Details

analyze137.0ms (6.1%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample16.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify69.0ms (3%)

Algorithm

1×	egg-herbie

Rules

365×	`times-frac_binary64`
344×	`div-sub_binary64`
156×	`associate-/l*_binary64`
143×	`distribute-rgt-in_binary64`
129×	`sub-neg_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	29	10
4	49	10
5	75	10
6	111	10
7	163	10
8	251	10
9	569	10
10	683	10
11	967	10
12	866	10
13	877	10
14	879	10
15	883	10
16	883	10
17	782	10

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 18 to 10 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

rewrite65.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 46

Calls

1 calls:

6.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 580 to 131 computations (77.4% saved)

series28.0ms (1.2%)

Error

0.0b

Counts

1 → 21

Calls

1 calls:

24.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 439 to 346 computations (21.2% saved)

simplify90.0ms (4%)

Algorithm

1×	egg-herbie

Rules

730×	`div-sub_binary64`
392×	`associate-/l/_binary64`
358×	`associate-/r/_binary64`
352×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`

Counts

67 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1178
1	258	1136
2	619	1098
3	1825	1071
4	4631	1071
5	6010	1071

prune18.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Error

0.0b

Counts

31 → 3

Alt Table

Status	Error	Program
	32.2b	(+.f64 1 (.f64 (/.f64 y x) (-.f64 (.f64 2 (/.f64 y x)) 2)))
	31.2b	(+.f64 -1 (*.f64 2 (/.f64 x y)))
▶	0.2b	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))

Compiler

Compiled 243 to 119 computations (51% saved)

localize11.0ms (0.5%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (+.f64 x y))
0.2b	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))

rewrite67.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`

Counts

2 → 91

Calls

2 calls:

18.0ms	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))
4.0ms	(/.f64 1 (+.f64 x y))

Compiler

Compiled 1384 to 577 computations (58.3% saved)

series51.0ms (2.3%)

Error

0.0b

Counts

2 → 42

Calls

2 calls:

22.0ms	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))
21.0ms	(/.f64 1 (+.f64 x y))

Compiler

Compiled 1018 to 736 computations (27.7% saved)

simplify120.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

495×	`div-sub_binary64`
351×	`cancel-sign-sub-inv_binary64`
262×	`associate-/l*_binary64`
256×	`times-frac_binary64`
236×	`distribute-rgt-in_binary64`

Counts

133 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1964
1	377	1808
2	1065	1745
3	2981	1745
4	4537	1745
5	5530	1745

prune31.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Error

Counts

102 → 4

Alt Table

Status	Error	Program
	32.2b	(+.f64 1 (.f64 (/.f64 y x) (-.f64 (.f64 2 (/.f64 y x)) 2)))
	31.2b	(+.f64 -1 (*.f64 2 (/.f64 x y)))
▶	1.3b	(.f64 (/.f64 (sqrt.f64 1) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (-.f64 x y) (cbrt.f64 (+.f64 x y))))
✓	0.2b	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))

Compiler

Compiled 828 to 320 computations (61.4% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
0.5b	(cbrt.f64 (+.f64 x y))
0.5b	(cbrt.f64 (+.f64 x y))
0.5b	(cbrt.f64 (+.f64 x y))

rewrite57.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 95

Calls

4 calls:

10.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
2.0ms	(cbrt.f64 (+.f64 x y))
2.0ms	(cbrt.f64 (+.f64 x y))
2.0ms	(cbrt.f64 (+.f64 x y))

Compiler

Compiled 2403 to 587 computations (75.6% saved)

series147.0ms (6.5%)

Error

Counts

4 → 60

Calls

4 calls:

39.0ms	(*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))
30.0ms	(cbrt.f64 (+.f64 x y))
29.0ms	(cbrt.f64 (+.f64 x y))
29.0ms	(cbrt.f64 (+.f64 x y))

Compiler

Compiled 3765 to 2577 computations (31.6% saved)

simplify186.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

551×	`unswap-sqr_binary64`
492×	`associate-l_binary64`
431×	`associate-r_binary64`
421×	`cancel-sign-sub-inv_binary64`
194×	`distribute-rgt-neg-in_binary64`

Counts

155 → 138

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	2761
1	335	2761
2	826	2634
3	2594	2614
4	4481	2406
5	4733	2406
6	4963	2406
7	4880	2406

prune37.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
	32.2b	(+.f64 1 (.f64 (/.f64 y x) (-.f64 (.f64 2 (/.f64 y x)) 2)))
▶	31.2b	(+.f64 -1 (*.f64 2 (/.f64 x y)))
✓	1.3b	(.f64 (/.f64 (sqrt.f64 1) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (-.f64 x y) (cbrt.f64 (+.f64 x y))))
✓	0.2b	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))

Compiler

Compiled 1943 to 746 computations (61.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 -1 (*.f64 2 (/.f64 x y)))
0.0b	(*.f64 2 (/.f64 x y))

rewrite31.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

6.0ms	(*.f64 2 (/.f64 x y))
2.0ms	(+.f64 -1 (*.f64 2 (/.f64 x y)))

Compiler

Compiled 599 to 361 computations (39.7% saved)

series33.0ms (1.5%)

Error

Counts

2 → 18

Calls

2 calls:

21.0ms	(+.f64 -1 (*.f64 2 (/.f64 x y)))
11.0ms	(*.f64 2 (/.f64 x y))

Compiler

Compiled 268 to 206 computations (23.1% saved)

simplify90.0ms (4%)

Algorithm

1×	egg-herbie

Rules

631×	`associate-/l*_binary64`
326×	`div-sub_binary64`
270×	`associate-/l/_binary64`
237×	`distribute-rgt-in_binary64`
222×	`times-frac_binary64`

Counts

61 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	646
1	221	622
2	576	622
3	1605	622
4	4214	622
5	4957	622

prune10.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	27	4	31

Error

Counts

31 → 4

Alt Table

Status	Error	Program
	32.2b	(+.f64 1 (.f64 (/.f64 y x) (-.f64 (.f64 2 (/.f64 y x)) 2)))
	31.2b	(+.f64 -1 (*.f64 2 (/.f64 x y)))
	1.3b	(.f64 (/.f64 (sqrt.f64 1) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (-.f64 x y) (cbrt.f64 (+.f64 x y))))
	0.2b	(*.f64 (/.f64 1 (+.f64 x y)) (-.f64 x y))

Compiler

Compiled 281 to 180 computations (35.9% saved)

regimes148.0ms (6.5%)

Accuracy

Total 0.0b remaining (48.9%)

Threshold costs 0.0b (48.9%)

Compiler

Compiled 2757 to 1542 computations (44.1% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	16	16
2	21	16
3	24	16
4	25	16
5	25	16

end0.0ms (0%)

Compiler: Compiled 13 to 6 computations (53.8% saved)

sample795.0ms (35.2%)

Algorithm

1×

intervals

Results

538.0ms

8000×

body

128

valid

Compiler

Compiled 83 to 49 computations (41% saved)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	29	10
4	49	10
5	75	10
6	111	10
7	163	10
8	251	10
9	569	10
10	683	10
11	967	10
12	866	10
13	877	10
14	879	10
15	883	10
16	883	10
17	782	10

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	29	10
4	49	10
5	75	10
6	111	10
7	163	10
8	251	10
9	569	10
10	683	10
11	967	10
12	866	10
13	877	10
14	879	10
15	883	10
16	883	10
17	782	10

Details

analyze137.0ms (6.1%)

sample16.0ms (0.7%)

simplify69.0ms (3%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

rewrite65.0ms (2.9%)

series28.0ms (1.2%)

simplify90.0ms (4%)

prune18.0ms (0.8%)

localize11.0ms (0.5%)

rewrite67.0ms (3%)

series51.0ms (2.3%)

simplify120.0ms (5.3%)

prune31.0ms (1.4%)

localize11.0ms (0.5%)

rewrite57.0ms (2.5%)

series147.0ms (6.5%)

simplify186.0ms (8.2%)

prune37.0ms (1.6%)

localize4.0ms (0.2%)

rewrite31.0ms (1.4%)

series33.0ms (1.5%)

simplify90.0ms (4%)

prune10.0ms (0.4%)

regimes148.0ms (6.5%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample795.0ms (35.2%)

Profiling

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	29	10
4	49	10
5	75	10
6	111	10
7	163	10
8	251	10
9	569	10
10	683	10
11	967	10
12	866	10
13	877	10
14	879	10
15	883	10
16	883	10
17	782	10