Details

analyze204.0ms (2.2%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
87.4%	12.5%	0.1%	9
87.4%	12.5%	0.1%	10
87.4%	12.5%	0.1%	11
93.6%	6.2%	0.1%	12
93.6%	6.2%	0.1%	13
93.6%	6.2%	0.1%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.3s (14.7%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	19

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

8.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 63 to 36 computations (42.9% saved)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
✓	3.7b	(-.f64 (.f64 z z) (.f64 x x))
✓	5.5b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series126.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

80.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
34.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
11.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite95.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`add-sqr-sqrt_binary64`
98×	`*-un-lft-identity_binary64`
97×	`prod-diff_binary64`
96×	`add-cube-cbrt_binary64`
85×	`times-frac_binary64`

Counts

3 → 182

Calls

3 calls:

27.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
10.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
7.0ms	(-.f64 (.f64 z z) (.f64 x x))

simplify308.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
460×	`distribute-rgt-in_binary64`
438×	`distribute-lft-in_binary64`
185×	`fma-neg_binary64`
147×	`cancel-sign-sub-inv_binary64`

Counts

278 → 252

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	6753
1	512	6204
2	1861	5381
3	4951	5381

prune318.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	4	253

Error

0.2b

Counts

253 → 4

Alt Table

Status	Error	Program
	8.2b	(.f64 -1/2 (-.f64 (/.f64 1 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x)))) y))
▶	0.3b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
	1.0b	(.f64 (.f64 (cbrt.f64 (.f64 -1/2 (fma.f64 (+.f64 x z) (/.f64 (-.f64 z x) y) (neg.f64 y)))) (cbrt.f64 (.f64 -1/2 (fma.f64 (+.f64 x z) (/.f64 (-.f64 z x) y) (neg.f64 y))))) (cbrt.f64 (*.f64 -1/2 (fma.f64 (+.f64 x z) (/.f64 (-.f64 z x) y) (neg.f64 y)))))
	0.3b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 7553 to 1914 computations (74.7% saved)

localize20.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) y)
✓	0.1b	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
✓	0.2b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))

series115.0ms (1.3%)

Counts

3 → 100

Calls

3 calls:

57.0ms	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
36.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
22.0ms	(/.f64 (-.f64 z x) y)

rewrite70.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
29×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

3 → 121

Calls

3 calls:

23.0ms	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
21.0ms	(*.f64 (+.f64 x z) (/.f64 (-.f64 z x) y))
10.0ms	(/.f64 (-.f64 z x) y)

simplify244.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
494×	`fma-neg_binary64`
218×	`associate-/l/_binary64`
187×	`associate-l_binary64`
163×	`associate-/r*_binary64`

Counts

221 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	3618
1	542	3365
2	2355	3300
3	4587	3300
4	4900	3300

prune237.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	193	4	197

Error

0.2b

Counts

197 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))) y))
	31.3b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (+.f64 x z)) (*.f64 (sqrt.f64 (+.f64 x z)) (/.f64 (-.f64 z x) y))) y))
✓	0.3b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
▶	0.3b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 4175 to 1274 computations (69.5% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z x))
✓	0.1b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
✓	0.2b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

series157.0ms (1.7%)

Counts

3 → 96

Calls

3 calls:

75.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
45.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
36.0ms	(/.f64 y (-.f64 z x))

rewrite465.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Rules

1090×	`*-un-lft-identity_binary64`
1041×	`times-frac_binary64`
803×	`add-sqr-sqrt_binary64`
610×	`add-cube-cbrt_binary64`
534×	`prod-diff_binary64`

Counts

3 → 735

Calls

3 calls:

89.0ms	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
23.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
8.0ms	(/.f64 y (-.f64 z x))

simplify1.3s (13.8%)

Algorithm

1×	egg-herbie

Rules

400×	`*-commutative_binary64`
294×	`fma-neg_binary64`
219×	`associate-*l/_binary64`
206×	`associate-/l*_binary64`
204×	`associate-/r/_binary64`

Counts

831 → 708

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	853	32384
1	1083	30805
2	4497	30805
3	4978	30805

prune774.0ms (8.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	708	0	708
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	708	4	712

Error

0.2b

Counts

712 → 4

Alt Table

Status	Error	Program
▶	0.6b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))) y))
	31.3b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (+.f64 x z)) (*.f64 (sqrt.f64 (+.f64 x z)) (/.f64 (-.f64 z x) y))) y))
✓	0.3b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
✓	0.3b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 26053 to 6163 computations (76.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 y (cbrt.f64 (-.f64 z x)))
✓	0.3b	(/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
✓	0.6b	(cbrt.f64 (-.f64 z x))

series779.0ms (8.5%)

Counts

4 → 120

Calls

4 calls:

628.0ms	(/.f64 y (cbrt.f64 (-.f64 z x)))
64.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
45.0ms	(cbrt.f64 (-.f64 z x))
41.0ms	(/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))

rewrite107.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
83×	`cbrt-prod_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 216

Calls

4 calls:

28.0ms	(/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))
21.0ms	(*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x)))
10.0ms	(/.f64 y (cbrt.f64 (-.f64 z x)))
4.0ms	(cbrt.f64 (-.f64 z x))

simplify381.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

369×	`associate-r_binary64`
316×	`associate-/l*_binary64`
290×	`associate-l_binary64`
267×	`*-commutative_binary64`
189×	`fma-def_binary64`

Counts

336 → 387

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	489	8415
1	1266	7648
2	4651	7328
3	4961	7328

prune1.2s (12.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	491	4	495

Error

0.2b

Counts

495 → 4

Alt Table

Status	Error	Program
✓	0.6b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (*.f64 (cbrt.f64 (-.f64 z x)) (cbrt.f64 (-.f64 z x))) (/.f64 y (cbrt.f64 (-.f64 z x))))) y))
	31.3b	(.f64 -1/2 (-.f64 (.f64 (sqrt.f64 (+.f64 x z)) (*.f64 (sqrt.f64 (+.f64 x z)) (/.f64 (-.f64 z x) y))) y))
✓	0.3b	(.f64 -1/2 (-.f64 (.f64 (+.f64 x z) (/.f64 (-.f64 z x) y)) y))
✓	0.3b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))

Compiler

Compiled 18136 to 6885 computations (62% saved)

regimes724.0ms (7.9%)

Accuracy

Total 0.0b remaining (59.2%)

Threshold costs 0.0b (59.2%)

Counts

63 → 1

Compiler

Compiled 8676 to 4951 computations (42.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	18	19
2	26	19
3	30	19
4	32	19
5	32	19

end103.0ms (1.1%)

Compiler: Compiled 113 to 65 computations (42.5% saved)

Details

analyze204.0ms (2.2%)

sample1.3s (14.7%)

simplify89.0ms (1%)

prune6.0ms (0.1%)

localize17.0ms (0.2%)

series126.0ms (1.4%)

rewrite95.0ms (1%)

simplify308.0ms (3.4%)

prune318.0ms (3.5%)

localize20.0ms (0.2%)

series115.0ms (1.3%)

rewrite70.0ms (0.8%)

simplify244.0ms (2.7%)

prune237.0ms (2.6%)

localize16.0ms (0.2%)

series157.0ms (1.7%)

rewrite465.0ms (5.1%)

simplify1.3s (13.8%)

prune774.0ms (8.5%)

localize15.0ms (0.2%)

series779.0ms (8.5%)

rewrite107.0ms (1.2%)

simplify381.0ms (4.2%)

prune1.2s (12.6%)

regimes724.0ms (7.9%)

simplify5.0ms (0.1%)

end103.0ms (1.1%)

Profiling