Details

analyze25.0ms (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)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	67×	body	1024	valid
6.0ms	135×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify15.0ms (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

30.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	30.2b	(-.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))
2.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite50.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

29.6b

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:

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

Compiler

Compiled 459 to 303 computations (34% saved)

series16.0ms (0.4%)

Error

29.3b

Counts

2 → 9

Calls

2 calls:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 232 to 177 computations (23.7% saved)

simplify112.0ms (2.5%)

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

prune24.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	2	38

Error

0.1b

Counts

38 → 2

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	30.2b	(*.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 365 to 252 computations (31% saved)

localize6.0ms (0.1%)

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)))

rewrite96.0ms (2.1%)

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:

10.0ms	(/.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))

Compiler

Compiled 1078 to 778 computations (27.8% saved)

series19.0ms (0.4%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

6.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
4.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

Compiler

Compiled 261 to 214 computations (18% saved)

simplify155.0ms (3.5%)

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

prune25.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	6	50

Error

0.0b

Counts

50 → 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)))
	10.5b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	30.2b	(*.f64 1 (-.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 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)))))
	9.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))

Compiler

Compiled 548 to 406 computations (25.9% saved)

localize10.0ms (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))

rewrite262.0ms (5.8%)

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:

14.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2925 to 2282 computations (22% saved)

series90.0ms (2%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

19.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
18.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
13.0ms	(cbrt.f64 (+.f64 1 x))
12.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1738 to 1450 computations (16.6% saved)

simplify180.0ms (4%)

Algorithm

1×	egg-herbie

Rules

377×	`*-commutative_binary64`
323×	`times-frac_binary64`
313×	`unswap-sqr_binary64`
258×	`distribute-rgt-in_binary64`
254×	`sub-neg_binary64`

Counts

147 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	3473
1	445	2672
2	1007	2179
3	1793	2150
4	3838	2150
5	4798	2150
6	4929	2150
7	4785	2150

prune92.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Error

0.0b

Counts

130 → 8

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)))
	10.5b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	30.2b	(*.f64 1 (-.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 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)))))
	9.5b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
▶	0.4b	(/.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))))
	0.7b	(/.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 1948 to 1446 computations (25.8% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

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))))
0.2b	(*.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))

rewrite610.0ms (13.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

387×	`times-frac_binary64`
347×	`*-un-lft-identity_binary64`
329×	`sqrt-prod_binary64`
227×	`add-sqr-sqrt_binary64`
192×	`add-cube-cbrt_binary64`

Counts

4 → 343

Calls

4 calls:

29.0ms	(/.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))))
13.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 11529 to 8765 computations (24% saved)

series124.0ms (2.8%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

42.0ms	(/.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))))
20.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
15.0ms	(cbrt.f64 (+.f64 1 x))
15.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2464 to 1988 computations (19.3% saved)

simplify757.0ms (16.9%)

Algorithm

1×	egg-herbie

Rules

417×	`*-commutative_binary64`
365×	`unswap-sqr_binary64`
272×	`associate-/r*_binary64`
251×	`associate-/l/_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

370 → 348

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	337	21989
1	732	18438
2	1626	14555
3	2354	13053
4	4379	12001
5	4747	11984
6	4955	11984
7	4973	11984
8	4849	11984

prune201.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	343	5	348
Fresh	3	2	5
Picked	1	0	1
Done	0	2	2
Total	347	9	356

Error

Counts

356 → 9

Alt Table

Status	Error	Program
	0.4b	(*.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.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)))))
	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (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 (fabs.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x))))
	0.1b	(/.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 (.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (fabs.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 x))))
	10.5b	(/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)))
	0.5b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (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 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)))))
	0.6b	(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (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))))))

Compiler

Compiled 4050 to 2952 computations (27.1% saved)

regimes526.0ms (11.7%)

Accuracy

Total 0.1b remaining (84.9%)

Threshold costs 0.1b (84.9%)

Compiler

Compiled 11723 to 9276 computations (20.9% 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)

sample1.0s (23.1%)

Algorithm

1×

intervals

Results

295.0ms	1976×	body	1024	valid
189.0ms	4275×	body	128	valid
113.0ms	1041×	body	512	valid
43.0ms	213×	body	2048	valid
35.0ms	495×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 272 to 209 computations (23.2% 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

analyze25.0ms (0.6%)

sample28.0ms (0.6%)

simplify15.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite50.0ms (1.1%)

series16.0ms (0.4%)

simplify112.0ms (2.5%)

prune24.0ms (0.5%)

localize6.0ms (0.1%)

rewrite96.0ms (2.1%)

series19.0ms (0.4%)

simplify155.0ms (3.5%)

prune25.0ms (0.6%)

localize10.0ms (0.2%)

rewrite262.0ms (5.8%)

series90.0ms (2%)

simplify180.0ms (4%)

prune92.0ms (2.1%)

localize17.0ms (0.4%)

rewrite610.0ms (13.6%)

series124.0ms (2.8%)

simplify757.0ms (16.9%)

prune201.0ms (4.5%)

regimes526.0ms (11.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (23.1%)

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