Details

analyze465.0ms (16.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.4%	10.1%	12
55%	30.3%	14.7%	13
59.5%	25.4%	15.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.0s (36.8%)

Symmetry

(sort x y)

Results

934.0ms	8253×	body	128	valid
56.0ms	597×	body	128	invalid
1.0ms	3×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

186×	`fma-def_binary64`
33×	`distribute-rgt-in_binary64`
26×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
21×	`distribute-lft-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	19	10
2	45	10
3	88	10
4	170	10
5	254	10
6	256	10
7	258	10
8	252	10

prune2.0ms (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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))

Compiler

Compiled 30 to 21 computations (30% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

6.0ms

(*.f64 (+.f64 x y) (+.f64 z 1))

simplify64.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-rgt-in_binary64`
724×	`distribute-lft-in_binary64`
449×	`fma-def_binary64`
414×	`fma-neg_binary64`
258×	`unsub-neg_binary64`

Counts

68 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	83	908
1	269	804
2	911	798
3	3385	798
4	4092	798
5	5126	798

prune36.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
▶	7.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
	34.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
	42.0b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

Compiler

Compiled 998 to 516 computations (48.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series36.0ms (1.3%)

Counts

2 → 64

Calls

2 calls:

28.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))
8.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-div_binary64`
33×	`flip-+_binary64`
33×	`flip3-+_binary64`
32×	`frac-times_binary64`
16×	`associate-*l/_binary64`

Counts

2 → 84

Calls

2 calls:

12.0ms	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
7.0ms	(*.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1)))

simplify111.0ms (4%)

Algorithm

1×	egg-herbie

Rules

713×	`associate--l+_binary64`
692×	`fma-def_binary64`
617×	`fma-neg_binary64`
373×	`*-commutative_binary64`
307×	`associate-+l+_binary64`

Counts

148 → 155

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	179	2758
1	485	2487
2	1499	2461
3	3173	2450
4	4729	2447
5	5021	2447

prune93.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	7.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
▶	34.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
	42.0b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

Compiler

Compiled 3849 to 2317 computations (39.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))
✓	0.2b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

series59.0ms (2.1%)

Counts

2 → 56

Calls

2 calls:

51.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))
7.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))

rewrite63.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-div_binary64`
33×	`flip-+_binary64`
33×	`flip3-+_binary64`
32×	`frac-times_binary64`
16×	`associate-*r/_binary64`

Counts

2 → 90

Calls

2 calls:

46.0ms	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
7.0ms	(*.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1))

simplify101.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

553×	`fma-neg_binary64`
464×	`associate-+r+_binary64`
394×	`cancel-sign-sub-inv_binary64`
336×	`+-commutative_binary64`
316×	`associate--l+_binary64`

Counts

146 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3139
1	690	2791
2	2306	2741
3	4098	2735
4	4979	2735

prune74.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	168	4	172

Error

Counts

172 → 4

Alt Table

Status	Error	Program
✓	7.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
✓	34.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
▶	42.0b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

Compiler

Compiled 4438 to 1885 computations (57.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 z) (+.f64 y x))
✓	0.1b	(pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3)
✓	39.7b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

series110.0ms (3.9%)

Counts

3 → 108

Calls

3 calls:

95.0ms	(pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3)
7.0ms	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))
7.0ms	(*.f64 (+.f64 1 z) (+.f64 y x))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`flip-+_binary64`
18×	`flip3-+_binary64`
16×	`cube-div_binary64`
12×	`frac-times_binary64`
11×	`*-un-lft-identity_binary64`

Counts

3 → 91

Calls

3 calls:

6.0ms	(pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3)
6.0ms	(*.f64 (+.f64 1 z) (+.f64 y x))
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

simplify133.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

568×	`fma-def_binary64`
559×	`associate-+r+_binary64`
310×	`associate-r_binary64`
304×	`unswap-sqr_binary64`
290×	`+-commutative_binary64`

Counts

199 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	352	6412
1	1006	5969
2	4137	5953
3	5146	5953

prune118.0ms (4.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	177	4	181

Error

Counts

181 → 4

Alt Table

Status	Error	Program
✓	7.9b	(.f64 (.f64 (+.f64 x y) (sqrt.f64 (+.f64 z 1))) (sqrt.f64 (+.f64 z 1)))
✓	34.0b	(.f64 (sqrt.f64 (+.f64 x y)) (.f64 (sqrt.f64 (+.f64 x y)) (+.f64 z 1)))
✓	0.0b	(*.f64 (+.f64 x y) (+.f64 z 1))
✓	42.0b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 1 z) (+.f64 y x)) 3))

Compiler

Compiled 5477 to 3443 computations (37.1% saved)

regimes142.0ms (5%)

Accuracy

Total 0.0b remaining (52.7%)

Threshold costs 0.0b (52.7%)

Counts

22 → 1

Compiler

Compiled 1691 to 1109 computations (34.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	14	16
2	14	16

end64.0ms (2.3%)

Remove: (sort x y)
Compiler: Compiled 111 to 70 computations (36.9% saved)

Details

analyze465.0ms (16.5%)

sample1.0s (36.8%)

simplify10.0ms (0.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify64.0ms (2.3%)

prune36.0ms (1.3%)

localize6.0ms (0.2%)

series36.0ms (1.3%)

rewrite29.0ms (1%)

simplify111.0ms (4%)

prune93.0ms (3.3%)

localize6.0ms (0.2%)

series59.0ms (2.1%)

rewrite63.0ms (2.3%)

simplify101.0ms (3.6%)

prune74.0ms (2.6%)

localize7.0ms (0.2%)

series110.0ms (3.9%)

rewrite23.0ms (0.8%)

simplify133.0ms (4.7%)

prune118.0ms (4.2%)

regimes142.0ms (5%)

simplify4.0ms (0.1%)

end64.0ms (2.3%)

Profiling