Details

analyze94.0ms (3.2%)

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
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)

sample795.0ms (27.1%)

Results

713.0ms	8256×	body	128	valid
17.0ms	191×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify23.0ms (0.8%)

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%)

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)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite10.0ms (0.3%)

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:

6.0ms

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

simplify109.0ms (3.7%)

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

prune52.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Error

0.0b

Counts

74 → 4

Alt Table

Status	Error	Program
	35.6b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
	5.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
▶	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	11.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))

Compiler

Compiled 1375 to 582 computations (57.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.4%)

Counts

2 → 28

Calls

2 calls:

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

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`associate-l_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(*.f64 (-.f64 1 y) x)
5.0ms	(.f64 y (.f64 (-.f64 1 y) x))

simplify55.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-def_binary64`
371×	`unsub-neg_binary64`
324×	`unswap-sqr_binary64`
288×	`*-commutative_binary64`
245×	`associate-+l+_binary64`

Counts

75 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	819
1	186	726
2	553	723
3	1335	720
4	2735	720
5	4950	720

prune47.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

0.0b

Counts

85 → 5

Alt Table

Status	Error	Program
	35.6b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
	5.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	11.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
▶	1.1b	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))

Compiler

Compiled 1131 to 607 computations (46.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (*.f64 (-.f64 1 y) x)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (*.f64 (-.f64 1 y) x)))
✓	0.6b	(cbrt.f64 (*.f64 (-.f64 1 y) x))

series673.0ms (22.9%)

Counts

4 → 96

Calls

4 calls:

338.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (*.f64 (-.f64 1 y) x)))
297.0ms	(cbrt.f64 (*.f64 (-.f64 1 y) x))
21.0ms	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))
17.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (*.f64 (-.f64 1 y) x)))

rewrite55.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`associate-*l/_binary64`
122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`

Counts

4 → 164

Calls

4 calls:

12.0ms	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))
10.0ms	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (*.f64 (-.f64 1 y) x)))
5.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (*.f64 (-.f64 1 y) x)))
3.0ms	(cbrt.f64 (*.f64 (-.f64 1 y) x))

simplify208.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
389×	`fma-neg_binary64`
320×	`associate-r_binary64`
316×	`associate-l_binary64`
287×	`cancel-sign-sub-inv_binary64`

Counts

260 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	320	6124
1	732	5708
2	2318	5172
3	4639	5156
4	5018	5156

prune314.0ms (10.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	408	0	408
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	408	5	413

Error

0.0b

Counts

413 → 5

Alt Table

Status	Error	Program
	35.6b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
▶	5.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	11.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	1.1b	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))

Compiler

Compiled 13596 to 8858 computations (34.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (pow.f64 y 2))
✓	4.8b	(*.f64 (-.f64 y (pow.f64 y 2)) x)

series12.0ms (0.4%)

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:

7.0ms	(*.f64 (-.f64 y (pow.f64 y 2)) x)
4.0ms	(-.f64 y (pow.f64 y 2))

simplify99.0ms (3.4%)

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

prune117.0ms (4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	123	6	129

Error

0.0b

Counts

129 → 6

Alt Table

Status	Error	Program
	35.6b	(.f64 (.f64 (*.f64 x y) (+.f64 1 (sqrt.f64 y))) (-.f64 1 (sqrt.f64 y)))
✓	5.1b	(*.f64 (-.f64 y (pow.f64 y 2)) x)
	6.0b	(.f64 (.f64 (-.f64 y (pow.f64 y 2)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	0.1b	(.f64 y (.f64 (-.f64 1 y) x))
	11.4b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 (-.f64 1 y))) (sqrt.f64 (-.f64 1 y)))
✓	1.1b	(.f64 y (.f64 (.f64 (cbrt.f64 (.f64 (-.f64 1 y) x)) (cbrt.f64 (.f64 (-.f64 1 y) x))) (cbrt.f64 (.f64 (-.f64 1 y) x))))

Compiler

Compiled 2272 to 1250 computations (45% saved)

regimes122.0ms (4.2%)

Accuracy

Total 0.1b remaining (75.2%)

Threshold costs 0.1b (75.2%)

Counts

43 → 1

Compiler

Compiled 2047 to 1366 computations (33.3% 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

end76.0ms (2.6%)

Compiler: Compiled 106 to 71 computations (33% 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

analyze94.0ms (3.2%)

sample795.0ms (27.1%)

simplify23.0ms (0.8%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite10.0ms (0.3%)

simplify109.0ms (3.7%)

prune52.0ms (1.8%)

localize4.0ms (0.1%)

series11.0ms (0.4%)

rewrite16.0ms (0.5%)

simplify55.0ms (1.9%)

prune47.0ms (1.6%)

localize8.0ms (0.3%)

series673.0ms (22.9%)

rewrite55.0ms (1.9%)

simplify208.0ms (7.1%)

prune314.0ms (10.7%)

localize4.0ms (0.1%)

series12.0ms (0.4%)

rewrite16.0ms (0.6%)

simplify99.0ms (3.4%)

prune117.0ms (4%)

regimes122.0ms (4.2%)

simplify2.0ms (0.1%)

end76.0ms (2.6%)

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