Details

analyze58.0ms (2.8%)

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
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)

sample929.0ms (45.7%)

Results

768.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify139.0ms (6.8%)

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

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	6.6b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	6.6b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series22.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

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

rewrite4.0ms (0.2%)

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:

2.0ms	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
0.0ms	(fma.f64 1/2 (/.f64 x y) -1/2)

simplify100.0ms (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

prune37.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	5	64

Error

0.0b

Counts

64 → 5

Alt Table

Status	Error	Program
	18.5b	(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
▶	6.7b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	6.6b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
	33.9b	(*.f64 2 y)

Compiler

Compiled 1024 to 604 computations (41% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 1/2 (/.f64 x y) -1/2)
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	6.6b	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

series23.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)
11.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
2.0ms	(/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x)

simplify124.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-neg_binary64`
408×	`times-frac_binary64`
399×	`cancel-sign-sub-inv_binary64`
256×	`fma-def_binary64`
247×	`associate-/l*_binary64`

Counts

155 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	3160
1	313	2887
2	929	2794
3	3176	2787
4	4747	2787
5	4935	2787

prune106.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	172	5	177

Error

0.0b

Counts

177 → 5

Alt Table

Status	Error	Program
	18.5b	(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	6.7b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
✓	6.6b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
	33.9b	(*.f64 2 y)

Compiler

Compiled 3387 to 2124 computations (37.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.6b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

series11.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

6.0ms

(/.f64 (*.f64 (*.f64 x 2) y) (-.f64 x y))

simplify67.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

642×	`associate-l_binary64`
479×	`associate-*l/_binary64`
433×	`associate-/r*_binary64`
421×	`associate-/l/_binary64`
317×	`associate-*r/_binary64`

Counts

55 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1110
1	320	982
2	1370	939
3	4937	936
4	5014	936

prune32.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	2	2
Picked	1	0	1
Done	1	1	2
Total	60	4	64

Error

Counts

64 → 4

Alt Table

Status	Error	Program
	18.5b	(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	6.7b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
▶	6.6b	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))
	33.9b	(*.f64 2 y)

Compiler

Compiled 1030 to 543 computations (47.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) y)
✓	6.6b	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))

series21.0ms (1%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))
4.0ms	(/.f64 (-.f64 x y) y)

rewrite23.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`times-frac_binary64`
50×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 100

Calls

2 calls:

10.0ms	(/.f64 (-.f64 x y) y)
6.0ms	(/.f64 (*.f64 x 2) (/.f64 (-.f64 x y) y))

simplify92.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

579×	`associate-*l/_binary64`
562×	`associate-/r/_binary64`
429×	`associate-/r*_binary64`
314×	`div-sub_binary64`
303×	`associate-*r/_binary64`

Counts

148 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	2459
1	488	2272
2	1724	2219
3	4577	2216
4	5433	2216

prune71.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
	18.5b	(/.f64 x (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	6.7b	(/.f64 1 (/.f64 (fma.f64 1/2 (/.f64 x y) -1/2) x))
	7.7b	(.f64 (/.f64 x (-.f64 x y)) (.f64 2 y))

Compiler

Compiled 2740 to 1062 computations (61.2% saved)

regimes76.0ms (3.8%)

Accuracy

Total 0.2b remaining (97%)

Threshold costs 0.2b (97%)

Counts

29 → 1

Compiler

Compiled 1060 to 736 computations (30.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	13	13
2	12	13

end51.0ms (2.5%)

Compiler: Compiled 57 to 43 computations (24.6% saved)

Details

analyze58.0ms (2.8%)

sample929.0ms (45.7%)

simplify139.0ms (6.8%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series22.0ms (1.1%)

rewrite4.0ms (0.2%)

simplify100.0ms (4.9%)

prune37.0ms (1.8%)

localize6.0ms (0.3%)

series23.0ms (1.1%)

rewrite13.0ms (0.6%)

simplify124.0ms (6.1%)

prune106.0ms (5.2%)

localize5.0ms (0.2%)

series11.0ms (0.5%)

rewrite7.0ms (0.4%)

simplify67.0ms (3.3%)

prune32.0ms (1.6%)

localize5.0ms (0.3%)

series21.0ms (1%)

rewrite23.0ms (1.1%)

simplify92.0ms (4.5%)

prune71.0ms (3.5%)

regimes76.0ms (3.8%)

simplify2.0ms (0.1%)

end51.0ms (2.5%)

Profiling