Details

analyze48.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample779.0ms (29%)

Results

746.0ms	8256×	body	128	valid
3.0ms	40×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series26.0ms (1%)

Counts

1 → 24

Calls

1 calls:

26.0ms

(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite44.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
485×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	2102	13

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

43.0ms

(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

463×	`times-frac_binary64`
306×	`associate-+l+_binary64`
281×	`associate-/l*_binary64`
270×	`fma-def_binary64`
240×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	782
1	280	745
2	982	729

Stop Event

1×	node limit

Counts

59 → 49

prune49.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	47	2	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	3	50

Error

0.2b

Counts

50 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
▶	10.0b	(+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))))
	10.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 1290 to 644 computations (50.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 1 (exp.f64 b)))
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
✓	0.0b	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
✓	0.0b	(-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))

series149.0ms (5.6%)

Counts

4 → 40

Calls

4 calls:

72.0ms	(-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))
56.0ms	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
18.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
3.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)

rewrite96.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

467×	`fma-def_binary64`
251×	`egg-rr`
235×	`fma-neg_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	248	53
2	3563	53

Stop Event

1×	node limit

Counts

4 → 251

Calls

4 calls:

90.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
90.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) 2)
90.0ms	(/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))
90.0ms	(-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2)))

simplify43.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

629×	`cancel-sign-sub-inv_binary64`
563×	`fma-neg_binary64`
356×	`fma-def_binary64`
215×	`distribute-lft-out_binary64`
206×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	819
1	238	790
2	685	743
3	2367	691

Stop Event

1×	node limit

Counts

291 → 289

prune285.0ms (10.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	289	3	292

Error

0.2b

Counts

292 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	10.0b	(+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))))
▶	10.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 9835 to 6367 computations (35.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))

series9.0ms (0.3%)

Counts

2 → 8

Calls

2 calls:

7.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite43.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`log1p-expm1-u_binary64`
554×	`expm1-log1p-u_binary64`
253×	`log-prod_binary64`
129×	`fma-def_binary64`
104×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	125	15
2	1543	15

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

42.0ms	(+.f64 1 (exp.f64 b))
42.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))

simplify31.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1075×	`fma-neg_binary64`
445×	`unswap-sqr_binary64`
346×	`fma-def_binary64`
328×	`cancel-sign-sub-inv_binary64`
204×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	85
1	79	79
2	211	73
3	664	66
4	1780	66
5	3453	66

Stop Event

1×	node limit

Counts

77 → 83

prune83.0ms (3.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	83	3	86

Error

0.2b

Counts

86 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	10.0b	(+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))))
▶	10.7b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2) 2)

Compiler

Compiled 955 to 677 computations (29.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 b)) -1/2)
✓	0.5b	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2) 2)

series285.0ms (10.6%)

Counts

2 → 24

Calls

2 calls:

149.0ms	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2) 2)
135.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) -1/2)

rewrite42.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`log1p-expm1-u_binary64`
733×	`expm1-log1p-u_binary64`
143×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	191	18
2	2088	18

Stop Event

1×	node limit

Counts

2 → 41

Calls

2 calls:

42.0ms	(pow.f64 (+.f64 1 (exp.f64 b)) -1/2)
41.0ms	(pow.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2) 2)

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

563×	`cancel-sign-sub-inv_binary64`
527×	`fma-neg_binary64`
424×	`unswap-sqr_binary64`
305×	`*-commutative_binary64`
237×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	336
1	124	284
2	402	272
3	1451	263
4	4171	263

Stop Event

1×	node limit

Counts

65 → 55

prune77.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	103	3	106

Error

0.2b

Counts

106 → 3

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	10.0b	(+.f64 (/.f64 1 (+.f64 1 (exp.f64 b))) (-.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (/.f64 a (pow.f64 (+.f64 1 (exp.f64 b)) 2))))
	10.9b	(pow.f64 (expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2))) 2)

Compiler

Compiled 1385 to 1055 computations (23.8% saved)

regimes440.0ms (16.4%)

Accuracy

Total 0.3b remaining (49.2%)

Threshold costs 0.3b (49.2%)

Counts

106 → 1

Compiler

Compiled 8332 to 6567 computations (21.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	24	15
4	25	15

Stop Event

1×

saturated

end57.0ms (2.1%)

Compiler: Compiled 68 to 50 computations (26.5% saved)

Details

analyze48.0ms (1.8%)

sample779.0ms (29%)

simplify7.0ms (0.3%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

series26.0ms (1%)

rewrite44.0ms (1.6%)

simplify29.0ms (1.1%)

prune49.0ms (1.8%)

localize10.0ms (0.4%)

series149.0ms (5.6%)

rewrite96.0ms (3.6%)

simplify43.0ms (1.6%)

prune285.0ms (10.6%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite43.0ms (1.6%)

simplify31.0ms (1.2%)

prune83.0ms (3.1%)

localize6.0ms (0.2%)

series285.0ms (10.6%)

rewrite42.0ms (1.6%)

simplify35.0ms (1.3%)

prune77.0ms (2.9%)

regimes440.0ms (16.4%)

simplify2.0ms (0.1%)

end57.0ms (2.1%)

Profiling