Details

analyze527.0ms (10.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
45.2%	53.8%	0.9%	9
50.3%	47.8%	1.9%	10
54%	43.6%	2.4%	11
61.7%	32.9%	5.4%	12
64.1%	28.3%	7.6%	13
66.2%	24.7%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (29.3%)

Results

1.1s	8256×	body	128	valid
170.0ms	1249×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1167×	`fma-def_binary64`
1073×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	43	18
3	75	18
4	123	16
5	213	16
6	302	16
7	472	16
8	1009	13
9	1328	13
10	1542	13
11	1559	13
12	1556	13
13	1556	13
14	1453	13

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
	4.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
▶	2.3b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 78 to 51 computations (34.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
✓	0.0b	(/.f64 (+.f64 x 4) y)
✓	3.7b	(*.f64 (/.f64 x y) z)

series46.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

24.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
12.0ms	(*.f64 (/.f64 x y) z)
10.0ms	(/.f64 (+.f64 x 4) y)

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
16×	`fma-neg_binary64`

Counts

3 → 117

Calls

3 calls:

10.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
5.0ms	(*.f64 (/.f64 x y) z)
4.0ms	(/.f64 (+.f64 x 4) y)

simplify127.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-l_binary64`
381×	`fma-def_binary64`
379×	`associate-*l/_binary64`
369×	`associate-r_binary64`
310×	`fma-neg_binary64`

Counts

213 → 177

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	187	3147
1	457	2896
2	1229	2394
3	3977	2382
4	4927	2330
5	4911	2330

prune160.0ms (3.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	170	7	177
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	8	179

Error

Counts

179 → 8

Alt Table

Status	Error	Program
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	35.0b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y)) (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y))))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) z))))
	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	2.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
▶	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))

Compiler

Compiled 3834 to 1822 computations (52.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	0.6b	(cbrt.f64 x)

series158.0ms (3.3%)

Counts

4 → 48

Calls

4 calls:

52.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
37.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
38×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 110

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 x)

simplify111.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
708×	`log-prod_binary64`
594×	`unswap-sqr_binary64`
324×	`exp-prod_binary64`
238×	`*-commutative_binary64`

Counts

158 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1220
1	174	1108
2	558	1032
3	895	1004
4	2346	820
5	4061	820
6	4265	820
7	4815	820

prune234.0ms (4.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	220	8	228

Error

Counts

228 → 8

Alt Table

Status	Error	Program
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	35.0b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y)) (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y))))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) z))))
	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
▶	2.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))

Compiler

Compiled 6914 to 2349 computations (66% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))
✓	0.0b	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
	3.7b	(*.f64 (/.f64 x y) z)

series26.0ms (0.5%)

Counts

2 → 57

Calls

2 calls:

19.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
7.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`fma-def_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`

Counts

2 → 57

Calls

2 calls:

7.0ms	(-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z))
6.0ms	(+.f64 (/.f64 x y) (*.f64 4 (/.f64 1 y)))

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

444×	`fma-def_binary64`
442×	`associate-l_binary64`
409×	`associate-r_binary64`
329×	`distribute-rgt-in_binary64`
305×	`distribute-lft-in_binary64`

Counts

114 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1890
1	318	1799
2	1069	1342
3	4351	1342
4	4995	1342
5	4939	1342

prune163.0ms (3.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	35.0b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y)) (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y))))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) z))))
▶	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))

Compiler

Compiled 3773 to 1787 computations (52.6% saved)

localize14.0ms (0.3%)

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)
✓	1.0b	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	2.9b	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))

series735.0ms (15.1%)

Counts

4 → 96

Calls

4 calls:

639.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
37.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
33.0ms	(cbrt.f64 z)
26.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64`
33×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

10.0ms	(.f64 (/.f64 x y) (.f64 (cbrt.f64 z) (cbrt.f64 z)))
9.0ms	(.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify117.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

807×	`unswap-sqr_binary64`
622×	`associate-*l/_binary64`
554×	`*-commutative_binary64`
396×	`associate-*r/_binary64`
354×	`associate-/l*_binary64`

Counts

219 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	2506
1	333	2092
2	1282	1957
3	3491	1929
4	4944	1929
5	4942	1929

prune215.0ms (4.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	219	8	227

Error

Counts

227 → 8

Alt Table

Status	Error	Program
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 x (.f64 (/.f64 1 y) z))))
	4.4b	(fabs.f64 (/.f64 (-.f64 x (fma.f64 x z -4)) y))
	35.0b	(fabs.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y)) (sqrt.f64 (/.f64 (fma.f64 -1 (fma.f64 z x -4) x) y))))
	2.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) z))))
✓	2.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (/.f64 x y) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.3b	(fabs.f64 (-.f64 (+.f64 (/.f64 x y) (.f64 4 (/.f64 1 y))) (.f64 (/.f64 x y) z)))
✓	0.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) z))))

Compiler

Compiled 5359 to 2165 computations (59.6% saved)

regimes397.0ms (8.2%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Counts

79 → 1

Compiler

Compiled 7277 to 4844 computations (33.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`*-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	28	40
2	42	40
3	61	40
4	82	40
5	96	40
6	103	40
7	105	40
8	104	40

end115.0ms (2.4%)

Compiler: Compiled 221 to 135 computations (38.9% saved)

Details

analyze527.0ms (10.8%)

sample1.4s (29.3%)

simplify64.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series46.0ms (0.9%)

rewrite25.0ms (0.5%)

simplify127.0ms (2.6%)

prune160.0ms (3.3%)

localize17.0ms (0.3%)

series158.0ms (3.3%)

rewrite16.0ms (0.3%)

simplify111.0ms (2.3%)

prune234.0ms (4.8%)

localize9.0ms (0.2%)

series26.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify94.0ms (1.9%)

prune163.0ms (3.3%)

localize14.0ms (0.3%)

series735.0ms (15.1%)

rewrite33.0ms (0.7%)

simplify117.0ms (2.4%)

prune215.0ms (4.4%)

regimes397.0ms (8.2%)

simplify4.0ms (0.1%)

end115.0ms (2.4%)

Profiling