Details

analyze55.0ms (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)

sample911.0ms (46.9%)

Results

751.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify141.0ms (7.2%)

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

prune4.0ms (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
	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
▶	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series14.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

14.0ms

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

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify53.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

539×	`associate-/r/_binary64`
418×	`fma-neg_binary64`
375×	`cancel-sign-sub-inv_binary64`
232×	`fma-def_binary64`
195×	`times-frac_binary64`

Counts

53 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1094
1	218	1030
2	655	982
3	2331	968
4	4993	968

prune27.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	2	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
▶	8.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	32.0b	(*.f64 2 y)

Compiler

Compiled 838 to 488 computations (41.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.6b	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
✓	5.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))

series119.0ms (6.1%)

Counts

4 → 72

Calls

4 calls:

36.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
35.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
34.0ms	(cbrt.f64 x)
13.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))

rewrite32.0ms (1.6%)

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:

11.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
8.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
2.0ms	(/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2))
1.0ms	(cbrt.f64 x)

simplify166.0ms (8.5%)

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

prune123.0ms (6.3%)

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
▶	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
✓	8.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	32.0b	(*.f64 2 y)

Compiler

Compiled 6412 to 3042 computations (52.6% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	15.7b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

series11.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

11.0ms

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

rewrite8.0ms (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))

simplify60.0ms (3.1%)

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

prune29.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	59	4	63

Error

Counts

63 → 4

Alt Table

Status	Error	Program
✓	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
✓	8.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
▶	32.0b	(*.f64 2 y)

Compiler

Compiled 1010 to 526 computations (47.9% saved)

localize2.0ms (0.1%)

prune2.0ms (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
✓	16.1b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))
✓	8.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (fma.f64 1/2 (/.f64 x y) -1/2)))
✓	6.8b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
✓	32.0b	(*.f64 2 y)

Compiler

Compiled 43 to 28 computations (34.9% saved)

regimes77.0ms (3.9%)

Accuracy

Total 0.6b remaining (98.6%)

Threshold costs 0.6b (98.6%)

Counts

11 → 5

Compiler

Compiled 481 to 316 computations (34.3% saved)

bsearch1.0ms (0%)

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

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	28	135
1	33	135
2	38	135
3	40	135
4	41	135
5	41	135

end83.0ms (4.3%)

Compiler: Compiled 231 to 130 computations (43.7% saved)

Details

analyze55.0ms (2.8%)

sample911.0ms (46.9%)

simplify141.0ms (7.2%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

series14.0ms (0.7%)

rewrite3.0ms (0.2%)

simplify53.0ms (2.7%)

prune27.0ms (1.4%)

localize8.0ms (0.4%)

series119.0ms (6.1%)

rewrite32.0ms (1.6%)

simplify166.0ms (8.5%)

prune123.0ms (6.3%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite8.0ms (0.4%)

simplify60.0ms (3.1%)

prune29.0ms (1.5%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

regimes77.0ms (3.9%)

bsearch1.0ms (0%)

simplify5.0ms (0.3%)

end83.0ms (4.3%)

Profiling