Details

analyze24.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	65×	body	1024	valid
5.0ms	135×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	20×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

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

30.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`sqrt-prod_binary64`
52×	`*-un-lft-identity_binary64`
42×	`prod-diff_binary64`
39×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`

Counts

1 → 75

Calls

1 calls:

8.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series13.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

13.0ms

(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify197.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

485×	`sqr-pow_binary64`
481×	`fma-neg_binary64`
455×	`unsub-neg_binary64`
425×	`unswap-sqr_binary64`
380×	`exp-prod_binary64`

Counts

76 → 149

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	87	2325
1	154	1099
2	417	889
3	1547	889
4	3056	889
5	4410	889
6	4523	889
7	4696	853
8	4047	853
9	4796	853
10	4713	853

prune93.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	3	150

Error

0.1b

Counts

150 → 3

Alt Table

Status	Error	Program
	30.6b	(+.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 1) (sqrt.f64 x)))
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	30.7b	(.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 1588 to 802 computations (49.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 70

Calls

2 calls:

8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series20.0ms (0.6%)

Counts

2 → 2

Calls

2 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify141.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

744×	`div-sub_binary64`
483×	`fma-neg_binary64`
334×	`times-frac_binary64`
317×	`associate-/l*_binary64`
310×	`distribute-rgt-in_binary64`

Counts

72 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	1097
1	123	1012
2	243	1012
3	504	1010
4	1190	1010
5	2283	1010
6	4202	1010
7	4971	1010
8	4998	1010
9	4828	1010

prune96.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	100	9	109
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Error

0.0b

Counts

112 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.3b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
▶	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.4b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	30.6b	(*.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	11.7b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 1549 to 1124 computations (27.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
✓	0.1b	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
✓	0.1b	(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))
✓	0.1b	(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`
9×	`times-frac_binary64`

Counts

3 → 67

Calls

3 calls:

3.0ms

(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

2.0ms

(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

0.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))

series99.0ms (3.2%)

Counts

3 → 14

Calls

3 calls:

76.0ms

(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

18.0ms

(fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))

5.0ms

(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

simplify111.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
652×	`times-frac_binary64`
572×	`fma-neg_binary64`
338×	`associate-/l*_binary64`
259×	`associate-/r*_binary64`

Counts

81 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1459
1	270	1361
2	587	1255
3	1552	1216
4	4229	1216
5	4840	1216
6	4884	1216

prune327.0ms (10.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	197	10	207

Error

0.0b

Counts

207 → 10

Alt Table

Status	Error	Program
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
▶	0.3b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
	0.4b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	30.6b	(*.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	11.7b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 4142 to 3170 computations (23.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.1b	(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

rewrite59.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64`
65×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`pow1_binary64`
28×	`distribute-lft-out_binary64`

Counts

3 → 148

Calls

3 calls:

20.0ms

(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

19.0ms

(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

7.0ms

(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series57.0ms (1.9%)

Counts

3 → 3

Calls

3 calls:

36.0ms

(sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

13.0ms

(/.f64 1 (*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

8.0ms

(*.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

simplify145.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-/r/_binary64`
490×	`fma-def_binary64`
421×	`distribute-rgt-in_binary64`
401×	`distribute-lft-in_binary64`
247×	`associate-l_binary64`

Counts

151 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	2468
1	203	2255
2	557	2152
3	1705	2070
4	4280	2070
5	4753	2070
6	4886	2070

prune305.0ms (9.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	306	5	311
Fresh	3	4	7
Picked	1	0	1
Done	2	0	2
Total	312	9	321

Error

0.0b

Counts

321 → 9

Alt Table

Status	Error	Program
	11.7b	(.f64 (/.f64 1 (fma.f64 x (sqrt.f64 x) (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.8b	(/.f64 1 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 4) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	10.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
	0.1b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1/2)
	0.3b	(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -2)
	0.3b	(/.f64 1 (*.f64 (hypot.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	1.0b	(/.f64 1 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 5) (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.7b	(/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 5323 to 3728 computations (30% saved)

regimes276.0ms (9%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Compiler

Compiled 5191 to 3757 computations (27.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	19	16
2	27	16
3	33	16
4	35	16
5	34	16

end0.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample996.0ms (32.4%)

Algorithm

1×

intervals

Results

291.0ms	1971×	body	1024	valid
168.0ms	4257×	body	128	valid
112.0ms	1028×	body	512	valid
40.0ms	219×	body	2048	valid
39.0ms	525×	body	256	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 219 to 166 computations (24.2% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze24.0ms (0.8%)

sample26.0ms (0.8%)

simplify14.0ms (0.5%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

rewrite14.0ms (0.5%)

series13.0ms (0.4%)

simplify197.0ms (6.4%)

prune93.0ms (3%)

localize6.0ms (0.2%)

rewrite18.0ms (0.6%)

series20.0ms (0.6%)

simplify141.0ms (4.6%)

prune96.0ms (3.1%)

localize7.0ms (0.2%)

rewrite9.0ms (0.3%)

series99.0ms (3.2%)

simplify111.0ms (3.6%)

prune327.0ms (10.6%)

localize8.0ms (0.3%)

rewrite59.0ms (1.9%)

series57.0ms (1.9%)

simplify145.0ms (4.7%)

prune305.0ms (9.9%)

regimes276.0ms (9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample996.0ms (32.4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11