Details

analyze897.0ms (14.7%)

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)

sample1.9s (30.8%)

Symmetry

(sort y t)

Results

1.4s	8256×	body	128	valid
305.0ms	1962×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (1.1%)

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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.0b	(.f64 y (.f64 t (-.f64 x z)))
▶	7.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (.f64 x y) (.f64 z y))
✓	7.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series48.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
13.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite24.0ms (0.4%)

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:

8.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
4.0ms	(-.f64 (.f64 x y) (.f64 z y))

simplify117.0ms (1.9%)

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

prune96.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Error

0.0b

Counts

85 → 10

Alt Table

Status	Error	Program
	20.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
▶	6.7b	(.f64 (-.f64 x z) (.f64 y t))
	36.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.8b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	41.6b	(.f64 (/.f64 (.f64 y (.f64 y (-.f64 (.f64 x x) (.f64 z z)))) (.f64 y (+.f64 z x))) t)
	8.0b	(.f64 y (.f64 t (-.f64 x z)))
	8.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	8.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
✓	7.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	32.1b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))

Compiler

Compiled 1582 to 448 computations (71.7% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.6b	(.f64 (-.f64 x z) (.f64 y t))

series23.0ms (0.4%)

Counts

1 → 32

Calls

1 calls:

22.0ms

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

rewrite14.0ms (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:

12.0ms

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

simplify75.0ms (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

prune49.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	42	10	52

Error

0.0b

Counts

52 → 10

Alt Table

Status	Error	Program
	44.1b	(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) (.f64 y t)) (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))
▶	8.0b	(.f64 y (.f64 t (-.f64 x z)))
	20.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	6.7b	(.f64 (-.f64 x z) (.f64 y t))
	41.6b	(.f64 (/.f64 (.f64 y (.f64 y (-.f64 (.f64 x x) (.f64 z z)))) (.f64 y (+.f64 z x))) t)
	32.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))
	8.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	8.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
✓	7.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	32.1b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))

Compiler

Compiled 920 to 341 computations (62.9% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(.f64 y (.f64 t (-.f64 x z)))

series25.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

25.0ms

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

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
36×	`prod-diff_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`

Counts

1 → 74

Calls

1 calls:

12.0ms

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

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

428×	`*-commutative_binary64`
395×	`distribute-lft-neg-out_binary64`
381×	`distribute-rgt-neg-out_binary64`
379×	`distribute-rgt-in_binary64`
356×	`distribute-lft-in_binary64`

Counts

122 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	1842
1	287	1707
2	914	1599
3	2773	1383
4	4944	1383

prune112.0ms (1.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	94	10	104

Error

0.0b

Counts

104 → 10

Alt Table

Status	Error	Program
	44.1b	(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) (.f64 y t)) (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))
✓	8.0b	(.f64 y (.f64 t (-.f64 x z)))
	20.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	6.7b	(.f64 (-.f64 x z) (.f64 y t))
▶	7.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	34.9b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	8.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	8.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
✓	7.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	32.1b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))

Compiler

Compiled 2260 to 654 computations (71.1% saved)

localize16.0ms (0.3%)

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)
✓	2.6b	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
✓	3.5b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

series683.0ms (11.2%)

Counts

4 → 120

Calls

4 calls:

517.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
68.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
53.0ms	(cbrt.f64 y)
44.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

rewrite55.0ms (0.9%)

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:

21.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
11.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
8.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify121.0ms (2%)

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

prune145.0ms (2.4%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	193	1	194
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	193	11	204

Error

0.0b

Counts

204 → 11

Alt Table

Status	Error	Program
	44.1b	(/.f64 (.f64 (-.f64 (pow.f64 x 3) (pow.f64 z 3)) (.f64 y t)) (+.f64 (.f64 x x) (+.f64 (.f64 z z) (*.f64 x z))))
✓	8.0b	(.f64 y (.f64 t (-.f64 x z)))
	20.6b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	6.7b	(.f64 (-.f64 x z) (.f64 y t))
	6.3b	(.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) t) (.f64 (-.f64 x z) (cbrt.f64 y)))
✓	7.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	7.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	34.9b	(/.f64 (.f64 y (.f64 t (-.f64 (.f64 x x) (.f64 z z)))) (+.f64 x z))
	8.9b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
	8.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
	32.1b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))

Compiler

Compiled 3830 to 887 computations (76.8% saved)

regimes921.0ms (15.1%)

Accuracy

Total 2.1b remaining (99.2%)

Threshold costs 0b (0%)

Counts

47 → 3

Compiler

Compiled 5504 to 2946 computations (46.5% saved)

bsearch3.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-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	23	66
1	38	66
2	49	66
3	55	66
4	59	66
5	60	66
6	60	66

end547.0ms (8.9%)

Compiler: Compiled 409 to 201 computations (50.9% 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

analyze897.0ms (14.7%)

sample1.9s (30.8%)

simplify65.0ms (1.1%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

series48.0ms (0.8%)

rewrite24.0ms (0.4%)

simplify117.0ms (1.9%)

prune96.0ms (1.6%)

localize11.0ms (0.2%)

series23.0ms (0.4%)

rewrite14.0ms (0.2%)

simplify75.0ms (1.2%)

prune49.0ms (0.8%)

localize10.0ms (0.2%)

series25.0ms (0.4%)

rewrite30.0ms (0.5%)

simplify118.0ms (1.9%)

prune112.0ms (1.8%)

localize16.0ms (0.3%)

series683.0ms (11.2%)

rewrite55.0ms (0.9%)

simplify121.0ms (2%)

prune145.0ms (2.4%)

regimes921.0ms (15.1%)

bsearch3.0ms (0%)

simplify7.0ms (0.1%)

end547.0ms (8.9%)

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