Details

analyze890.0ms (21.5%)

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)

sample1.2s (28%)

Symmetry

(sort a1 a2)

(sort b1 b2)

Results

901.0ms	8256×	body	128	valid
220.0ms	1938×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	67	10
4	79	10
5	79	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

8.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	14.5b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
✓	6.1b	(/.f64 a2 (*.f64 b1 b2))

series46.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
16.0ms	(/.f64 a2 (*.f64 b1 b2))

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	2305	17

Stop Event

1×	node limit

Counts

2 → 68

Calls

2 calls:

41.0ms	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
41.0ms	(/.f64 a2 (*.f64 b1 b2))

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	20	732
2	41	732
3	69	732
4	79	732
5	79	732

Stop Event

1×

saturated

Counts

152 → 71

prune50.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	9	71
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Error

Counts

73 → 9

Alt Table

Status	Error	Program
▶	10.7b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b1) b2)))
	14.9b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	13.4b	(/.f64 (/.f64 (*.f64 a2 a1) b2) b1)
	11.8b	(.f64 a1 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (.f64 b1 b2)))))
	11.8b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
	16.0b	(/.f64 (/.f64 (*.f64 a2 a1) b1) b2)
	14.6b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))
	11.3b	(.f64 a1 (neg.f64 (/.f64 a2 (.f64 b1 (neg.f64 b2)))))
	12.4b	(*.f64 a1 (pow.f64 (cbrt.f64 (/.f64 (/.f64 a2 b1) b2)) 3))

Compiler

Compiled 1001 to 430 computations (57% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b1) b2)
✓	5.3b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b1) b2)))
✓	5.4b	(*.f64 a2 (/.f64 (/.f64 1 b1) b2))

series55.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

30.0ms	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b1) b2)))
16.0ms	(*.f64 a2 (/.f64 (/.f64 1 b1) b2))
9.0ms	(/.f64 (/.f64 1 b1) b2)

rewrite45.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`log-prod_binary64`
191×	`pow1/3_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
173×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	207	24
2	2737	24

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

43.0ms	(/.f64 (/.f64 1 b1) b2)
43.0ms	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b1) b2)))
43.0ms	(*.f64 a2 (/.f64 (/.f64 1 b1) b2))

simplify31.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	900
1	26	900
2	49	900
3	77	900
4	87	900
5	87	900

Stop Event

1×

saturated

Counts

202 → 98

prune73.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Error

Counts

107 → 8

Alt Table

Status	Error	Program
	14.9b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	13.4b	(/.f64 (/.f64 (*.f64 a2 a1) b2) b1)
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.8b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
	16.0b	(/.f64 (/.f64 (*.f64 a2 a1) b1) b2)
	14.6b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))
▶	10.7b	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))
	12.4b	(*.f64 a1 (pow.f64 (cbrt.f64 (/.f64 (/.f64 a2 b1) b2)) 3))

Compiler

Compiled 1388 to 683 computations (50.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 b1) (/.f64 1 b2))
✓	5.3b	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))
✓	5.4b	(.f64 a2 (.f64 (/.f64 1 b1) (/.f64 1 b2)))

series53.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

27.0ms	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))
17.0ms	(.f64 a2 (.f64 (/.f64 1 b1) (/.f64 1 b2)))
9.0ms	(*.f64 (/.f64 1 b1) (/.f64 1 b2))

rewrite46.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

612×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
186×	`log-pow_binary64`
114×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	229	24
2	3010	24

Stop Event

1×	node limit

Counts

3 → 96

Calls

3 calls:

45.0ms	(*.f64 (/.f64 1 b1) (/.f64 1 b2))
45.0ms	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))
45.0ms	(.f64 a2 (.f64 (/.f64 1 b1) (/.f64 1 b2)))

simplify27.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	900
1	26	900
2	49	900
3	77	900
4	87	900
5	87	900

Stop Event

1×

saturated

Counts

204 → 100

prune65.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Error

Counts

108 → 8

Alt Table

Status	Error	Program
	14.9b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	13.4b	(/.f64 (/.f64 (*.f64 a2 a1) b2) b1)
▶	10.6b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b2) b1)))
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.8b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
	16.0b	(/.f64 (/.f64 (*.f64 a2 a1) b1) b2)
	14.6b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))
✓	10.7b	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))

Compiler

Compiled 1337 to 659 computations (50.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 b2) b1)
✓	5.3b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b2) b1)))
✓	5.4b	(*.f64 a2 (/.f64 (/.f64 1 b2) b1))

series51.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

27.0ms	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b2) b1)))
16.0ms	(*.f64 a2 (/.f64 (/.f64 1 b2) b1))
8.0ms	(/.f64 (/.f64 1 b2) b1)

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`log-prod_binary64`
191×	`pow1/3_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`
173×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	207	24
2	2737	24

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

42.0ms	(/.f64 (/.f64 1 b2) b1)
42.0ms	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b2) b1)))
42.0ms	(*.f64 a2 (/.f64 (/.f64 1 b2) b1))

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	900
1	26	900
2	49	900
3	77	900
4	87	900
5	87	900

Stop Event

1×

saturated

Counts

202 → 98

prune62.0ms (1.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	98	8	106

Error

Counts

106 → 8

Alt Table

Status	Error	Program
	14.9b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	13.4b	(/.f64 (/.f64 (*.f64 a2 a1) b2) b1)
✓	10.6b	(.f64 a1 (.f64 a2 (/.f64 (/.f64 1 b2) b1)))
	11.3b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.8b	(/.f64 a1 (/.f64 b2 (/.f64 a2 b1)))
	16.0b	(/.f64 (/.f64 (*.f64 a2 a1) b1) b2)
	14.6b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))
✓	10.7b	(.f64 a1 (.f64 a2 (*.f64 (/.f64 1 b1) (/.f64 1 b2))))

Compiler

Compiled 1292 to 619 computations (52.1% saved)

regimes920.0ms (22.2%)

Accuracy

Total 3.3b remaining (99.3%)

Threshold costs 0b (0%)

Counts

49 → 5

Compiler

Compiled 4821 to 3269 computations (32.2% saved)

bsearch1.0ms (0%)

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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	110
1	38	110

Stop Event

1×

saturated

end387.0ms (9.3%)

Compiler: Compiled 568 to 212 computations (62.7% saved)

Details

analyze890.0ms (21.5%)

sample1.2s (28%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series46.0ms (1.1%)

rewrite42.0ms (1%)

simplify23.0ms (0.5%)

prune50.0ms (1.2%)

localize7.0ms (0.2%)

series55.0ms (1.3%)

rewrite45.0ms (1.1%)

simplify31.0ms (0.8%)

prune73.0ms (1.8%)

localize9.0ms (0.2%)

series53.0ms (1.3%)

rewrite46.0ms (1.1%)

simplify27.0ms (0.7%)

prune65.0ms (1.6%)

localize7.0ms (0.2%)

series51.0ms (1.2%)

rewrite44.0ms (1.1%)

simplify30.0ms (0.7%)

prune62.0ms (1.5%)

regimes920.0ms (22.2%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end387.0ms (9.3%)

Profiling