Details

analyze2.2s (27.4%)

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%	69.4%	3.3%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample63.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
5.0ms	74×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify47.0ms (0.6%)

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

prune6.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.3b	(.f64 y (.f64 t (-.f64 x z)))
	7.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 t (-.f64 x z))
✓	5.0b	(.f64 y (.f64 t (-.f64 x z)))

series44.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(.f64 y (.f64 t (-.f64 x z)))
14.0ms	(*.f64 t (-.f64 x z))

rewrite50.0ms (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:

15.0ms	(.f64 y (.f64 t (-.f64 x z)))
12.0ms	(*.f64 t (-.f64 x z))

simplify197.0ms (2.4%)

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

prune201.0ms (2.5%)

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
	6.2b	(.f64 (.f64 (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z))))) (cbrt.f64 (.f64 y (.f64 t (-.f64 x z)))))
▶	5.3b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
	6.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
	5.3b	(.f64 (-.f64 x z) (.f64 y t))
	20.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
	33.9b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	7.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 3198 to 821 computations (74.3% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.9b	(.f64 y (.f64 t x))
✓	5.4b	(.f64 y (.f64 t z))

series73.0ms (0.9%)

Counts

3 → 30

Calls

3 calls:

36.0ms	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
19.0ms	(.f64 y (.f64 t z))
17.0ms	(.f64 y (.f64 t x))

rewrite103.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
6×	`associate-l_binary64`
6×	`cbrt-unprod_binary64`

Counts

3 → 57

Calls

3 calls:

83.0ms	(.f64 y (.f64 t z))
8.0ms	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
7.0ms	(.f64 y (.f64 t x))

simplify115.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
456×	`cancel-sign-sub-inv_binary64`
405×	`fma-def_binary64`
402×	`*-commutative_binary64`
367×	`distribute-rgt-neg-in_binary64`

Counts

87 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	950
1	285	914
2	967	898
3	2492	898
4	4590	898
5	4892	898

prune140.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Error

0.0b

Counts

104 → 8

Alt Table

Status	Error	Program
	33.0b	(/.f64 (-.f64 (.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t x))) (.f64 (.f64 y (.f64 t z)) (.f64 y (.f64 t z)))) (+.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z))))
	33.9b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	6.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
▶	5.3b	(.f64 (-.f64 x z) (.f64 y t))
	20.4b	(.f64 y (.f64 (sqrt.f64 t) (*.f64 (sqrt.f64 t) (-.f64 x z))))
✓	5.3b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
	7.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	24.1b	(-.f64 (.f64 y (.f64 t x)) (cbrt.f64 (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 y (.f64 t z))) (.f64 y (.f64 t z)))))

Compiler

Compiled 1829 to 469 computations (74.4% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.2b	(.f64 (-.f64 x z) (.f64 y t))

series28.0ms (0.4%)

Counts

1 → 32

Calls

1 calls:

28.0ms

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

rewrite15.0ms (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:

13.0ms

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

simplify85.0ms (1.1%)

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

prune53.0ms (0.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	42	8	50

Error

Counts

50 → 8

Alt Table

Status	Error	Program
▶	6.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
✓	5.3b	(.f64 (-.f64 x z) (.f64 y t))
	36.6b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))
	32.5b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))
	32.7b	(.f64 (sqrt.f64 (.f64 (-.f64 x z) (.f64 y t))) (sqrt.f64 (.f64 (-.f64 x z) (*.f64 y t))))
✓	5.3b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
	7.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	24.1b	(-.f64 (.f64 y (.f64 t x)) (cbrt.f64 (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 y (.f64 t z))) (.f64 y (.f64 t z)))))

Compiler

Compiled 802 to 270 computations (66.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	1.5b	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))
✓	3.8b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))

series854.0ms (10.6%)

Counts

4 → 120

Calls

4 calls:

656.0ms	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))
81.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
62.0ms	(cbrt.f64 y)
56.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))

rewrite147.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

208×	`distribute-lft-in_binary64`
208×	`distribute-rgt-in_binary64`
108×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`

Counts

4 → 268

Calls

4 calls:

36.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
20.0ms	(.f64 (cbrt.f64 y) (.f64 t (-.f64 x z)))
11.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify306.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

750×	`distribute-rgt-in_binary64`
697×	`associate-l_binary64`
650×	`associate-r_binary64`
420×	`fma-def_binary64`
326×	`unswap-sqr_binary64`

Counts

388 → 331

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	424	6052
1	556	5508
2	2084	5133
3	5116	5133

prune320.0ms (4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	367	8	375

Error

Counts

375 → 8

Alt Table

Status	Error	Program
✓	6.1b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 t (-.f64 x z))))
✓	5.3b	(.f64 (-.f64 x z) (.f64 y t))
	36.6b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))
	32.5b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))
	32.7b	(.f64 (sqrt.f64 (.f64 (-.f64 x z) (.f64 y t))) (sqrt.f64 (.f64 (-.f64 x z) (*.f64 y t))))
✓	5.3b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
	7.2b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	24.1b	(-.f64 (.f64 y (.f64 t x)) (cbrt.f64 (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 y (.f64 t z))) (.f64 y (.f64 t z)))))

Compiler

Compiled 10135 to 1914 computations (81.1% saved)

regimes1.3s (15.8%)

Accuracy

Total 1.4b remaining (98%)

Threshold costs 0b (0%)

Counts

79 → 3

Compiler

Compiled 8110 to 4646 computations (42.7% saved)

bsearch4.0ms (0.1%)

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	66
1	42	66
2	60	66
3	70	66
4	76	66
5	77	66
6	77	66

end12.0ms (0.2%)

Remove: (sort y t)
Compiler: Compiled 147 to 63 computations (57.1% saved)

sample1.6s (20.4%)

Algorithm

1×

intervals

Results

678.0ms	8000×	body	128	valid
140.0ms	1876×	body	128	invalid

Compiler

Compiled 209 to 109 computations (47.8% 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

analyze2.2s (27.4%)

sample63.0ms (0.8%)

simplify47.0ms (0.6%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

series44.0ms (0.6%)

rewrite50.0ms (0.6%)

simplify197.0ms (2.4%)

prune201.0ms (2.5%)

localize15.0ms (0.2%)

series73.0ms (0.9%)

rewrite103.0ms (1.3%)

simplify115.0ms (1.4%)

prune140.0ms (1.7%)

localize11.0ms (0.1%)

series28.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify85.0ms (1.1%)

prune53.0ms (0.7%)

localize21.0ms (0.3%)

series854.0ms (10.6%)

rewrite147.0ms (1.8%)

simplify306.0ms (3.8%)

prune320.0ms (4%)

regimes1.3s (15.8%)

bsearch4.0ms (0.1%)

simplify11.0ms (0.1%)

end12.0ms (0.2%)

sample1.6s (20.4%)

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