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)

sample46.0ms (1.3%)

Algorithm

1×

intervals

Results

8.0ms	57×	body	1024	valid
6.0ms	142×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	20×	body	256	valid
1.0ms	8×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify10.0ms (0.3%)

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

27.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	2.2b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series25.0ms (0.7%)

Counts

2 → 5

Calls

2 calls:

15.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(sqrt.f64 (+.f64 x 1))

rewrite17.0ms (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:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 x 1))

simplify161.0ms (4.6%)

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

prune113.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Error

0.1b

Counts

99 → 3

Alt Table

Status	Error	Program
	27.5b	(fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	27.6b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 1934 to 1040 computations (46.2% saved)

localize6.0ms (0.2%)

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)))

series33.0ms (0.9%)

Counts

3 → 6

Calls

3 calls:

16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
7.0ms	(sqrt.f64 (+.f64 1 x))

rewrite54.0ms (1.5%)

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:

41.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

simplify134.0ms (3.9%)

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

prune127.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Error

0.0b

Counts

98 → 7

Alt Table

Status	Error	Program
	0.6b	(/.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))))
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 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)))))
	0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	0.3b	(/.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))))
	9.4b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	27.6b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (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)))

Compiler

Compiled 1860 to 1342 computations (27.8% saved)

localize7.0ms (0.2%)

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)))

series108.0ms (3.1%)

Counts

3 → 14

Calls

3 calls:

89.0ms

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

14.0ms

(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)))

rewrite9.0ms (0.2%)

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))

simplify97.0ms (2.8%)

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

prune298.0ms (8.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	215	7	222

Error

0.0b

Counts

222 → 7

Alt Table

Status	Error	Program
	0.6b	(/.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))))
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 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)))))
▶	0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	0.3b	(/.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))))
	9.4b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	27.6b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (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)))

Compiler

Compiled 5178 to 3945 computations (23.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
✓	0.1b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
✓	0.2b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
✓	0.2b	(cbrt.f64 (+.f64 1 x))

series168.0ms (4.8%)

Counts

4 → 37

Calls

4 calls:

148.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
5.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
5.0ms	(cbrt.f64 (+.f64 1 x))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
30×	`cbrt-prod_binary64`
29×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`add-cube-cbrt_binary64`

Counts

4 → 135

Calls

4 calls:

13.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify142.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

771×	`times-frac_binary64`
753×	`fma-neg_binary64`
281×	`associate-/r*_binary64`
273×	`associate-/l*_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

172 → 260

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	280	4455
1	675	3809
2	1794	3051
3	4087	2701
4	4930	2701
5	4872	2701

prune485.0ms (13.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	301	2	303
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	302	8	310

Error

0.0b

Counts

310 → 8

Alt Table

Status	Error	Program
	9.3b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 (sqrt.f64 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)))))
	0.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))) (cbrt.f64 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))) (cbrt.f64 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
✓	0.2b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	0.3b	(/.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))))
	9.4b	(cbrt.f64 (/.f64 (.f64 (.f64 1 1) 1) (.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)))))
	0.3b	(/.f64 1 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (.f64 (sqrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (+.f64 1 x)))))) (sqrt.f64 x)))
	27.6b	(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (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)))

Compiler

Compiled 8026 to 6205 computations (22.7% saved)

regimes346.0ms (9.9%)

Accuracy

Total 0.1b remaining (75.4%)

Threshold costs 0.1b (75.4%)

Counts

194 → 1

Compiler

Compiled 7262 to 5410 computations (25.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	13	14

end0.0ms (0%)

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

sample1.0s (29.9%)

Algorithm

1×

intervals

Results

315.0ms	1993×	body	1024	valid
187.0ms	4255×	body	128	valid
123.0ms	1042×	body	512	valid
39.0ms	215×	body	2048	valid
38.0ms	495×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 227 to 176 computations (22.5% 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%)

sample46.0ms (1.3%)

simplify10.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series25.0ms (0.7%)

rewrite17.0ms (0.5%)

simplify161.0ms (4.6%)

prune113.0ms (3.2%)

localize6.0ms (0.2%)

series33.0ms (0.9%)

rewrite54.0ms (1.5%)

simplify134.0ms (3.9%)

prune127.0ms (3.6%)

localize7.0ms (0.2%)

series108.0ms (3.1%)

rewrite9.0ms (0.2%)

simplify97.0ms (2.8%)

prune298.0ms (8.5%)

localize9.0ms (0.2%)

series168.0ms (4.8%)

rewrite39.0ms (1.1%)

simplify142.0ms (4.1%)

prune485.0ms (13.9%)

regimes346.0ms (9.9%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (29.9%)

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