Details

analyze1.3s (22.7%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0.8%	98.9%	0.3%	12
1.9%	97.5%	0.5%	13
3.9%	95.1%	1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.8s (31%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

1.0s	8256×	body	128	valid
640.0ms	1068×	body	8192	exit
118.0ms	925×	body	128	invalid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify8.0ms (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

prune2.0ms (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

11.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.9b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series30.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

30.0ms

(/.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))

simplify89.0ms (1.5%)

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

prune32.0ms (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
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	11.8b	(.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))))
✓	11.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.4b	(/.f64 (*.f64 a2 (/.f64 a1 b1)) b2)
▶	10.6b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	15.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.7b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))

Compiler

Compiled 657 to 226 computations (65.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.2b	(/.f64 (*.f64 a1 a2) b1)
✓	7.1b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)

series47.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
13.0ms	(/.f64 (*.f64 a1 a2) b1)

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

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

821×	`associate-/l*_binary64`
608×	`associate-/l/_binary64`
389×	`associate-*l/_binary64`
362×	`associate-/r*_binary64`
291×	`associate-*r/_binary64`

Counts

121 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	127	1639
1	304	1510
2	967	1510
3	4038	1510
4	4410	1510
5	4842	1510
6	5018	1510

prune82.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	100	8	108

Error

0.0b

Counts

108 → 8

Alt Table

Status	Error	Program
	12.8b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.9b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
	11.3b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	13.1b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	22.2b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 b2)) a2) (/.f64 (/.f64 1 (sqrt.f64 b2)) b1))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
▶	10.7b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 1558 to 461 computations (70.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	4.2b	(/.f64 (*.f64 a1 a2) b1)
✓	7.2b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

series32.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

32.0ms

(*.f64 (/.f64 (*.f64 a1 a2) b1) (/.f64 1 b2))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
22×	`add-cbrt-cube_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`prod-exp_binary64`
14×	`times-frac_binary64`

Counts

1 → 56

Calls

1 calls:

10.0ms

(*.f64 (/.f64 (*.f64 a1 a2) b1) (/.f64 1 b2))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
668×	`associate-/l*_binary64`
255×	`fma-neg_binary64`
241×	`sqr-pow_binary64`
238×	`unswap-sqr_binary64`

Counts

104 → 80

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	104	1350
1	257	1173
2	892	1173
3	3059	1173
4	3544	1173
5	4192	1173
6	4891	1173
7	4969	1173

prune69.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Error

0.0b

Counts

116 → 8

Alt Table

Status	Error	Program
	12.8b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.9b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
▶	11.3b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	13.1b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	22.2b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 b2)) a2) (/.f64 (/.f64 1 (sqrt.f64 b2)) b1))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	10.7b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 1814 to 723 computations (60.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b1) b2)
✓	10.9b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))

series44.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

33.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
11.0ms	(/.f64 (/.f64 1 b1) b2)

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`times-frac_binary64`
106×	`add-exp-log_binary64`
93×	`add-sqr-sqrt_binary64`
82×	`*-un-lft-identity_binary64`
81×	`add-cube-cbrt_binary64`

Counts

2 → 176

Calls

2 calls:

17.0ms	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
5.0ms	(/.f64 (/.f64 1 b1) b2)

simplify160.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

413×	`unswap-sqr_binary64`
407×	`associate-/r/_binary64`
404×	`*-commutative_binary64`
368×	`associate-/r*_binary64`
319×	`sqr-pow_binary64`

Counts

248 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	3471
1	399	3103
2	1588	3091
3	2613	3091
4	3184	3091
5	3960	3091
6	5072	3091

prune151.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	247	8	255

Error

0.0b

Counts

255 → 8

Alt Table

Status	Error	Program
	12.8b	(/.f64 (/.f64 a1 (/.f64 b1 a2)) b2)
	13.9b	(*.f64 (/.f64 (/.f64 a1 1) 1) (/.f64 (/.f64 a2 b1) b2))
	13.1b	(/.f64 a1 (/.f64 (*.f64 b1 b2) a2))
✓	11.3b	(.f64 (/.f64 (.f64 a1 a2) 1) (/.f64 (/.f64 1 b1) b2))
	13.1b	(/.f64 (*.f64 a1 (/.f64 a2 b1)) b2)
	22.2b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 b2)) a2) (/.f64 (/.f64 1 (sqrt.f64 b2)) b1))
	12.4b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
✓	10.7b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 4895 to 2535 computations (48.2% saved)

regimes1.4s (23.4%)

Accuracy

Total 3.2b remaining (99.3%)

Threshold costs 0b (0%)

Counts

72 → 5

Compiler

Compiled 9479 to 5541 computations (41.5% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	105
1	40	105
2	39	105

end279.0ms (4.8%)

Remove: (sort b1 b2)
Compiler: Compiled 704 to 310 computations (56% saved)

Details

analyze1.3s (22.7%)

sample1.8s (31%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series30.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify89.0ms (1.5%)

prune32.0ms (0.5%)

localize6.0ms (0.1%)

series47.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify103.0ms (1.8%)

prune82.0ms (1.4%)

localize6.0ms (0.1%)

series32.0ms (0.5%)

rewrite14.0ms (0.2%)

simplify103.0ms (1.8%)

prune69.0ms (1.2%)

localize8.0ms (0.1%)

series44.0ms (0.8%)

rewrite41.0ms (0.7%)

simplify160.0ms (2.7%)

prune151.0ms (2.6%)

regimes1.4s (23.4%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end279.0ms (4.8%)

Profiling