Details

analyze396.0ms (6.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample3.8s (63.7%)

Results

2.5s	2508×	body	8192	exit
1.0s	7630×	body	128	valid
144.0ms	228×	body	1024	valid
98.0ms	242×	body	512	valid
38.0ms	155×	body	256	valid
8.0ms	63×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 24 to 18 computations (25% saved)

preprocess43.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

732×	`times-frac_binary64`
438×	`associate-/r/_binary64`
300×	`fma-def_binary64`
232×	`unswap-sqr_binary64`
157×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	32	22
2	45	22
3	71	22
4	101	22
5	150	22
6	231	22
7	320	22
8	425	22
9	543	22
10	635	22
11	675	22
12	823	22
13	1264	22
14	2823	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

369×	`times-frac_binary64`
363×	`associate-l_binary64`
285×	`associate-/l/_binary64`
280×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	30	11
3	47	11
4	66	11
5	100	11
6	154	11
7	205	11
8	273	11
9	352	11
10	414	11
11	440	11
12	519	11
13	747	11
14	1549	11
15	4642	11

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.2b	(log1p.f64 (exp.f64 x))

series212.0ms (3.5%)

Counts

2 → 36

Calls

9 calls:

78.0ms	(log1p.f64 (exp.f64 x))	x	inf
73.0ms	(log1p.f64 (exp.f64 x))	x	-inf
13.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	y	0
13.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	x	-inf
12.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	y	inf

rewrite45.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

792×	`pow1_binary64`
733×	`expm1-log1p-u_binary64`
732×	`log1p-expm1-u_binary64`
78×	`add-sqr-sqrt_binary64`
77×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	16
2	2012	16

Stop Event

1×	node limit

Counts

2 → 55

simplify38.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-def_binary64`
237×	`distribute-lft-out_binary64`
196×	`sub-neg_binary64`
194×	`*-commutative_binary64`
188×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	356
1	81	350
2	201	337
3	652	321
4	2594	321
5	4861	321

Stop Event

1×	node limit

Counts

91 → 74

prune50.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Error

Counts

75 → 3

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	14.2b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
	12.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3))))

Compiler

Compiled 1128 to 431 computations (61.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	0.2b	(log1p.f64 (exp.f64 x))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.7b	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))

series345.0ms (5.7%)

Counts

3 → 48

Calls

12 calls:

71.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)	x	inf
70.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)	x	-inf
69.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))	x	inf
66.0ms	(cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3))	x	-inf
16.0ms	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))	y	0

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

885×	`expm1-log1p-u_binary64`
884×	`log1p-expm1-u_binary64`
97×	`add-sqr-sqrt_binary64`
94×	`pow1_binary64`
93×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	214	24
2	2471	24

Stop Event

1×	node limit

Counts

3 → 81

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

832×	`fma-neg_binary64`
522×	`associate-+l+_binary64`
329×	`fma-def_binary64`
318×	`distribute-lft-out_binary64`
310×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	559
1	167	551
2	470	524
3	1812	506
4	4621	506

Stop Event

1×	node limit

Counts

129 → 108

prune85.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	133	3	136

Error

Counts

136 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
	14.2b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
▶	12.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3))))

Compiler

Compiled 2080 to 958 computations (53.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
✓	12.0b	(/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)))

series261.0ms (4.3%)

Counts

3 → 60

Calls

15 calls:

75.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)	x	inf
73.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)	x	-inf
21.0ms	(.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))	y	0
16.0ms	(.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))	y	-inf
15.0ms	(.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))	x	-inf

rewrite41.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

182×	`add-sqr-sqrt_binary64`
181×	`pow1_binary64`
177×	`*-un-lft-identity_binary64`
174×	`add-log-exp_binary64`
174×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	71
1	374	37

Stop Event

1×	node limit

Counts

3 → 87

simplify45.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-def_binary64`
656×	`associate-/l*_binary64`
472×	`associate-/r*_binary64`
126×	`associate-/r/_binary64`
112×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1773
1	401	1735
2	1562	1603

Stop Event

1×	node limit

Counts

147 → 133

prune137.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
▶	14.2b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
✓	12.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3))))

Compiler

Compiled 6116 to 2909 computations (52.4% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))

series10.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	0
2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	inf
2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	-inf
1.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	x	0
1.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	x	-inf

rewrite43.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`prod-diff_binary64`
409×	`log-prod_binary64`
225×	`fma-def_binary64`
181×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	208	14
2	2499	14

Stop Event

1×	node limit

Counts

1 → 27

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-neg_binary64`
547×	`cancel-sign-sub-inv_binary64`
410×	`fma-def_binary64`
238×	`associate-l_binary64`
223×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	424
1	49	370
2	109	349
3	286	282
4	825	282
5	2321	282

Stop Event

1×	node limit

Counts

51 → 40

prune27.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	40	3	43

Error

Counts

43 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (cbrt.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3)) (*.f64 x y))
✓	14.2b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
✓	12.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 2) (.f64 (.f64 x y) (+.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)))) (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3))))

Compiler

Compiled 638 to 470 computations (26.3% saved)

regimes145.0ms (2.4%)

Accuracy

Total 0.3b remaining (58.5%)

Threshold costs 0.3b (58.5%)

Counts

47 → 1

Compiler

Compiled 1801 to 1320 computations (26.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	18	11
2	29	11
3	35	11
4	39	11
5	40	11

Stop Event

1×

saturated

end62.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 75 to 48 computations (36% saved)

Details

analyze396.0ms (6.6%)

sample3.8s (63.7%)

preprocess43.0ms (0.7%)

simplify38.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series212.0ms (3.5%)

rewrite45.0ms (0.8%)

simplify38.0ms (0.6%)

prune50.0ms (0.8%)

localize11.0ms (0.2%)

series345.0ms (5.7%)

rewrite53.0ms (0.9%)

simplify44.0ms (0.7%)

prune85.0ms (1.4%)

localize16.0ms (0.3%)

series261.0ms (4.3%)

rewrite41.0ms (0.7%)

simplify45.0ms (0.7%)

prune137.0ms (2.3%)

localize8.0ms (0.1%)

series10.0ms (0.2%)

rewrite43.0ms (0.7%)

simplify29.0ms (0.5%)

prune27.0ms (0.4%)

regimes145.0ms (2.4%)

simplify3.0ms (0%)

end62.0ms (1%)

Profiling