Details

analyze123.0ms (4.9%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample63.0ms (2.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
148×	`fma-neg_binary64`
84×	`distribute-rgt-in_binary64`
50×	`distribute-lft-in_binary64`
50×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
16×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

1 → 51

Calls

1 calls:

10.0ms

(*.f64 (*.f64 x y) (-.f64 1 y))

simplify105.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
433×	`exp-prod_binary64`
400×	`*-commutative_binary64`
343×	`fma-def_binary64`
288×	`associate-+r+_binary64`

Counts

75 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1085
1	223	985
2	948	871
3	2323	814
4	4186	814
5	4991	814
6	4915	814
7	4901	814

prune55.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
	11.7b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	36.5b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
	6.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 1406 to 606 computations (56.9% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
✓	0.2b	(cbrt.f64 (-.f64 1 y))
✓	0.2b	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
✓	0.2b	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))

series365.0ms (14.6%)

Counts

4 → 72

Calls

4 calls:

348.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
7.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
5.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
4.0ms	(cbrt.f64 (-.f64 1 y))

rewrite59.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
44×	`cbrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
41×	`pow1_binary64`

Counts

4 → 172

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
11.0ms	(*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))
10.0ms	(.f64 (.f64 x y) (*.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y))))
2.0ms	(cbrt.f64 (-.f64 1 y))

simplify150.0ms (6%)

Algorithm

1×	egg-herbie

Rules

758×	`fma-def_binary64`
549×	`associate-l_binary64`
390×	`associate-r_binary64`
385×	`fma-neg_binary64`
325×	`cancel-sign-sub-inv_binary64`

Counts

244 → 289

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	5321
1	760	4846
2	2552	4532
3	4553	4491
4	4984	4491

prune336.0ms (13.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	375	7	382

Error

Counts

382 → 7

Alt Table

Status	Error	Program
	36.7b	(.f64 (.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 y))) (cbrt.f64 (+.f64 1 (sqrt.f64 y)))) (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 y))) (cbrt.f64 (-.f64 1 (sqrt.f64 y)))))) (cbrt.f64 (-.f64 1 y)))
▶	6.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	11.7b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 (.f64 x y) (cbrt.f64 (.f64 y y))) (cbrt.f64 (-.f64 1 y)))
	36.5b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 10715 to 7511 computations (29.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	5.7b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series12.0ms (0.5%)

Counts

2 → 15

Calls

2 calls:

10.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
2.0ms	(-.f64 y (pow.f64 y 2))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`
14×	`unpow-prod-down_binary64`

Counts

2 → 82

Calls

2 calls:

6.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
6.0ms	(-.f64 y (pow.f64 y 2))

simplify94.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
456×	`fma-def_binary64`
377×	`exp-prod_binary64`
263×	`cancel-sign-sub-inv_binary64`
232×	`difference-of-squares_binary64`

Counts

97 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1889
1	261	1074
2	791	924
3	2087	924
4	3779	924
5	4661	924
6	4794	924

prune90.0ms (3.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	124	7	131

Error

Counts

131 → 7

Alt Table

Status	Error	Program
	36.7b	(.f64 (.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 y))) (cbrt.f64 (+.f64 1 (sqrt.f64 y)))) (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 y))) (cbrt.f64 (-.f64 1 (sqrt.f64 y)))))) (cbrt.f64 (-.f64 1 y)))
✓	6.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
▶	11.7b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 (.f64 x y) (cbrt.f64 (.f64 y y))) (cbrt.f64 (-.f64 1 y)))
	36.5b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 2380 to 1328 computations (44.2% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 y))
✓	0.1b	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
✓	0.1b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

series31.0ms (1.2%)

Counts

3 → 44

Calls

3 calls:

16.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
8.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
7.0ms	(sqrt.f64 (-.f64 1 y))

rewrite27.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
18×	`associate-r_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`pow1_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 85

Calls

3 calls:

12.0ms	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
6.0ms	(.f64 (.f64 x y) (sqrt.f64 (-.f64 1 y)))
3.0ms	(sqrt.f64 (-.f64 1 y))

simplify95.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

524×	`*-commutative_binary64`
460×	`fma-def_binary64`
361×	`associate-l_binary64`
333×	`fma-neg_binary64`
321×	`cancel-sign-sub-inv_binary64`

Counts

129 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1853
1	373	1689
2	1352	1668
3	2949	1656
4	4698	1656
5	4966	1656

prune130.0ms (5.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	166	7	173

Error

Counts

173 → 7

Alt Table

Status	Error	Program
	36.7b	(.f64 (.f64 (.f64 x y) (.f64 (.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 y))) (cbrt.f64 (+.f64 1 (sqrt.f64 y)))) (.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 y))) (cbrt.f64 (-.f64 1 (sqrt.f64 y)))))) (cbrt.f64 (-.f64 1 y)))
✓	6.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	11.7b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	0.5b	(.f64 (.f64 (.f64 x y) (.f64 (cbrt.f64 (-.f64 1 y)) (cbrt.f64 (-.f64 1 y)))) (cbrt.f64 (-.f64 1 y)))
	33.2b	(.f64 (.f64 (.f64 x y) (cbrt.f64 (.f64 y y))) (cbrt.f64 (-.f64 1 y)))
	36.5b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	0.1b	(.f64 (.f64 x y) (-.f64 1 y))

Compiler

Compiled 3383 to 2201 computations (34.9% saved)

regimes107.0ms (4.3%)

Accuracy

Total 0.1b remaining (77.5%)

Threshold costs 0.1b (77.5%)

Counts

37 → 1

Compiler

Compiled 1977 to 1334 computations (32.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	17	10
3	19	10
4	20	10
5	19	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample572.0ms (22.9%)

Algorithm

1×

intervals

Results

272.0ms	8000×	body	128	valid
5.0ms	195×	body	128	invalid

Compiler

Compiled 138 to 97 computations (29.7% saved)

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10

Details

analyze123.0ms (4.9%)

sample63.0ms (2.5%)

simplify25.0ms (1%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite13.0ms (0.5%)

simplify105.0ms (4.2%)

prune55.0ms (2.2%)

localize7.0ms (0.3%)

series365.0ms (14.6%)

rewrite59.0ms (2.4%)

simplify150.0ms (6%)

prune336.0ms (13.4%)

localize4.0ms (0.2%)

series12.0ms (0.5%)

rewrite16.0ms (0.6%)

simplify94.0ms (3.8%)

prune90.0ms (3.6%)

localize6.0ms (0.2%)

series31.0ms (1.2%)

rewrite27.0ms (1.1%)

simplify95.0ms (3.8%)

prune130.0ms (5.2%)

regimes107.0ms (4.3%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample572.0ms (22.9%)

Profiling

Iter	Nodes	Cost
0	7	10
1	15	10
2	37	10
3	71	10
4	148	10
5	211	10
6	297	10
7	526	10
8	560	10
9	559	10
10	595	10
11	544	10