Details

analyze105.0ms (2.6%)

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
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample1.1s (25.8%)

Symmetry

(sort x y)

Results

928.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify136.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

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

19.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	19.6b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
▶	19.6b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
✓	0.0b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
✓	19.4b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

series50.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

34.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
11.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
5.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

rewrite100.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

647×	`fma-def_binary64`
312×	`fma-neg_binary64`
204×	`log1p-udef_binary64`
202×	`expm1-udef_binary64`
181×	`egg-rr`

Counts

3 → 181

Calls

3 calls:

96.0ms	(*.f64 (+.f64 x y) (+.f64 x y))
96.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
96.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	238	45
2	3601	45
3	5115	45
0	0	0
1	0	0

simplify78.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

295×	`associate-+r+_binary64`
295×	`fma-def_binary64`
239×	`cancel-sign-sub-inv_binary64`
229×	`associate-/r*_binary64`
228×	`times-frac_binary64`

Counts

253 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2982
1	833	2847
2	3655	2817
3	4983	2817

prune237.0ms (5.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	241	6	247
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	243	6	249

Error

3.3b

Counts

249 → 6

Alt Table

Status	Error	Program
▶	4.2b	(.f64 (/.f64 y (+.f64 x y)) (/.f64 x (.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
	12.2b	(.f64 x (.f64 y (/.f64 1 (*.f64 (pow.f64 (+.f64 x y) 2) (+.f64 (+.f64 x y) 1)))))
	24.1b	(.f64 (/.f64 x (.f64 (+.f64 x y) (sqrt.f64 (+.f64 (+.f64 x y) 1)))) (/.f64 y (*.f64 (+.f64 x y) (sqrt.f64 (+.f64 (+.f64 x y) 1)))))
	9.9b	(*.f64 x (/.f64 1 (/.f64 (pow.f64 (+.f64 x y) 2) (/.f64 y (+.f64 (+.f64 x y) 1)))))
	16.6b	(.f64 (/.f64 1 (+.f64 x y)) (/.f64 (.f64 x y) (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
	8.7b	(*.f64 (/.f64 x (+.f64 (+.f64 x y) 1)) (/.f64 y (pow.f64 (+.f64 x y) 2)))

Compiler

Compiled 7216 to 3573 computations (50.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x y))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))
✓	0.1b	(.f64 (/.f64 y (+.f64 x y)) (/.f64 x (.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
✓	15.3b	(/.f64 x (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1)))

series71.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(.f64 (/.f64 y (+.f64 x y)) (/.f64 x (.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
23.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1)))
7.0ms	(/.f64 y (+.f64 x y))
7.0ms	(*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))

rewrite101.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

763×	`prod-diff_binary64`
189×	`egg-rr`
120×	`add-sqr-sqrt_binary64`
115×	`log1p-expm1-u_binary64`
115×	`expm1-log1p-u_binary64`

Counts

4 → 189

Calls

4 calls:

97.0ms	(/.f64 y (+.f64 x y))
97.0ms	(*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))
97.0ms	(.f64 (/.f64 y (+.f64 x y)) (/.f64 x (.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))))
96.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	61
1	237	58
2	3652	58
3	5189	58
0	0	0
1	0	0

simplify81.0ms (2%)

Algorithm

1×	egg-herbie

Rules

413×	`associate-+r+_binary64`
358×	`fma-def_binary64`
313×	`times-frac_binary64`
307×	`associate-/r*_binary64`
298×	`associate-+l+_binary64`

Counts

285 → 279

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	363	4455
1	1195	4312
2	5201	4312

prune283.0ms (7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	274	5	279
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	279	6	285

Error

0.0b

Counts

285 → 6

Alt Table

Status	Error	Program
	47.6b	(*.f64 (/.f64 y (+.f64 x y)) (pow.f64 (/.f64 (sqrt.f64 x) (hypot.f64 (+.f64 x y) (sqrt.f64 (+.f64 x y)))) 2))
	9.9b	(*.f64 x (/.f64 1 (/.f64 (pow.f64 (+.f64 x y) 2) (/.f64 y (+.f64 (+.f64 x y) 1)))))
▶	0.1b	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
	0.1b	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
	0.8b	(/.f64 (/.f64 x (+.f64 x y)) (*.f64 (/.f64 (+.f64 x y) y) (+.f64 (+.f64 x y) 1)))
	4.3b	(/.f64 (/.f64 x (*.f64 (+.f64 x y) (+.f64 (+.f64 x y) 1))) (/.f64 (+.f64 x y) y))

Compiler

Compiled 9043 to 4586 computations (49.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (+.f64 x y))
✓	0.0b	(/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y))
✓	0.1b	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
✓	6.6b	(*.f64 x (/.f64 y (+.f64 x y)))

series52.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

32.0ms	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
11.0ms	(/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y))
8.0ms	(*.f64 x (/.f64 y (+.f64 x y)))

rewrite90.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

627×	`prod-diff_binary64`
214×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
116×	`egg-rr`
114×	`log1p-expm1-u_binary64`

Counts

3 → 116

Calls

3 calls:

88.0ms	(/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y))
88.0ms	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
88.0ms	(*.f64 x (/.f64 y (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	51
1	235	45
2	3645	45
3	5303	45
0	0	0
1	0	0

simplify79.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

325×	`cancel-sign-sub-inv_binary64`
256×	`sub-neg_binary64`
255×	`times-frac_binary64`
248×	`associate-/r*_binary64`
214×	`associate-+r+_binary64`

Counts

188 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	265	3008
1	824	2962
2	3565	2890
3	5126	2890

prune212.0ms (5.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	224	7	231

Error

0.0b

Counts

231 → 7

Alt Table

Status	Error	Program
	0.8b	(/.f64 (.f64 x (/.f64 1 (.f64 (+.f64 x y) (/.f64 (+.f64 x y) y)))) (+.f64 (+.f64 x y) 1))
	47.6b	(*.f64 (/.f64 y (+.f64 x y)) (pow.f64 (/.f64 (sqrt.f64 x) (hypot.f64 (+.f64 x y) (sqrt.f64 (+.f64 x y)))) 2))
	9.9b	(*.f64 x (/.f64 1 (/.f64 (pow.f64 (+.f64 x y) 2) (/.f64 y (+.f64 (+.f64 x y) 1)))))
✓	0.1b	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
	14.7b	(/.f64 (/.f64 (*.f64 x (log.f64 (exp.f64 (/.f64 y (+.f64 x y))))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
▶	0.1b	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
	0.8b	(/.f64 (/.f64 x (+.f64 x y)) (*.f64 (/.f64 (+.f64 x y) y) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 6766 to 3450 computations (49% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (+.f64 x y))
✓	0.0b	(/.f64 1 (+.f64 (+.f64 x y) 1))
✓	0.1b	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
✓	0.1b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1)))

series68.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

33.0ms	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
23.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1)))
11.0ms	(/.f64 1 (+.f64 (+.f64 x y) 1))

rewrite87.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

635×	`prod-diff_binary64`
132×	`add-sqr-sqrt_binary64`
127×	`egg-rr`
126×	`log1p-expm1-u_binary64`
126×	`expm1-log1p-u_binary64`

Counts

3 → 127

Calls

3 calls:

85.0ms	(/.f64 1 (+.f64 (+.f64 x y) 1))
85.0ms	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
85.0ms	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
1	262	48
2	3872	48
3	5128	48
0	0	0
1	0	0

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Rules

438×	`associate-+r+_binary64`
355×	`fma-def_binary64`
321×	`associate-/r*_binary64`
317×	`times-frac_binary64`
316×	`associate-+l+_binary64`

Counts

199 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	381	4547
1	1276	4503
2	5579	4503

prune298.0ms (7.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	262	7	269

Error

Counts

269 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (/.f64 (*.f64 x (/.f64 y (+.f64 x y))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
	0.2b	(/.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 (+.f64 x y) 1)) (/.f64 (+.f64 x y) y))
	0.3b	(.f64 (/.f64 y (+.f64 x y)) (/.f64 1 (.f64 (/.f64 (+.f64 x y) x) (+.f64 (+.f64 x y) 1))))
	14.7b	(/.f64 (/.f64 (*.f64 x (log.f64 (exp.f64 (/.f64 y (+.f64 x y))))) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
	9.9b	(*.f64 x (/.f64 1 (/.f64 (pow.f64 (+.f64 x y) 2) (/.f64 y (+.f64 (+.f64 x y) 1)))))
✓	0.1b	(.f64 (/.f64 y (+.f64 x y)) (.f64 (/.f64 x (+.f64 x y)) (/.f64 1 (+.f64 (+.f64 x y) 1))))
	0.8b	(/.f64 (/.f64 x (+.f64 x y)) (*.f64 (/.f64 (+.f64 x y) y) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 9050 to 4900 computations (45.9% saved)

regimes550.0ms (13.5%)

Accuracy

Total 0.1b remaining (75.8%)

Threshold costs 0.1b (75.8%)

Counts

199 → 1

Compiler

Compiled 11942 to 6818 computations (42.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	15	25
2	14	25

end220.0ms (5.4%)

Compiler: Compiled 215 to 108 computations (49.8% saved)

Details

analyze105.0ms (2.6%)

sample1.1s (25.8%)

simplify136.0ms (3.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series50.0ms (1.2%)

rewrite100.0ms (2.5%)

simplify78.0ms (1.9%)

prune237.0ms (5.8%)

localize8.0ms (0.2%)

series71.0ms (1.8%)

rewrite101.0ms (2.5%)

simplify81.0ms (2%)

prune283.0ms (7%)

localize8.0ms (0.2%)

series52.0ms (1.3%)

rewrite90.0ms (2.2%)

simplify79.0ms (1.9%)

prune212.0ms (5.2%)

localize8.0ms (0.2%)

series68.0ms (1.7%)

rewrite87.0ms (2.1%)

simplify83.0ms (2%)

prune298.0ms (7.3%)

regimes550.0ms (13.5%)

simplify3.0ms (0.1%)

end220.0ms (5.4%)

Profiling