Details

analyze22.0ms (0.5%)

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)

sample27.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	71×	body	1024	valid
5.0ms	144×	body	128	valid
3.0ms	19×	body	512	valid
1.0ms	8×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

28.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite61.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

27.6b

Rules

15×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 459 to 303 computations (34% saved)

series19.0ms (0.4%)

Error

27.6b

Counts

2 → 9

Calls

2 calls:

9.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 232 to 177 computations (23.7% saved)

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-/l*_binary64`
324×	`cancel-sign-sub-inv_binary64`
278×	`distribute-rgt-in_binary64`
267×	`associate-/l/_binary64`
234×	`distribute-lft-in_binary64`

Counts

49 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	625
1	199	602
2	483	596
3	1673	589
4	4960	589

prune23.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Error

0.1b

Counts

38 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	28.3b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
✓	28.3b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 389 to 268 computations (31.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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)))

rewrite103.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

3 → 75

Calls

3 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))
2.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1078 to 778 computations (27.8% saved)

series19.0ms (0.4%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

6.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (+.f64 1 x))
3.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 261 to 214 computations (18% saved)

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

558×	`cancel-sign-sub-inv_binary64`
389×	`associate-l_binary64`
320×	`div-sub_binary64`
311×	`associate-r_binary64`
287×	`distribute-rgt-out_binary64`

Counts

87 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1262
1	196	1181
2	404	1175
3	878	1168
4	2187	1168
5	4251	1168
6	4974	1168
7	4871	1168

prune55.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	46	5	51

Error

0.1b

Counts

51 → 5

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	28.3b	(/.f64 1 (/.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	11.2b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.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)))))
	10.2b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))

Compiler

Compiled 526 to 388 computations (26.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite217.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
29×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 120

Calls

4 calls:

19.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
14.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
2.0ms	(cbrt.f64 (+.f64 1 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2925 to 2282 computations (22% saved)

series66.0ms (1.4%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

16.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
13.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
11.0ms	(cbrt.f64 (+.f64 1 x))
9.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1460 to 1213 computations (16.9% saved)

simplify193.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

352×	`cancel-sign-sub-inv_binary64`
345×	`*-commutative_binary64`
323×	`times-frac_binary64`
293×	`unswap-sqr_binary64`
258×	`distribute-rgt-in_binary64`

Counts

144 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	3347
1	411	2552
2	907	2067
3	1585	2046
4	3438	2046
5	4567	2046
6	4950	2046
7	4997	2046
8	4761	2046

prune84.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Error

0.0b

Counts

126 → 6

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
✓	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	28.3b	(/.f64 1 (/.f64 1 (-.f64 (sqrt.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 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	11.2b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.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)))))
	0.7b	(/.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 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))

Compiler

Compiled 1803 to 1333 computations (26.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (+.f64 1 x))

rewrite601.0ms (13.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

414×	`times-frac_binary64`
383×	`*-un-lft-identity_binary64`
352×	`sqrt-prod_binary64`
204×	`add-sqr-sqrt_binary64`
204×	`add-cube-cbrt_binary64`

Counts

4 → 343

Calls

4 calls:

31.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
11.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
6.0ms	(cbrt.f64 (+.f64 1 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 11339 to 8599 computations (24.2% saved)

series80.0ms (1.8%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

33.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
12.0ms	(cbrt.f64 (+.f64 1 x))
11.0ms	(cbrt.f64 (+.f64 1 x))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 1681 to 1366 computations (18.7% saved)

simplify645.0ms (14.1%)

Algorithm

1×	egg-herbie

Rules

700×	`times-frac_binary64`
370×	`associate-l_binary64`
359×	`log-prod_binary64`
338×	`unswap-sqr_binary64`
281×	`associate-r_binary64`

Counts

363 → 331

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	248	21296
1	541	18095
2	1163	17691
3	2622	14214
4	3698	13201
5	4521	12193
6	4903	12193
7	4885	12193

prune176.0ms (3.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	326	5	331
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	329	8	337

Error

Counts

337 → 8

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (pow.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 3))
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.6b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.5b	(/.f64 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (sqrt.f64 (+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	0.4b	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.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 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	11.2b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.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 (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))

Compiler

Compiled 3359 to 2461 computations (26.7% saved)

regimes959.0ms (21%)

Accuracy

Total 0.1b remaining (83.1%)

Threshold costs 0.1b (83.1%)

Compiler

Compiled 23489 to 18504 computations (21.2% saved)

simplify3.0ms (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

end0.0ms (0%)

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

sample996.0ms (21.8%)

Algorithm

1×

intervals

Results

277.0ms	1968×	body	1024	valid
211.0ms	4266×	body	128	valid
102.0ms	1000×	body	512	valid
43.0ms	251×	body	2048	valid
37.0ms	515×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 267 to 206 computations (22.8% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Details

analyze22.0ms (0.5%)

sample27.0ms (0.6%)

simplify12.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite61.0ms (1.3%)

series19.0ms (0.4%)

simplify52.0ms (1.1%)

prune23.0ms (0.5%)

localize7.0ms (0.2%)

rewrite103.0ms (2.3%)

series19.0ms (0.4%)

simplify121.0ms (2.7%)

prune55.0ms (1.2%)

localize9.0ms (0.2%)

rewrite217.0ms (4.8%)

series66.0ms (1.4%)

simplify193.0ms (4.2%)

prune84.0ms (1.8%)

localize15.0ms (0.3%)

rewrite601.0ms (13.1%)

series80.0ms (1.8%)

simplify645.0ms (14.1%)

prune176.0ms (3.9%)

regimes959.0ms (21%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample996.0ms (21.8%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11