Details

analyze35.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample35.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	30×	body	256	valid
8.0ms	148×	body	128	valid
7.0ms	35×	body	1024	valid
6.0ms	43×	body	512	valid

Compiler

Compiled 34 to 28 computations (17.6% saved)

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
41×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

prune2.0ms (0%)

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

10.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 48 to 39 computations (18.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.6b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite905.0ms (18.8%)

Algorithm

1×	rewrite-expression-head

Error

9.7b

Rules

757×	`*-un-lft-identity_binary64`
733×	`times-frac_binary64`
558×	`add-sqr-sqrt_binary64`
508×	`add-cube-cbrt_binary64`
468×	`prod-diff_binary64`

Counts

4 → 668

Calls

4 calls:

55.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
22.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
4.0ms	(/.f64 1 (-.f64 x 1))
4.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 24496 to 18897 computations (22.9% saved)

series71.0ms (1.5%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

15.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
11.0ms	(/.f64 1 (-.f64 x 1))
9.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 1486 to 1208 computations (18.7% saved)

simplify525.0ms (10.9%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-neg_binary64`
457×	`times-frac_binary64`
241×	`fma-def_binary64`
173×	`+-commutative_binary64`
140×	`unsub-neg_binary64`

Counts

716 → 666

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	451	28932
1	1087	15566
2	3100	15224
3	4943	15224
4	5010	15224

prune286.0ms (5.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	662	4	666
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	663	4	667

Error

0.1b

Counts

667 → 4

Alt Table

Status	Error	Program
	32.8b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (/.f64 2 (pow.f64 x 7)) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 9)))))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
	48.4b	(/.f64 (fma.f64 (-.f64 x 1) (-.f64 (pow.f64 (/.f64 1 (+.f64 x 1)) 3) (pow.f64 (/.f64 2 x) 3)) (+.f64 (/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 x 1)) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 2 (fma.f64 x x x))))) (*.f64 (-.f64 x 1) (+.f64 (/.f64 (/.f64 1 (+.f64 x 1)) (+.f64 x 1)) (+.f64 (/.f64 (/.f64 4 x) x) (/.f64 2 (fma.f64 x x x))))))
▶	25.5b	(/.f64 (fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))

Compiler

Compiled 10287 to 8077 computations (21.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))
0.0b	(*.f64 x (fma.f64 x x -1))
0.2b	(-.f64 x (+.f64 2 (*.f64 x 2)))
29.4b	(fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))

rewrite102.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`prod-diff_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 95

Calls

4 calls:

8.0ms	(/.f64 (fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))
5.0ms	(-.f64 x (+.f64 2 (*.f64 x 2)))
3.0ms	(*.f64 x (fma.f64 x x -1))
0.0ms	(fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))

Compiler

Compiled 3206 to 1943 computations (39.4% saved)

series67.0ms (1.4%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

23.0ms	(/.f64 (fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (.f64 x 2))) (fma.f64 x x x)) (.f64 x (fma.f64 x x -1)))
14.0ms	(*.f64 x (fma.f64 x x -1))
14.0ms	(fma.f64 (-.f64 x 1) (-.f64 x (+.f64 2 (*.f64 x 2))) (fma.f64 x x x))
7.0ms	(-.f64 x (+.f64 2 (*.f64 x 2)))

Compiler

Compiled 878 to 617 computations (29.7% saved)

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-def_binary64`
524×	`times-frac_binary64`
440×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
140×	`cancel-sign-sub-inv_binary64`

Counts

122 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	3007
1	443	2237
2	1548	1846
3	4946	1846

prune45.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	109	2	111

Error

0.0b

Counts

111 → 2

Alt Table

Status	Error	Program
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
▶	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1601 to 931 computations (41.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite118.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

76×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
27×	`times-frac_binary64`

Counts

2 → 125

Calls

2 calls:

28.0ms	(-.f64 (pow.f64 x 3) x)
7.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1966 to 1131 computations (42.5% saved)

series27.0ms (0.6%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

13.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
9.0ms	(-.f64 (pow.f64 x 3) x)

Compiler

Compiled 415 to 347 computations (16.4% saved)

simplify153.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-neg_binary64`
649×	`fma-def_binary64`
342×	`associate-/r*_binary64`
268×	`exp-prod_binary64`
264×	`unswap-sqr_binary64`

Counts

143 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2160
1	378	1953
2	1229	1838
3	3822	1838
4	4450	1838
5	4883	1838
6	4896	1838

prune24.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Error

0.0b

Counts

92 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1 x) (/.f64 2 (fma.f64 x x -1)))
	0.6b	(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (-.f64 (pow.f64 x 3) x)))
	25.6b	(cbrt.f64 (pow.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x)) 3))
	31.6b	(fma.f64 -2 (pow.f64 x 5) (fma.f64 -2 (+.f64 x (pow.f64 x 3)) (/.f64 -2 x)))
✓	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 517 to 361 computations (30.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (/.f64 1 x) (/.f64 2 (fma.f64 x x -1)))
0.3b	(/.f64 2 (fma.f64 x x -1))

rewrite86.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 87

Calls

2 calls:

10.0ms	(*.f64 (/.f64 1 x) (/.f64 2 (fma.f64 x x -1)))
2.0ms	(/.f64 2 (fma.f64 x x -1))

Compiler

Compiled 1569 to 1158 computations (26.2% saved)

series43.0ms (0.9%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

16.0ms	(*.f64 (/.f64 1 x) (/.f64 2 (fma.f64 x x -1)))
16.0ms	(/.f64 2 (fma.f64 x x -1))

Compiler

Compiled 737 to 625 computations (15.2% saved)

simplify175.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-def_binary64`
424×	`times-frac_binary64`
352×	`associate-/l*_binary64`
292×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

111 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2025
1	521	1771
2	1638	1759
3	4776	1747
4	4986	1747
5	4996	1747
6	4938	1747

prune47.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	86	5	91

Error

Counts

91 → 5

Alt Table

Status	Error	Program
	32.5b	(*.f64 (/.f64 (/.f64 1 x) (sqrt.f64 (fma.f64 x x -1))) (/.f64 2 (sqrt.f64 (fma.f64 x x -1))))
	0.1b	(/.f64 (/.f64 2 x) (fma.f64 x x -1))
	0.1b	(/.f64 (/.f64 2 (fma.f64 x x -1)) x)
	25.6b	(cbrt.f64 (pow.f64 (/.f64 2 (-.f64 (pow.f64 x 3) x)) 3))
✓	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 957 to 681 computations (28.8% saved)

regimes753.0ms (15.6%)

Accuracy

Total 0.3b remaining (97%)

Threshold costs 0.3b (97%)

Compiler

Compiled 13501 to 10582 computations (21.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	9	10
2	14	10
3	16	10
4	17	10
5	17	10

end1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample1.2s (24.5%)

Algorithm

1×

intervals

Results

291.0ms	1336×	body	1024	valid
274.0ms	4417×	body	128	valid
265.0ms	1484×	body	512	valid
76.0ms	763×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 81 to 61 computations (24.7% saved)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22

Details

analyze35.0ms (0.7%)

sample35.0ms (0.7%)

simplify19.0ms (0.4%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite905.0ms (18.8%)

series71.0ms (1.5%)

simplify525.0ms (10.9%)

prune286.0ms (5.9%)

localize13.0ms (0.3%)

rewrite102.0ms (2.1%)

series67.0ms (1.4%)

simplify78.0ms (1.6%)

prune45.0ms (0.9%)

localize4.0ms (0.1%)

rewrite118.0ms (2.4%)

series27.0ms (0.6%)

simplify153.0ms (3.2%)

prune24.0ms (0.5%)

localize9.0ms (0.2%)

rewrite86.0ms (1.8%)

series43.0ms (0.9%)

simplify175.0ms (3.6%)

prune47.0ms (1%)

regimes753.0ms (15.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (24.5%)

Profiling

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	61	22
4	109	22
5	186	22
6	246	22
7	296	22
8	348	22
9	368	22
10	344	22