Details

analyze217.0ms (6.4%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify144.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`
248×	`distribute-rgt-in_binary64`
231×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	137	18
4	197	18
5	297	18
6	671	18
7	1065	18
8	1544	18
9	1657	18
10	1839	18
11	1771	18
12	1745	18
13	1745	18
14	1943	18
15	1776	18
16	1776	18
17	1776	18
18	1583	18

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
▶	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Compiler

Compiled 74 to 59 computations (20.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.2b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite112.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

23×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`

Counts

4 → 99

Calls

4 calls:

11.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
4.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

Compiler

Compiled 1852 to 1376 computations (25.7% saved)

series54.0ms (1.6%)

Error

0.2b

Counts

4 → 27

Calls

4 calls:

22.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
16.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(/.f64 1 (*.f64 x 9))

Compiler

Compiled 834 to 650 computations (22.1% saved)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

595×	`times-frac_binary64`
452×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
286×	`associate-/l*_binary64`
247×	`associate-/r*_binary64`

Counts

126 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1708
1	384	1404
2	1215	1401
3	4867	1401
4	4924	1401

prune58.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Error

0.0b

Counts

90 → 10

Alt Table

Status	Error	Program
	32.8b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/9 x) y) 3)) 1))
	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 x) (cbrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	29.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (+.f64 y (-.f64 (/.f64 1/9 x) 1)))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))
▶	0.4b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	20.2b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	28.6b	(/.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 -1 (.f64 (+.f64 (/.f64 1/9 x) y) (+.f64 (/.f64 1/9 x) y)))) (+.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
	0.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) 1))

Compiler

Compiled 1248 to 940 computations (24.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 x))
0.1b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.5b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite144.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

42×	`add-sqr-sqrt_binary64`
33×	`sqrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

4 → 115

Calls

4 calls:

7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
6.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
6.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
2.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 2210 to 1625 computations (26.5% saved)

series49.0ms (1.4%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

19.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
15.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
5.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
4.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 945 to 729 computations (22.9% saved)

simplify109.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

451×	`distribute-rgt-in_binary64`
433×	`distribute-lft-in_binary64`
351×	`times-frac_binary64`
300×	`*-commutative_binary64`
253×	`+-commutative_binary64`

Counts

139 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	161	1607
1	342	1520
2	958	1516
3	2380	1516
4	4218	1516
5	5020	1516

prune61.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Error

0.0b

Counts

94 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (+.f64 y -1) (sqrt.f64 (sqrt.f64 x))))))
	0.5b	(+.f64 (.f64 1/3 (.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 x))))) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
▶	0.4b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 x) (cbrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	20.2b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (/.f64 1/9 x) (+.f64 y -1)))
	0.4b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))
	0.4b	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))

Compiler

Compiled 1322 to 981 computations (25.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
0.1b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite136.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
16×	`sqrt-prod_binary64`

Counts

4 → 108

Calls

4 calls:

10.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
7.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
6.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
4.0ms	(/.f64 1/3 (sqrt.f64 x))

Compiler

Compiled 2024 to 1277 computations (36.9% saved)

series71.0ms (2.1%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

26.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
16.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
14.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
7.0ms	(/.f64 1/3 (sqrt.f64 x))

Compiler

Compiled 1091 to 788 computations (27.8% saved)

simplify103.0ms (3%)

Algorithm

1×	egg-herbie

Rules

757×	`distribute-rgt-in_binary64`
715×	`distribute-lft-in_binary64`
153×	`associate-r_binary64`
144×	`associate-l_binary64`
104×	`cancel-sign-sub-inv_binary64`

Counts

138 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2048
1	466	1967
2	1410	1920
3	4724	1920
4	4999	1920

prune56.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Error

0.0b

Counts

93 → 7

Alt Table

Status	Error	Program
	0.6b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (+.f64 y -1) (sqrt.f64 (sqrt.f64 x))))))
	16.9b	(/.f64 (-.f64 (/.f64 1/9 x) (.f64 (.f64 (+.f64 y -1) (+.f64 y -1)) (.f64 x 9))) (+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (*.f64 -3 (sqrt.f64 x)) (+.f64 y -1))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	16.9b	(/.f64 (+.f64 (.f64 1/3 (+.f64 y 1)) (.f64 (/.f64 x 1/3) (+.f64 -1 (.f64 y y)))) (.f64 (sqrt.f64 x) (+.f64 y 1)))
	0.5b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 x) (cbrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
▶	0.3b	(+.f64 (/.f64 1 (.f64 3 (sqrt.f64 x))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))

Compiler

Compiled 1244 to 847 computations (31.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.2b	(/.f64 1 (*.f64 3 (sqrt.f64 x)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite127.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
16×	`pow1_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 102

Calls

4 calls:

7.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
6.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
4.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))
4.0ms	(*.f64 3 (sqrt.f64 x))

Compiler

Compiled 1847 to 1248 computations (32.4% saved)

series51.0ms (1.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

17.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
14.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
9.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 1 (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 949 to 714 computations (24.8% saved)

simplify101.0ms (3%)

Algorithm

1×	egg-herbie

Rules

473×	`times-frac_binary64`
459×	`distribute-rgt-in_binary64`
439×	`distribute-lft-in_binary64`
420×	`associate-/l*_binary64`
300×	`div-sub_binary64`

Counts

126 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1373
1	331	1256
2	1028	1253
3	2738	1253
4	4419	1253
5	5123	1253

prune48.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Error

Counts

86 → 6

Alt Table

Status	Error	Program
	16.9b	(/.f64 (-.f64 (/.f64 1/9 x) (.f64 (.f64 (+.f64 y -1) (+.f64 y -1)) (.f64 x 9))) (+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 (*.f64 -3 (sqrt.f64 x)) (+.f64 y -1))))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.4b	(+.f64 (/.f64 1 (.f64 3 (sqrt.f64 x))) (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 3)) (+.f64 y -1))))
	0.4b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 x) 1/3) (+.f64 y -1)))
	0.4b	(+.f64 (/.f64 1 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (sqrt.f64 x) (cbrt.f64 3)))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
	0.4b	(+.f64 (/.f64 1 (.f64 3 (sqrt.f64 x))) (.f64 (sqrt.f64 x) (+.f64 -3 (*.f64 3 y))))

Compiler

Compiled 891 to 624 computations (30% saved)

regimes853.0ms (25.1%)

Accuracy

Total 0.3b remaining (91.7%)

Threshold costs 0.3b (91.7%)

Compiler

Compiled 14533 to 11445 computations (21.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	21	23
2	19	23

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample754.0ms (22.2%)

Algorithm

1×

intervals

Results

424.0ms	8000×	body	128	valid
7.0ms	136×	body	128	nan
3.0ms	64×	body	128	invalid

Compiler

Compiled 167 to 133 computations (20.4% saved)

Details

analyze217.0ms (6.4%)

sample21.0ms (0.6%)

simplify144.0ms (4.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite112.0ms (3.3%)

series54.0ms (1.6%)

simplify85.0ms (2.5%)

prune58.0ms (1.7%)

localize10.0ms (0.3%)

rewrite144.0ms (4.2%)

series49.0ms (1.4%)

simplify109.0ms (3.2%)

prune61.0ms (1.8%)

localize8.0ms (0.2%)

rewrite136.0ms (4%)

series71.0ms (2.1%)

simplify103.0ms (3%)

prune56.0ms (1.6%)

localize9.0ms (0.3%)

rewrite127.0ms (3.7%)

series51.0ms (1.5%)

simplify101.0ms (3%)

prune48.0ms (1.4%)

regimes853.0ms (25.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample754.0ms (22.2%)

Profiling