Details

analyze1.1s (18%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
2.0ms	69×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	63	10
4	69	10
5	68	10
6	68	10

prune1.0ms (0%)

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

13.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series29.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

29.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

1 → 23

Calls

1 calls:

5.0ms

(/.f64 (*.f64 a1 a2) (*.f64 b1 b2))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-/r*_binary64`
476×	`associate-l_binary64`
457×	`associate-*l/_binary64`
355×	`associate-*r/_binary64`
344×	`associate-r_binary64`

Counts

71 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	859
1	161	754
2	820	754
3	3799	754
4	4127	754
5	4478	754
6	4861	754
7	5308	754

prune30.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Error

0.0b

Counts

37 → 8

Alt Table

Status	Error	Program
	14.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2)))) (cbrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))))
✓	13.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	13.6b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
	14.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	11.6b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
▶	11.2b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	13.6b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 657 to 226 computations (65.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.4b	(/.f64 (*.f64 b1 b2) a2)
✓	7.0b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))

series49.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
13.0ms	(/.f64 (*.f64 b1 b2) a2)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`

Counts

2 → 73

Calls

2 calls:

5.0ms	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
4.0ms	(/.f64 (*.f64 b1 b2) a2)

simplify80.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
673×	`associate-/l*_binary64`
506×	`associate-/l/_binary64`
500×	`associate-*l/_binary64`
480×	`associate-/r/_binary64`

Counts

157 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1914
1	291	1782
2	1078	1770
3	4951	1770
4	5016	1770

prune95.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	122	7	129

Error

0.0b

Counts

129 → 7

Alt Table

Status	Error	Program
	11.9b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
▶	11.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	14.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	49.8b	(*.f64 (/.f64 (sqrt.f64 a1) (/.f64 b1 (sqrt.f64 a2))) (/.f64 (sqrt.f64 a1) (/.f64 b2 (sqrt.f64 a2))))
	13.6b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	24.0b	(*.f64 (/.f64 1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 a1 (/.f64 b2 (sqrt.f64 a2))))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 1813 to 498 computations (72.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.6b	(/.f64 a2 (*.f64 b2 b1))
✓	7.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))

series49.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
18.0ms	(/.f64 a2 (*.f64 b2 b1))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
3.0ms	(/.f64 a2 (*.f64 b2 b1))

simplify108.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
492×	`associate-l_binary64`
425×	`associate-*r/_binary64`
417×	`associate-*l/_binary64`
415×	`associate-r_binary64`

Counts

100 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	83	1170
1	194	1041
2	738	1041
3	3961	1041
4	4334	1041
5	4876	1041
6	4978	1041
7	4997	1041

prune40.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Error

0.0b

Counts

73 → 7

Alt Table

Status	Error	Program
	13.6b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.6b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
▶	11.9b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
✓	11.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	14.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	24.0b	(*.f64 (/.f64 1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 a1 (/.f64 b2 (sqrt.f64 a2))))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 991 to 307 computations (69% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	6.3b	(*.f64 b1 (/.f64 b2 a2))
✓	7.0b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))

series43.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
12.0ms	(*.f64 b1 (/.f64 b2 a2))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

8.0ms	(*.f64 b1 (/.f64 b2 a2))
4.0ms	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

932×	`times-frac_binary64`
529×	`associate-/l*_binary64`
394×	`associate-*l/_binary64`
385×	`associate-/r*_binary64`
361×	`associate-*r/_binary64`

Counts

144 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1527
1	256	1398
2	952	1398
3	4087	1395
4	4343	1395
5	4779	1395
6	4961	1395
7	4965	1395

prune47.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	7	96

Error

0.0b

Counts

96 → 7

Alt Table

Status	Error	Program
	13.6b	(.f64 (.f64 a1 a2) (/.f64 1 (*.f64 b1 b2)))
	12.6b	(*.f64 (/.f64 a1 b2) (/.f64 a2 b1))
✓	11.9b	(/.f64 a1 (*.f64 b1 (/.f64 b2 a2)))
✓	11.4b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	14.3b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	24.0b	(*.f64 (/.f64 1 (/.f64 b1 (sqrt.f64 a2))) (/.f64 a1 (/.f64 b2 (sqrt.f64 a2))))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 1204 to 359 computations (70.2% saved)

regimes1.8s (28.5%)

Accuracy

Total 2.5b remaining (99.2%)

Threshold costs 0b (0%)

Counts

83 → 5

Compiler

Compiled 9845 to 5950 computations (39.6% saved)

bsearch4.0ms (0.1%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	122
1	38	122
2	38	122

end65.0ms (1.1%)

Compiler: Compiled 430 to 155 computations (64% saved)

sample2.3s (37.9%)

Algorithm

1×

intervals

Results

602.0ms	8000×	body	128	valid
117.0ms	1767×	body	128	invalid

Compiler

Compiled 187 to 98 computations (47.6% saved)

Details

analyze1.1s (18%)

sample41.0ms (0.7%)

simplify9.0ms (0.1%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series29.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify86.0ms (1.4%)

prune30.0ms (0.5%)

localize6.0ms (0.1%)

series49.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify80.0ms (1.3%)

prune95.0ms (1.5%)

localize5.0ms (0.1%)

series49.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify108.0ms (1.8%)

prune40.0ms (0.6%)

localize5.0ms (0.1%)

series43.0ms (0.7%)

rewrite16.0ms (0.3%)

simplify114.0ms (1.8%)

prune47.0ms (0.8%)

regimes1.8s (28.5%)

bsearch4.0ms (0.1%)

simplify7.0ms (0.1%)

end65.0ms (1.1%)

sample2.3s (37.9%)

Profiling