Details

analyze35.0ms (1.4%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample816.0ms (32.4%)

Results

718.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify71.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

5.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify75.0ms (3%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
387×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`
161×	`associate-/l*_binary64`

Counts

71 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1282
1	280	1222
2	785	1160
3	2516	1148
4	4566	1139
5	5172	1139

prune38.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Error

Counts

58 → 5

Alt Table

Status	Error	Program
	31.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
	31.4b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	32.4b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 1008 to 344 computations (65.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)

series29.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)
14.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))

rewrite28.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
76×	`add-sqr-sqrt_binary64`
58×	`cbrt-prod_binary64`
52×	`cube-prod_binary64`

Counts

2 → 144

Calls

2 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
7.0ms	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3)

simplify127.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

362×	`fma-def_binary64`
329×	`unswap-sqr_binary64`
285×	`distribute-rgt-in_binary64`
236×	`associate-/l/_binary64`
235×	`distribute-lft-in_binary64`

Counts

192 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	4190
1	648	3881
2	2075	3745
3	4846	3745
4	5066	3745

prune125.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	201	5	206

Error

Counts

206 → 5

Alt Table

Status	Error	Program
▶	31.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
	31.4b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	32.4b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 3859 to 1517 computations (60.7% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.2b	(/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	0.6b	(cbrt.f64 (-.f64 x y))

series294.0ms (11.7%)

Counts

4 → 64

Calls

4 calls:

125.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))))
105.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y)))
38.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
25.0ms	(cbrt.f64 (-.f64 x y))

rewrite52.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

105×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
73×	`cbrt-prod_binary64`
63×	`times-frac_binary64`
51×	`add-cube-cbrt_binary64`

Counts

4 → 205

Calls

4 calls:

18.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
7.0ms	(/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y)))
2.0ms	(cbrt.f64 (-.f64 x y))

simplify229.0ms (9.1%)

Algorithm

1×	egg-herbie

Rules

679×	`times-frac_binary64`
355×	`associate-r_binary64`
287×	`fma-neg_binary64`
264×	`associate-l_binary64`
197×	`fma-def_binary64`

Counts

269 → 349

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	444	7150
1	1089	6821
2	3497	6642
3	4825	6569
4	4995	6569
5	4935	6569

prune188.0ms (7.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	451	0	451
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	451	5	456

Error

Counts

456 → 5

Alt Table

Status	Error	Program
✓	31.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
▶	31.4b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	32.4b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 16801 to 4767 computations (71.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.7%)

Counts

2 → 30

Calls

2 calls:

13.0ms	(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))
4.0ms	(+.f64 (/.f64 y x) 1)

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 66

Calls

2 calls:

8.0ms	(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))
5.0ms	(+.f64 (/.f64 y x) 1)

simplify78.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

332×	`associate-l_binary64`
268×	`associate-r_binary64`
245×	`associate-*l/_binary64`
242×	`associate-*r/_binary64`
228×	`distribute-rgt-in_binary64`

Counts

96 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	99	1262
1	235	1095
2	779	1015
3	2612	1014
4	4070	1002
5	4976	1002

prune54.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
✓	31.1b	(.f64 (/.f64 (sqrt.f64 (+.f64 x y)) (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))) (/.f64 (sqrt.f64 (+.f64 x y)) (cbrt.f64 (-.f64 x y))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) 3))
✓	31.4b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	32.4b	(fma.f64 -2 (+.f64 (/.f64 x y) (fma.f64 (/.f64 x y) (/.f64 x y) (pow.f64 (/.f64 x y) 3))) -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 1878 to 913 computations (51.4% saved)

regimes126.0ms (5%)

Accuracy

Total 0.0b remaining (87.4%)

Threshold costs 0.0b (87.4%)

Counts

52 → 1

Compiler

Compiled 2292 to 1353 computations (41% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end69.0ms (2.8%)

Compiler: Compiled 106 to 58 computations (45.3% saved)

Details

analyze35.0ms (1.4%)

sample816.0ms (32.4%)

simplify71.0ms (2.8%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.3%)

rewrite8.0ms (0.3%)

simplify75.0ms (3%)

prune38.0ms (1.5%)

localize6.0ms (0.2%)

series29.0ms (1.2%)

rewrite28.0ms (1.1%)

simplify127.0ms (5.1%)

prune125.0ms (5%)

localize11.0ms (0.5%)

series294.0ms (11.7%)

rewrite52.0ms (2.1%)

simplify229.0ms (9.1%)

prune188.0ms (7.5%)

localize6.0ms (0.2%)

series17.0ms (0.7%)

rewrite16.0ms (0.6%)

simplify78.0ms (3.1%)

prune54.0ms (2.1%)

regimes126.0ms (5%)

simplify2.0ms (0.1%)

end69.0ms (2.8%)

Profiling