Details

analyze3.0ms (0.1%)

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)

sample1.5s (41.8%)

Results

690.0ms	2122×	body	1024	valid
410.0ms	4321×	body	128	valid
251.0ms	1051×	body	512	valid
83.0ms	539×	body	256	valid
79.0ms	223×	body	2048	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify13.0ms (0.4%)

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

prune1.0ms (0%)

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

30.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.9b	(-.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
✓	2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series15.0ms (0.4%)

Counts

1 → 1

Calls

1 calls:

15.0ms

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

rewrite14.0ms (0.4%)

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:

7.0ms

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

simplify179.0ms (4.9%)

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 → 69

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

prune86.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

0.1b

Counts

70 → 3

Alt Table

Status	Error	Program
	30.9b	(+.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)))
	31.4b	(/.f64 (-.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3) (pow.f64 (sqrt.f64 x) 3)) (+.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))

Compiler

Compiled 1606 to 814 computations (49.3% saved)

localize5.0ms (0.1%)

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)))

series23.0ms (0.6%)

Counts

2 → 2

Calls

2 calls:

14.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite19.0ms (0.5%)

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:

7.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify124.0ms (3.4%)

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 → 67

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

prune78.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	61	6	67
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	63	7	70

Error

0.0b

Counts

70 → 7

Alt Table

Status	Error	Program
▶	0.3b	(*.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)))))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.3b	(/.f64 1 (cbrt.f64 (.f64 (.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (+.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))))
	0.8b	(/.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))))
	30.9b	(*.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	9.5b	(cbrt.f64 (.f64 (.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))

Compiler

Compiled 1424 to 1027 computations (27.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(*.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)))))

series39.0ms (1.1%)

Counts

2 → 2

Calls

2 calls:

26.0ms

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

13.0ms

(*.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)))))

rewrite77.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`sqrt-prod_binary64`
236×	`*-un-lft-identity_binary64`
148×	`times-frac_binary64`
144×	`add-sqr-sqrt_binary64`
84×	`distribute-lft-out_binary64`

Counts

2 → 204

Calls

2 calls:

31.0ms

(*.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)))))

10.0ms

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

simplify217.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

635×	`unswap-sqr_binary64`
539×	`times-frac_binary64`
411×	`div-sub_binary64`
403×	`fma-def_binary64`
378×	`associate-/l*_binary64`

Counts

206 → 200

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	111	4253
1	186	4015
2	493	3961
3	1230	3833
4	2521	3833
5	4243	3833
6	4256	3829
7	4926	3829
8	4788	3829

prune474.0ms (12.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	376	6	382

Error

Counts

382 → 6

Alt Table

Status	Error	Program
	0.3b	(pow.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 4) (/.f64 -1 2))
▶	0.1b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
	0.8b	(/.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 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.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))))))
✓	0.3b	(*.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)))))
	10.3b	(cbrt.f64 (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))

Compiler

Compiled 11361 to 8400 computations (26.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.0b	(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))
✓	0.2b	(*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

series42.0ms (1.1%)

Counts

2 → 2

Calls

2 calls:

25.0ms

(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))

17.0ms

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

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
24×	`distribute-lft-out_binary64`
17×	`pow1_binary64`
15×	`add-sqr-sqrt_binary64`

Counts

2 → 83

Calls

2 calls:

18.0ms

(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 -1 2))

16.0ms

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

simplify117.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

606×	`distribute-rgt-in_binary64`
583×	`distribute-lft-in_binary64`
315×	`fma-def_binary64`
271×	`times-frac_binary64`
267×	`exp-prod_binary64`

Counts

85 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	2287
1	290	2023
2	994	1593
3	3376	1570
4	4509	1472
5	4992	1472
6	4831	1472

prune179.0ms (4.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	3	1	4
Picked	1	0	1
Done	1	0	1
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
	9.5b	(cbrt.f64 (pow.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) -1/2) 3))
	0.1b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) -1/2)))
	0.4b	(.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (sqrt.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))))))
	0.0b	(pow.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) (+.f64 1 x)) (fma.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x) x)) (/.f64 -1 2))

Compiler

Compiled 4163 to 2983 computations (28.3% saved)

regimes286.0ms (7.8%)

Accuracy

Total 0.1b remaining (70.3%)

Threshold costs 0.1b (70.3%)

Counts

163 → 1

Compiler

Compiled 7544 to 5579 computations (26% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	18	32
2	16	32

end89.0ms (2.4%)

Compiler: Compiled 132 to 99 computations (25% 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

analyze3.0ms (0.1%)

sample1.5s (41.8%)

simplify13.0ms (0.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series15.0ms (0.4%)

rewrite14.0ms (0.4%)

simplify179.0ms (4.9%)

prune86.0ms (2.3%)

localize5.0ms (0.1%)

series23.0ms (0.6%)

rewrite19.0ms (0.5%)

simplify124.0ms (3.4%)

prune78.0ms (2.1%)

localize7.0ms (0.2%)

series39.0ms (1.1%)

rewrite77.0ms (2.1%)

simplify217.0ms (5.9%)

prune474.0ms (12.9%)

localize10.0ms (0.3%)

series42.0ms (1.1%)

rewrite40.0ms (1.1%)

simplify117.0ms (3.2%)

prune179.0ms (4.8%)

regimes286.0ms (7.8%)

simplify2.0ms (0.1%)

end89.0ms (2.4%)

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