Details

analyze270.0ms (12.5%)

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
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
31.2%	68.6%	0.1%	8
39%	56.2%	4.8%	9
50.7%	43.7%	5.6%	10
60.3%	33.7%	6%	11
64.6%	26.5%	8.9%	12
70.5%	20.3%	9.2%	13
74.6%	16.1%	9.4%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample17.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`associate-+l+_binary64` `associate-+r+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	20	13
4	20	13

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite39.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64` `*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`
1×	`distribute-lft-out_binary64` `associate-+l+_binary64`

Counts

2 → 25

Calls

2 calls:

8.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
6.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))

Compiler

Compiled 445 to 232 computations (47.9% saved)

series58.0ms (2.7%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

31.0ms	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
17.0ms	(+.f64 (/.f64 x 2) (*.f64 y x))

Compiler

Compiled 502 to 325 computations (35.3% saved)

simplify82.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

367×	`associate-l_binary64`
366×	`cancel-sign-sub-inv_binary64`
329×	`sub-neg_binary64`
279×	`distribute-rgt-out_binary64`
264×	`associate-r_binary64`

Counts

52 → 34

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	670
1	183	643
2	491	628
3	1474	622
4	2686	622
5	4484	622
6	5010	622

prune20.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Error

0.0b

Counts

35 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 z (*.f64 x (+.f64 y 1/2)))
✓	0.0b	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
	34.1b	(+.f64 (/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2)))))) z)

Compiler

Compiled 430 to 246 computations (42.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite39.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `associate-r_binary64`
3×	`associate-l_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `distribute-lft-out_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 36

Calls

2 calls:

6.0ms	(*.f64 x (+.f64 y 1/2))
3.0ms	(+.f64 z (*.f64 x (+.f64 y 1/2)))

Compiler

Compiled 467 to 298 computations (36.2% saved)

series57.0ms (2.6%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

33.0ms	(+.f64 z (*.f64 x (+.f64 y 1/2)))
15.0ms	(*.f64 x (+.f64 y 1/2))

Compiler

Compiled 507 to 329 computations (35.1% saved)

simplify72.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

584×	`distribute-rgt-in_binary64`
575×	`distribute-lft-in_binary64`
406×	`associate-l_binary64`
322×	`associate-r_binary64`
271×	`sub-neg_binary64`

Counts

63 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	614
1	199	593
2	676	593
3	2395	593
4	3586	593
5	4976	593

prune19.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	34	3	37

Error

0.0b

Counts

37 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 z (*.f64 x (+.f64 y 1/2)))
✓	0.0b	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
▶	34.1b	(+.f64 (/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2)))))) z)

Compiler

Compiled 323 to 203 computations (37.2% saved)

localize17.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 x y) 3)
1.5b	(.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (*.f64 x y) (/.f64 x 2)))))
3.0b	(+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (*.f64 x y) 3))
35.5b	(/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2))))))

rewrite178.0ms (8.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`*-un-lft-identity_binary64` `distribute-lft-out_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`unpow-prod-down_binary64` `div-inv_binary64` `cube-prod_binary64`
12×	`associate-*r/_binary64`
11×	`add-sqr-sqrt_binary64`

Counts

4 → 102

Calls

4 calls:

30.0ms	(/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2))))))
22.0ms	(+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (*.f64 x y) 3))
11.0ms	(.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (*.f64 x y) (/.f64 x 2)))))
4.0ms	(pow.f64 (*.f64 x y) 3)

Compiler

Compiled 3662 to 2191 computations (40.2% saved)

series211.0ms (9.8%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

70.0ms	(/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2))))))
50.0ms	(.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (*.f64 x y) (/.f64 x 2)))))
44.0ms	(+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (*.f64 x y) 3))
25.0ms	(pow.f64 (*.f64 x y) 3)

Compiler

Compiled 2123 to 1520 computations (28.4% saved)

simplify165.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

515×	`times-frac_binary64`
275×	`log-prod_binary64`
271×	`cancel-sign-sub-inv_binary64`
267×	`exp-prod_binary64`
245×	`associate-l_binary64`

Counts

138 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	3744
1	549	3309
2	2252	3259
3	4477	3259
4	4969	3259
5	5021	3259

prune72.0ms (3.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	105	3	108

Error

0.0b

Counts

108 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f64 z (*.f64 x (+.f64 y 1/2)))
	0.0b	(+.f64 (+.f64 (/.f64 x 2) (*.f64 y x)) z)
	34.1b	(+.f64 (/.f64 (+.f64 (pow.f64 (/.f64 x 2) 3) (pow.f64 (.f64 x y) 3)) (.f64 x (+.f64 (/.f64 x 4) (.f64 y (-.f64 (.f64 x y) (/.f64 x 2)))))) z)

Compiler

Compiled 2244 to 1353 computations (39.7% saved)

regimes233.0ms (10.8%)

Accuracy

Total 0.0b remaining (50.7%)

Threshold costs 0.0b (50.7%)

Compiler

Compiled 3113 to 2002 computations (35.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample577.0ms (26.8%)

Algorithm

1×

intervals

Results

224.0ms	7998×	body	128	valid
17.0ms	303×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 80 to 55 computations (31.3% saved)

Details

analyze270.0ms (12.5%)

sample17.0ms (0.8%)

simplify8.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

rewrite39.0ms (1.8%)

series58.0ms (2.7%)

simplify82.0ms (3.8%)

prune20.0ms (0.9%)

localize5.0ms (0.2%)

rewrite39.0ms (1.8%)

series57.0ms (2.6%)

simplify72.0ms (3.4%)

prune19.0ms (0.9%)

localize17.0ms (0.8%)

rewrite178.0ms (8.3%)

series211.0ms (9.8%)

simplify165.0ms (7.7%)

prune72.0ms (3.3%)

regimes233.0ms (10.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample577.0ms (26.8%)

Profiling