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)

sample55.0ms (1.1%)

Algorithm

1×

intervals

Results

9.0ms	137×	body	128	valid
8.0ms	65×	body	1024	valid
4.0ms	36×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify11.0ms (0.2%)

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

prune2.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series29.0ms (0.6%)

Counts

2 → 5

Calls

2 calls:

16.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
13.0ms	(sqrt.f64 (+.f64 x 1))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`sqrt-prod_binary64`
57×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
33×	`add-cube-cbrt_binary64`

Counts

2 → 95

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify172.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1110×	`fma-neg_binary64`
566×	`unswap-sqr_binary64`
455×	`cancel-sign-sub-inv_binary64`
444×	`fma-def_binary64`
429×	`associate-l_binary64`

Counts

100 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	2533
1	224	1344
2	592	1128
3	2527	1125
4	4099	1093
5	4381	1093
6	4663	1093
7	4949	1093
8	4730	1093

prune178.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	4	99

Error

0.1b

Counts

99 → 4

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	29.7b	(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 x) (sqrt.f64 x))) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	30.2b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
✓	30.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 1950 to 1046 computations (46.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series34.0ms (0.7%)

Counts

3 → 6

Calls

3 calls:

15.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64`
28×	`sqrt-prod_binary64`
22×	`distribute-lft-out_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`times-frac_binary64`

Counts

3 → 91

Calls

3 calls:

17.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
8.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
3.0ms	(sqrt.f64 (+.f64 1 x))

simplify164.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-neg_binary64`
558×	`cancel-sign-sub-inv_binary64`
538×	`times-frac_binary64`
389×	`associate-l_binary64`
311×	`associate-r_binary64`

Counts

97 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1310
1	203	1217
2	444	1211
3	1133	1207
4	2556	1207
5	4229	1207
6	4956	1207
7	4998	1207
8	4837	1207

prune157.0ms (3.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	93	6	99

Error

0.0b

Counts

99 → 6

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)))))
	0.4b	(/.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))))
▶	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.0b	(.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)))))

Compiler

Compiled 1796 to 1290 computations (28.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(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)))

series170.0ms (3.4%)

Counts

3 → 14

Calls

3 calls:

152.0ms

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

13.0ms

(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)))

rewrite17.0ms (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)))

3.0ms

(/.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))

simplify126.0ms (2.6%)

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 → 113

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

prune479.0ms (9.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	215	6	221

Error

0.0b

Counts

221 → 6

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)))))
	0.4b	(/.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))))
✓	0.2b	(/.f64 1 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	10.0b	(.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)))))

Compiler

Compiled 5114 to 3893 computations (23.9% saved)

localize10.0ms (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)))))

series54.0ms (1.1%)

Counts

2 → 2

Calls

2 calls:

41.0ms

(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)))))

rewrite95.0ms (1.9%)

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:

37.0ms

(*.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)))))

8.0ms

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

simplify334.0ms (6.8%)

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

prune869.0ms (17.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	371	4	375
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	374	7	381

Error

Counts

381 → 7

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))
	0.5b	(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))
	0.5b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))
	0.8b	(.f64 (.f64 (cbrt.f64 (.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)))))) (cbrt.f64 (.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))))))) (cbrt.f64 (*.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)))
✓	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)))))
	10.0b	(.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)))))

Compiler

Compiled 11328 to 8368 computations (26.1% saved)

regimes590.0ms (11.9%)

Accuracy

Total 0.1b remaining (82.1%)

Threshold costs 0.1b (82.1%)

Counts

152 → 1

Compiler

Compiled 7898 to 5826 computations (26.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.3s (26.4%)

Algorithm

1×

intervals

Results

461.0ms	2035×	body	1024	valid
189.0ms	4255×	body	128	valid
142.0ms	974×	body	512	valid
75.0ms	488×	body	256	valid
42.0ms	248×	body	2048	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 233 to 178 computations (23.6% 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%)

sample55.0ms (1.1%)

simplify11.0ms (0.2%)

prune2.0ms (0%)

localize16.0ms (0.3%)

series29.0ms (0.6%)

rewrite24.0ms (0.5%)

simplify172.0ms (3.5%)

prune178.0ms (3.6%)

localize6.0ms (0.1%)

series34.0ms (0.7%)

rewrite32.0ms (0.7%)

simplify164.0ms (3.3%)

prune157.0ms (3.2%)

localize7.0ms (0.1%)

series170.0ms (3.4%)

rewrite17.0ms (0.3%)

simplify126.0ms (2.6%)

prune479.0ms (9.7%)

localize10.0ms (0.2%)

series54.0ms (1.1%)

rewrite95.0ms (1.9%)

simplify334.0ms (6.8%)

prune869.0ms (17.6%)

regimes590.0ms (11.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3s (26.4%)

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