64 1 (*.f64 i i))

rewrite93.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

3 → 104

Calls

3 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
4.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 1535 to 1136 computations (26% saved)

series32.0ms (1.4%)

Error

0.0b

Counts

3 → 19

Calls

3 calls:

12.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
7.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
5.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 405 to 355 computations (12.3% saved)

simplify147.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

592×	`cancel-sign-sub-inv_binary64`
459×	`div-sub_binary64`
293×	`neg-mul-1_binary64`
276×	`neg-sub0_binary64`
217×	`unswap-sqr_binary64`

Counts

123 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	166	1892
1	331	1759
2	713	1642
3	2094	1642
4	4013	1570
5	4454	1570
6	4997	1570
7	4868	1570

prune71.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	33.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))

Compiler

Compiled 941 to 699 computations (25.7% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite161.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

3 → 161

Calls

3 calls:

24.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
7.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
7.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

Compiler

Compiled 3456 to 3034 computations (12.2% saved)

series52.0ms (2.4%)

Error

Counts

3 → 34

Calls

3 calls:

14.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
12.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
10.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

Compiler

Compiled 1044 to 893 computations (14.5% saved)

simplify157.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

572×	`associate-*l/_binary64`
496×	`associate-/l*_binary64`
285×	`associate-/l/_binary64`
182×	`times-frac_binary64`
179×	`associate-/r*_binary64`

Counts

195 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	4066
1	664	3755
2	1971	3640
3	4553	3640
4	4969	3640
5	4921	3640

prune66.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	33.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))

Compiler

Compiled 1932 to 1629 computations (15.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite33.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`cancel-sign-sub-inv_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

2 → 37

Calls

2 calls:

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

Compiler

Compiled 585 to 371 computations (36.6% saved)

series18.0ms (0.8%)

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)

simplify82.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

702×	`unsub-neg_binary64`
280×	`*-commutative_binary64`
248×	`cancel-sign-sub-inv_binary64`
246×	`neg-sub0_binary64`
246×	`neg-mul-1_binary64`

Counts

46 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	541
1	208	502
2	611	487
3	1355	487
4	3356	487
5	4990	487
6	4912	487

prune13.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	33.5b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))

Compiler

Compiled 311 to 207 computations (33.4% saved)

regimes127.0ms (5.7%)

Accuracy

Total 0.1b remaining (95.9%)

Threshold costs 0.1b (95.9%)

Compiler

Compiled 1302 to 1055 computations (19% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample993.0ms (44.9%)

Algorithm

1×

intervals

Results

539.0ms	8000×	body	128	valid
111.0ms	8000×	pre	128	true

Compiler

Compiled 83 to 64 computations (22.9% saved)

Details

analyze63.0ms (2.8%)

sample30.0ms (1.4%)

simplify49.0ms (2.2%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

rewrite93.0ms (4.2%)

series32.0ms (1.4%)

simplify147.0ms (6.7%)

prune71.0ms (3.2%)

localize7.0ms (0.3%)

rewrite161.0ms (7.3%)

series52.0ms (2.4%)

simplify157.0ms (7.1%)

prune66.0ms (3%)

localize5.0ms (0.2%)

rewrite33.0ms (1.5%)

series18.0ms (0.8%)

simplify82.0ms (3.7%)

prune13.0ms (0.6%)

regimes127.0ms (5.7%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample993.0ms (44.9%)

Profiling