Details

analyze41.0ms (0.6%)

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)

sample52.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	55×	body	1024	valid
11.0ms	143×	body	128	valid
6.0ms	28×	body	512	valid
3.0ms	22×	body	256	valid
3.0ms	8×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify88.0ms (1.2%)

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

prune3.0ms (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

28.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	3.4b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series67.0ms (0.9%)

Counts

2 → 5

Calls

2 calls:

34.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
32.0ms	(sqrt.f64 (+.f64 x 1))

rewrite41.0ms (0.6%)

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:

20.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms	(sqrt.f64 (+.f64 x 1))

simplify307.0ms (4.3%)

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

prune227.0ms (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
	29.4b	(-.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	28.0b	(+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))

Compiler

Compiled 1962 to 1038 computations (47.1% saved)

localize12.0ms (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)))

series58.0ms (0.8%)

Counts

3 → 6

Calls

3 calls:

25.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
19.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
14.0ms	(sqrt.f64 (+.f64 1 x))

rewrite54.0ms (0.8%)

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:

23.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
16.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (+.f64 1 x))

simplify198.0ms (2.8%)

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

prune229.0ms (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	0	0	0
Total	92	6	98

Error

0.0b

Counts

98 → 6

Alt Table

Status	Error	Program
	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))))
	10.2b	(.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)))))
✓	0.1b	(/.f64 1 (+.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))))) (/.f64 1 (cbrt.f64 (+.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)))))
▶	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))

Compiler

Compiled 1812 to 1306 computations (27.9% saved)

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series268.0ms (3.8%)

Counts

4 → 37

Calls

4 calls:

240.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
10.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
9.0ms	(cbrt.f64 (+.f64 1 x))
9.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
33×	`cbrt-prod_binary64`
33×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
16×	`cbrt-div_binary64`

Counts

4 → 127

Calls

4 calls:

19.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
6.0ms	(sqrt.f64 (cbrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 x)))
4.0ms	(cbrt.f64 (+.f64 1 x))

simplify295.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
551×	`fma-neg_binary64`
318×	`associate-l_binary64`
292×	`associate-r_binary64`
213×	`unswap-sqr_binary64`

Counts

164 → 222

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	240	3511
1	533	3077
2	1298	2765
3	3736	2476
4	4812	2476
5	4977	2415
6	4874	2415

prune556.0ms (7.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	307	5	312

Error

0.0b

Counts

312 → 5

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)))))
▶	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (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)))
	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))))
	10.2b	(.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)))))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 9079 to 6952 computations (23.4% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series232.0ms (3.3%)

Counts

2 → 13

Calls

2 calls:

221.0ms

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

10.0ms

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

rewrite76.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`sqrt-prod_binary64`
98×	`add-sqr-sqrt_binary64`
44×	`sqrt-pow1_binary64`
40×	`*-un-lft-identity_binary64`
36×	`cbrt-prod_binary64`

Counts

2 → 156

Calls

2 calls:

28.0ms

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

4.0ms

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

simplify265.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

652×	`times-frac_binary64`
512×	`fma-neg_binary64`
279×	`associate-l_binary64`
239×	`fma-def_binary64`
233×	`associate-r_binary64`

Counts

169 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	204	3474
1	369	3095
2	880	2961
3	2307	2863
4	4320	2863
5	4916	2863
6	4904	2863

prune1.2s (17.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	438	0	438
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	438	5	443

Error

0.0b

Counts

443 → 5

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)))))
✓	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (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)))
	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))))
	10.2b	(.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)))))
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 16048 to 12714 computations (20.8% saved)

regimes934.0ms (13.2%)

Accuracy

Total 0.1b remaining (70%)

Threshold costs 0.1b (70%)

Counts

222 → 1

Compiler

Compiled 11005 to 8631 computations (21.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end1.0ms (0%)

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

sample1.7s (24.4%)

Algorithm

1×

intervals

Results

568.0ms	2027×	body	1024	valid
324.0ms	4242×	body	128	valid
216.0ms	1031×	body	512	valid
70.0ms	202×	body	2048	valid
65.0ms	498×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 139 to 107 computations (23% 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

analyze41.0ms (0.6%)

sample52.0ms (0.7%)

simplify88.0ms (1.2%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series67.0ms (0.9%)

rewrite41.0ms (0.6%)

simplify307.0ms (4.3%)

prune227.0ms (3.2%)

localize12.0ms (0.2%)

series58.0ms (0.8%)

rewrite54.0ms (0.8%)

simplify198.0ms (2.8%)

prune229.0ms (3.2%)

localize23.0ms (0.3%)

series268.0ms (3.8%)

rewrite51.0ms (0.7%)

simplify295.0ms (4.2%)

prune556.0ms (7.8%)

localize24.0ms (0.3%)

series232.0ms (3.3%)

rewrite76.0ms (1.1%)

simplify265.0ms (3.7%)

prune1.2s (17.6%)

regimes934.0ms (13.2%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample1.7s (24.4%)

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