Details

analyze253.0ms (8.2%)

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
0%	99.9%	0.1%	5
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample30.0ms (1%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify152.0ms (5%)

Algorithm

1×	egg-herbie

Rules

878×	`div-sub_binary64`
546×	`times-frac_binary64`
500×	`sub-neg_binary64`
408×	`fma-def_binary64`
395×	`neg-sub0_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	16	13
2	40	13
3	81	13
4	153	13
5	248	13
6	435	11
7	1077	11
8	3029	11
9	3558	11
10	3959	11
11	4158	11
12	4377	11
13	4552	11
14	5083	11

prune7.0ms (0.2%)

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
▶	6.4b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	13.8b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	6.2b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series35.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
11.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

simplify151.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-neg_binary64`
381×	`cancel-sign-sub-inv_binary64`
231×	`fma-def_binary64`
198×	`associate-/l*_binary64`
198×	`times-frac_binary64`

Counts

87 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1389
1	226	1308
2	679	1260
3	2411	1246
4	4577	1246
5	4993	1246
6	4941	1246

prune69.0ms (2.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
✓	6.4b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	7.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
	33.5b	(*.f64 2 y)
	32.6b	(.f64 -2 (+.f64 x (/.f64 (.f64 x x) y)))

Compiler

Compiled 1010 to 588 computations (41.8% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	2.9b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	3.3b	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))

series252.0ms (8.2%)

Counts

4 → 72

Calls

4 calls:

76.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
72.0ms	(cbrt.f64 x)
70.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))

rewrite56.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 143

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
6.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms	(cbrt.f64 x)

simplify258.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-neg_binary64`
359×	`unswap-sqr_binary64`
349×	`associate-l_binary64`
268×	`associate-r_binary64`
161×	`*-commutative_binary64`

Counts

215 → 241

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	263	4204
1	679	3708
2	2794	3566
3	4176	3493
4	4840	3490
5	5046	3490

prune262.0ms (8.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	277	4	281

Error

Counts

281 → 4

Alt Table

Status	Error	Program
✓	6.4b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	7.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
	33.5b	(*.f64 2 y)
▶	32.6b	(.f64 -2 (+.f64 x (/.f64 (.f64 x x) y)))

Compiler

Compiled 6412 to 3042 computations (52.6% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 x x) y))
✓	8.2b	(/.f64 (*.f64 x x) y)

series36.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(/.f64 (*.f64 x x) y)
15.0ms	(+.f64 x (/.f64 (*.f64 x x) y))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

8.0ms	(/.f64 (*.f64 x x) y)
7.0ms	(+.f64 x (/.f64 (*.f64 x x) y))

simplify103.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

751×	`unswap-sqr_binary64`
734×	`fma-def_binary64`
465×	`fma-neg_binary64`
313×	`*-commutative_binary64`
257×	`associate-/l*_binary64`

Counts

88 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	70	825
1	170	798
2	471	735
3	1925	735
4	3955	735
5	5800	735

prune47.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
✓	6.4b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	7.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
▶	33.5b	(*.f64 2 y)
✓	32.6b	(.f64 -2 (+.f64 x (/.f64 (.f64 x x) y)))

Compiler

Compiled 869 to 344 computations (60.4% saved)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	6.4b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	7.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	33.5b	(*.f64 2 y)
✓	32.6b	(.f64 -2 (+.f64 x (/.f64 (.f64 x x) y)))

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes222.0ms (7.2%)

Accuracy

Total 1.1b remaining (99.1%)

Threshold costs 0b (0%)

Counts

15 → 5

Compiler

Compiled 682 to 454 computations (33.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
3×	`if-not_binary64`
3×	`if-if-or-not_binary64`
3×	`not-not_bool`
3×	`not-or_bool`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	122
1	33	111
2	40	102
3	48	100
4	52	100
5	55	100
6	55	100
7	56	100
8	56	100

end2.0ms (0.1%)

Compiler: Compiled 69 to 42 computations (39.1% saved)

sample1.1s (34.3%)

Algorithm

1×

intervals

Results

526.0ms

8000×

body

128

valid

Compiler

Compiled 126 to 80 computations (36.5% saved)

Details

analyze253.0ms (8.2%)

sample30.0ms (1%)

simplify152.0ms (5%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

series35.0ms (1.1%)

rewrite8.0ms (0.3%)

simplify151.0ms (4.9%)

prune69.0ms (2.2%)

localize17.0ms (0.5%)

series252.0ms (8.2%)

rewrite56.0ms (1.8%)

simplify258.0ms (8.4%)

prune262.0ms (8.5%)

localize10.0ms (0.3%)

series36.0ms (1.2%)

rewrite18.0ms (0.6%)

simplify103.0ms (3.4%)

prune47.0ms (1.5%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

regimes222.0ms (7.2%)

bsearch1.0ms (0%)

simplify12.0ms (0.4%)

end2.0ms (0.1%)

sample1.1s (34.3%)

Profiling