Details

analyze1.2s (21.1%)

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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (24.1%)

Symmetry

(sort y t)

Results

955.0ms	8256×	body	128	valid
222.0ms	2000×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def_binary64`
304×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
90×	`associate-l_binary64`
87×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.1b	(.f64 y (.f64 t (-.f64 x z)))
▶	6.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(-.f64 (.f64 x y) (.f64 z y))
✓	5.8b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series24.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

17.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
7.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

5.0ms	(-.f64 (.f64 x y) (.f64 z y))
5.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

simplify77.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
443×	`neg-mul-1_binary64`
246×	`*-commutative_binary64`
223×	`fma-neg_binary64`
217×	`distribute-lft-neg-out_binary64`

Counts

124 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1269
1	221	1209
2	783	1202
3	1981	1199
4	4246	1199
5	5104	1199

prune54.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

0.0b

Counts

85 → 8

Alt Table

Status	Error	Program
	28.5b	(.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (sqrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
✓	6.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	6.9b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	33.3b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t) (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	6.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	35.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (.f64 t (sqrt.f64 (*.f64 y (-.f64 x z)))))
▶	6.1b	(.f64 y (.f64 t (-.f64 x z)))

Compiler

Compiled 1514 to 402 computations (73.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	5.8b	(.f64 y (.f64 t (-.f64 x z)))

series65.0ms (1.2%)

Counts

2 → 84

Calls

2 calls:

58.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

rewrite87.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

7.0ms	(.f64 y (.f64 t (-.f64 x z)))
5.0ms	(*.f64 t (-.f64 x z))

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

449×	`*-commutative_binary64`
402×	`distribute-rgt-in_binary64`
400×	`distribute-rgt-neg-out_binary64`
379×	`distribute-lft-in_binary64`
309×	`fma-def_binary64`

Counts

208 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	2765
1	326	2564
2	1079	2402
3	3077	2078
4	4965	2078
5	4751	2078

prune149.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Error

0.0b

Counts

161 → 9

Alt Table

Status	Error	Program
✓	6.1b	(.f64 y (.f64 t (-.f64 x z)))
	33.7b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	6.4b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
▶	4.4b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	29.1b	(.f64 (sqrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (sqrt.f64 (.f64 y (*.f64 t (-.f64 x z)))))
	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	35.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (.f64 t (sqrt.f64 (*.f64 y (-.f64 x z)))))
	20.7b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
✓	6.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 3260 to 862 computations (73.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	1.0b	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
✓	2.6b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

series447.0ms (8.1%)

Counts

4 → 120

Calls

4 calls:

352.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
31.0ms	(cbrt.f64 y)
28.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
6.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
697×	`distribute-lft-in_binary64`
346×	`associate-r_binary64`
331×	`associate-l_binary64`
193×	`fma-def_binary64`

Counts

229 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	3043
1	372	2345
2	1605	2289
3	5437	2289

prune97.0ms (1.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	194	9	203

Error

Counts

203 → 9

Alt Table

Status	Error	Program
✓	6.1b	(.f64 y (.f64 t (-.f64 x z)))
	33.7b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
▶	6.4b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
✓	4.4b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	29.1b	(.f64 (sqrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (sqrt.f64 (.f64 y (*.f64 t (-.f64 x z)))))
	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	35.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (.f64 t (sqrt.f64 (*.f64 y (-.f64 x z)))))
	43.1b	(/.f64 (.f64 (.f64 t y) (-.f64 (pow.f64 x 3) (pow.f64 z 3))) (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))
✓	6.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 3931 to 941 computations (76.1% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	5.8b	(.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y)
✓	60.9b	(fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

series160.0ms (2.9%)

Counts

4 → 84

Calls

4 calls:

51.0ms	(fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))
42.0ms	(cbrt.f64 z)
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
29.0ms	(.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
16×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y)
1.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z))))

simplify106.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

531×	`fma-def_binary64`
400×	`exp-prod_binary64`
339×	`unswap-sqr_binary64`
326×	`*-commutative_binary64`
265×	`fma-neg_binary64`

Counts

169 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1634
1	268	1382
2	864	1288
3	1986	1273
4	4150	1261
5	4946	1261
6	4730	1261

prune354.0ms (6.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	408	0	408
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	408	9	417

Error

Counts

417 → 9

Alt Table

Status	Error	Program
✓	6.1b	(.f64 y (.f64 t (-.f64 x z)))
	33.7b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
✓	6.4b	(+.f64 (.f64 (.f64 (fma.f64 1 x (neg.f64 (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 z) (cbrt.f64 z))))) t) y) (.f64 (.f64 (fma.f64 (neg.f64 (cbrt.f64 z)) (.f64 (cbrt.f64 z) (cbrt.f64 z)) (.f64 (cbrt.f64 z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) t) y))
✓	4.4b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	29.1b	(.f64 (sqrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (sqrt.f64 (.f64 y (*.f64 t (-.f64 x z)))))
	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	35.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (.f64 t (sqrt.f64 (*.f64 y (-.f64 x z)))))
	43.1b	(/.f64 (.f64 (.f64 t y) (-.f64 (pow.f64 x 3) (pow.f64 z 3))) (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))
✓	6.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 17230 to 4105 computations (76.2% saved)

regimes756.0ms (13.7%)

Accuracy

Total 1.0b remaining (97.6%)

Threshold costs 0b (0%)

Counts

72 → 5

Compiler

Compiled 10990 to 5381 computations (51% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	125
1	54	125
2	72	125
3	87	125
4	95	125
5	98	125
6	99	125
7	99	125

end288.0ms (5.2%)

Compiler: Compiled 534 to 218 computations (59.2% saved)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Details

analyze1.2s (21.1%)

sample1.3s (24.1%)

simplify48.0ms (0.9%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series24.0ms (0.4%)

rewrite12.0ms (0.2%)

simplify77.0ms (1.4%)

prune54.0ms (1%)

localize5.0ms (0.1%)

series65.0ms (1.2%)

rewrite87.0ms (1.6%)

simplify116.0ms (2.1%)

prune149.0ms (2.7%)

localize10.0ms (0.2%)

series447.0ms (8.1%)

rewrite31.0ms (0.6%)

simplify83.0ms (1.5%)

prune97.0ms (1.7%)

localize22.0ms (0.4%)

series160.0ms (2.9%)

rewrite13.0ms (0.2%)

simplify106.0ms (1.9%)

prune354.0ms (6.4%)

regimes756.0ms (13.7%)

bsearch3.0ms (0.1%)

simplify8.0ms (0.1%)

end288.0ms (5.2%)

Profiling

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10