Details

analyze624.0ms (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
49.1%	50.7%	0.2%	9
49.5%	50.3%	0.2%	10
49.7%	50.1%	0.2%	11
50.2%	49.6%	0.2%	12
60.5%	39.3%	0.2%	13
60.6%	37.9%	1.4%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.3s (30.6%)

Symmetry

(sort x y)

Results

909.0ms	8256×	body	128	valid
294.0ms	2904×	body	128	invalid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify158.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1491×	`fma-neg_binary64`
579×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
419×	`div-sub_binary64`
329×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	21	13
2	45	13
3	70	13
4	138	13
5	257	13
6	498	13
7	922	13
8	1615	13
9	2472	13
10	2435	13
11	2431	13
12	2427	13
13	2428	13
14	2428	13
15	3596	13
16	3260	13
17	3260	13
18	3260	13
19	3140	13

prune2.0ms (0%)

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 (+.f64 x y) z) (*.f64 t 2))

Compiler

Compiled 39 to 27 computations (30.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 x y) z)
✓	0.0b	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))

series61.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

57.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
4.0ms	(-.f64 (+.f64 x y) z)

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
7×	`distribute-lft-out_binary64`

Counts

2 → 69

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (+.f64 x y) z) (*.f64 t 2))
5.0ms	(-.f64 (+.f64 x y) z)

simplify75.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

474×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
454×	`fma-def_binary64`
279×	`associate-/l*_binary64`
254×	`div-sub_binary64`

Counts

153 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2065
1	353	1794
2	1280	1715
3	4371	1715
4	5146	1715

prune77.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
	0.2b	(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 x y) z)) (cbrt.f64 (-.f64 (+.f64 x y) z))) t) (/.f64 (cbrt.f64 (-.f64 (+.f64 x y) z)) 2))

Compiler

Compiled 1945 to 723 computations (62.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 t 2))
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))

series45.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
12.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`times-frac_binary64`
65×	`*-un-lft-identity_binary64`
56×	`prod-diff_binary64`
40×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`

Counts

2 → 118

Calls

2 calls:

13.0ms	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
5.0ms	(/.f64 (+.f64 x y) (*.f64 t 2))

simplify143.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
458×	`times-frac_binary64`
418×	`associate-/l*_binary64`
345×	`fma-neg_binary64`
184×	`distribute-rgt-in_binary64`

Counts

202 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4746
1	550	3965
2	1542	2814
3	4196	2814
4	4970	2814
5	4864	2814

prune113.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	167	3	170

Error

Counts

170 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
▶	0.2b	(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (+.f64 x y) z)) (cbrt.f64 (-.f64 (+.f64 x y) z))) t) (/.f64 (cbrt.f64 (-.f64 (+.f64 x y) z)) 2))

Compiler

Compiled 4714 to 2569 computations (45.5% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))

series19.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
23×	`add-exp-log_binary64`
19×	`associate-r_binary64`

Counts

1 → 64

Calls

1 calls:

14.0ms

(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

472×	`div-sub_binary64`
382×	`associate-l_binary64`
380×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
366×	`associate-*l/_binary64`

Counts

112 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	139	1836
1	365	1652
2	1165	1652
3	3466	1652
4	4992	1652
5	4968	1652

prune66.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	107	3	110

Error

Counts

110 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.2b	(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))
▶	32.3b	(.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t)))

Compiler

Compiled 2052 to 1001 computations (51.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 y x) z)
✓	0.1b	(/.f64 (*.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t))
✓	0.2b	(/.f64 1 (sqrt.f64 t))
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t)))

series109.0ms (2.5%)

Counts

4 → 89

Calls

4 calls:

57.0ms	(/.f64 (*.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t))
34.0ms	(.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t)))
14.0ms	(/.f64 1 (sqrt.f64 t))
4.0ms	(-.f64 (+.f64 y x) z)

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
52×	`add-exp-log_binary64`
48×	`add-cube-cbrt_binary64`

Counts

4 → 184

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t)))
8.0ms	(/.f64 (*.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t))
5.0ms	(-.f64 (+.f64 y x) z)
3.0ms	(/.f64 1 (sqrt.f64 t))

simplify133.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-def_binary64`
395×	`associate-/l/_binary64`
350×	`associate-/r/_binary64`
337×	`associate-/r*_binary64`
206×	`associate-r_binary64`

Counts

273 → 250

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	5253
1	559	3904
2	2089	3835
3	4416	3834
4	5000	3834

prune106.0ms (2.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	250	3	253

Error

Counts

253 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x y) (.f64 t 2)) (/.f64 z (.f64 t 2)))
✓	0.2b	(*.f64 (/.f64 1 t) (/.f64 (+.f64 y (-.f64 x z)) 2))
✓	32.3b	(.f64 (/.f64 1 (sqrt.f64 t)) (/.f64 (.f64 1/2 (-.f64 (+.f64 y x) z)) (sqrt.f64 t)))

Compiler

Compiled 5439 to 2334 computations (57.1% saved)

regimes806.0ms (18.7%)

Accuracy

Total 0.1b remaining (87.1%)

Threshold costs 0.1b (87.1%)

Counts

77 → 1

Compiler

Compiled 9783 to 6924 computations (29.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	12	13
1	17	13
2	21	13
3	23	13
4	24	13
5	24	13

end217.0ms (5%)

Compiler: Compiled 103 to 72 computations (30.1% saved)

Details

analyze624.0ms (14.5%)

sample1.3s (30.6%)

simplify158.0ms (3.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series61.0ms (1.4%)

rewrite20.0ms (0.5%)

simplify75.0ms (1.7%)

prune77.0ms (1.8%)

localize7.0ms (0.2%)

series45.0ms (1.1%)

rewrite28.0ms (0.7%)

simplify143.0ms (3.3%)

prune113.0ms (2.6%)

localize7.0ms (0.2%)

series19.0ms (0.5%)

rewrite20.0ms (0.5%)

simplify88.0ms (2%)

prune66.0ms (1.5%)

localize9.0ms (0.2%)

series109.0ms (2.5%)

rewrite48.0ms (1.1%)

simplify133.0ms (3.1%)

prune106.0ms (2.5%)

regimes806.0ms (18.7%)

simplify2.0ms (0%)

end217.0ms (5%)

Profiling