Details

analyze967.0ms (21.6%)

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 (30%)

Symmetry

(sort y t)

Results

974.0ms	8256×	body	128	valid
212.0ms	1947×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify45.0ms (1%)

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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.3b	(.f64 y (.f64 t (-.f64 x z)))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	7.9b	(.f64 y (.f64 t (-.f64 x z)))

series21.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

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

rewrite25.0ms (0.6%)

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:

8.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

simplify127.0ms (2.8%)

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

prune96.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	6	153
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	27.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	28.6b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	8.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	6.3b	(.f64 (-.f64 x z) (.f64 y t))
	8.3b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

Compiler

Compiled 3162 to 819 computations (74.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.2b	(.f64 (-.f64 x z) (.f64 y t))

series15.0ms (0.3%)

Counts

1 → 32

Calls

1 calls:

15.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

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

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
483×	`fma-def_binary64`
414×	`associate-r_binary64`
378×	`distribute-rgt-neg-out_binary64`
327×	`unsub-neg_binary64`

Counts

56 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	661
1	178	598
2	527	598
3	1835	598
4	3260	598
5	5376	598

prune27.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	41	8	49

Error

0.0b

Counts

49 → 8

Alt Table

Status	Error	Program
	37.2b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x z) (.f64 y t)) (.f64 (-.f64 x z) (.f64 y t))) (.f64 (-.f64 x z) (.f64 y t))))
	28.6b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	27.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	8.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	6.3b	(.f64 (-.f64 x z) (.f64 y t))
▶	8.3b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

Compiler

Compiled 799 to 271 computations (66.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 t x) (.f64 t z))
✓	7.9b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

series23.0ms (0.5%)

Counts

2 → 54

Calls

2 calls:

16.0ms	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)
7.0ms	(-.f64 (.f64 t x) (.f64 t z))

rewrite10.0ms (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 (.f64 t x) (*.f64 t z)) y)
3.0ms	(-.f64 (.f64 t x) (.f64 t z))

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

943×	`fma-def_binary64`
247×	`distribute-lft-neg-out_binary64`
237×	`distribute-rgt-neg-out_binary64`
230×	`*-commutative_binary64`
221×	`fma-neg_binary64`

Counts

94 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1023
1	219	963
2	773	956
3	2035	953
4	4486	953
5	4935	953

prune111.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	10	91

Error

0.0b

Counts

91 → 10

Alt Table

Status	Error	Program
	37.2b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x z) (.f64 y t)) (.f64 (-.f64 x z) (.f64 y t))) (.f64 (-.f64 x z) (.f64 y t))))
	28.6b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	28.7b	(/.f64 (.f64 y (.f64 t (.f64 (.f64 t (-.f64 x z)) (+.f64 x z)))) (+.f64 (.f64 t x) (.f64 t z)))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	27.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	25.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 t x) (.f64 t x)) (.f64 (.f64 t z) (.f64 t z))) y) (+.f64 (.f64 t x) (*.f64 t z)))
▶	8.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	6.3b	(.f64 (-.f64 x z) (.f64 y t))
✓	8.3b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)

Compiler

Compiled 1527 to 431 computations (71.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.7b	(cbrt.f64 y)
✓	3.3b	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
✓	4.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

series573.0ms (12.8%)

Counts

4 → 120

Calls

4 calls:

435.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
69.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
38.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
31.0ms	(cbrt.f64 y)

rewrite31.0ms (0.7%)

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:

12.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
7.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify85.0ms (1.9%)

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

prune86.0ms (1.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	193	11	204

Error

0.0b

Counts

204 → 11

Alt Table

Status	Error	Program
	37.2b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 x z) (.f64 y t)) (.f64 (-.f64 x z) (.f64 y t))) (.f64 (-.f64 x z) (.f64 y t))))
	28.6b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
	28.7b	(/.f64 (.f64 y (.f64 t (.f64 (.f64 t (-.f64 x z)) (+.f64 x z)))) (+.f64 (.f64 t x) (.f64 t z)))
✓	8.3b	(.f64 (-.f64 (.f64 t x) (*.f64 t z)) y)
	8.8b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y)))) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	27.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	25.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 t x) (.f64 t x)) (.f64 (.f64 t z) (.f64 t z))) y) (+.f64 (.f64 t x) (*.f64 t z)))
✓	8.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	8.6b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	6.3b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 3840 to 880 computations (77.1% saved)

regimes602.0ms (13.5%)

Accuracy

Total 1.4b remaining (98.4%)

Threshold costs 0b (0%)

Counts

52 → 3

Compiler

Compiled 5698 to 3086 computations (45.8% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	33	55
2	44	55
3	50	55
4	54	55
5	55	55
6	55	55

end121.0ms (2.7%)

Remove: (sort y t)
Compiler: Compiled 387 to 182 computations (53% 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

analyze967.0ms (21.6%)

sample1.3s (30%)

simplify45.0ms (1%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series21.0ms (0.5%)

rewrite25.0ms (0.6%)

simplify127.0ms (2.8%)

prune96.0ms (2.2%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify53.0ms (1.2%)

prune27.0ms (0.6%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite10.0ms (0.2%)

simplify72.0ms (1.6%)

prune111.0ms (2.5%)

localize9.0ms (0.2%)

series573.0ms (12.8%)

rewrite31.0ms (0.7%)

simplify85.0ms (1.9%)

prune86.0ms (1.9%)

regimes602.0ms (13.5%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end121.0ms (2.7%)

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