Details

analyze19.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample24.0ms (1%)

Algorithm

1×

intervals

Results

7.0ms	58×	body	1024	valid
4.0ms	133×	body	128	valid
4.0ms	44×	body	512	valid
1.0ms	7×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify12.0ms (0.5%)

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

prune3.0ms (0.1%)

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

31.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.5b	(cbrt.f64 x)
3.6b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

rewrite56.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

30.4b

Rules

18×	`cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cancel-sign-sub-inv_binary64`

Counts

3 → 49

Calls

3 calls:

6.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 648 to 401 computations (38.1% saved)

series39.0ms (1.7%)

Error

14.6b

Counts

3 → 15

Calls

3 calls:

12.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
10.0ms	(cbrt.f64 x)
8.0ms	(cbrt.f64 (+.f64 x 1))

Compiler

Compiled 519 to 429 computations (17.3% saved)

simplify88.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

478×	`unswap-sqr_binary64`
396×	`associate-l_binary64`
390×	`associate-r_binary64`
263×	`distribute-rgt-out_binary64`
247×	`log-prod_binary64`

Counts

64 → 50

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	806
1	255	771
2	634	743
3	2308	739
4	4471	725
5	4786	725

prune31.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

6.9b

Counts

51 → 5

Alt Table

Status	Error	Program
✓	31.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
▶	31.3b	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	31.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	35.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	43.7b	(-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (*.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5)))))

Compiler

Compiled 674 to 475 computations (29.5% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
0.5b	(cbrt.f64 x)
12.4b	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

rewrite125.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

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

Counts

4 → 98

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
10.0ms	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 2498 to 1876 computations (24.9% saved)

series59.0ms (2.6%)

Error

6.9b

Counts

4 → 23

Calls

4 calls:

12.0ms	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
12.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
11.0ms	(cbrt.f64 x)
9.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))

Compiler

Compiled 1129 to 926 computations (18% saved)

simplify109.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

422×	`distribute-rgt-in_binary64`
355×	`distribute-lft-in_binary64`
334×	`exp-sum_binary64`
315×	`*-commutative_binary64`
281×	`cancel-sign-sub-inv_binary64`

Counts

121 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	185	2173
1	399	2068
2	1123	1653
3	2287	1513
4	4266	1474
5	4863	1474

prune53.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Error

6.9b

Counts

96 → 6

Alt Table

Status	Error	Program
✓	31.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
	31.8b	(-.f64 (.f64 (cbrt.f64 (+.f64 1 (.f64 x 2/3))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
✓	31.3b	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
▶	31.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	35.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	43.7b	(-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (*.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5)))))

Compiler

Compiled 1331 to 991 computations (25.5% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.5b	(cbrt.f64 x)
22.1b	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

rewrite93.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

28×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
8×	`cbrt-div_binary64`

Counts

4 → 62

Calls

4 calls:

18.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1763 to 1333 computations (24.4% saved)

series59.0ms (2.6%)

Error

6.9b

Counts

4 → 22

Calls

4 calls:

13.0ms	(cbrt.f64 x)
11.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
10.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
10.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))

Compiler

Compiled 1232 to 1013 computations (17.8% saved)

simplify120.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

556×	`associate-l_binary64`
505×	`associate-r_binary64`
268×	`distribute-rgt-out_binary64`
202×	`distribute-rgt-neg-in_binary64`
193×	`log-prod_binary64`

Counts

84 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	1079
1	297	1044
2	748	991
3	2751	987
4	4452	972
5	4906	972
6	4785	972

prune34.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	52	6	58

Error

6.9b

Counts

58 → 6

Alt Table

Status	Error	Program
✓	31.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
▶	31.8b	(-.f64 (.f64 (cbrt.f64 (+.f64 1 (.f64 x 2/3))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
✓	31.3b	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
✓	31.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	35.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	43.7b	(-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (*.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5)))))

Compiler

Compiled 937 to 704 computations (24.9% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.3b	(*.f64 x 2/3)
0.5b	(cbrt.f64 x)

rewrite64.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

Rules

18×	`cbrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`

Counts

4 → 60

Calls

4 calls:

4.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
3.0ms	(*.f64 x 2/3)
2.0ms	(cbrt.f64 (+.f64 1 x))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1148 to 859 computations (25.2% saved)

series40.0ms (1.7%)

Error

6.9b

Counts

4 → 15

Calls

4 calls:

12.0ms	(cbrt.f64 x)
7.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
7.0ms	(cbrt.f64 (+.f64 1 x))
5.0ms	(*.f64 x 2/3)

Compiler

Compiled 729 to 596 computations (18.2% saved)

simplify96.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-r_binary64`
411×	`log-prod_binary64`
320×	`unswap-sqr_binary64`
283×	`exp-sum_binary64`
205×	`exp-prod_binary64`

Counts

75 → 47

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	110	667
1	194	651
2	548	648
3	1605	628
4	3459	616
5	4530	616
6	4895	616

prune33.0ms (1.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	47	6	53

Error

6.9b

Counts

53 → 6

Alt Table

Status	Error	Program
	31.2b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
	31.8b	(-.f64 (.f64 (cbrt.f64 (+.f64 1 (.f64 x 2/3))) (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))))) (cbrt.f64 x))
	31.3b	(-.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	31.4b	(-.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	35.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	43.7b	(-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (*.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5)))))

Compiler

Compiled 722 to 549 computations (24% saved)

regimes269.0ms (11.7%)

Accuracy

Total 0.4b remaining (4.7%)

Threshold costs 0.4b (4.7%)

Compiler

Compiled 3316 to 2590 computations (21.9% saved)

bsearch19.0ms (0.8%)

Steps

Iters	Range		Point
3	1.196452511146028e-9	346623198.2374257	0.0040513777446698
9	-216845372.84080893	-0.12306118255498638	-0.9958718557819843

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	78
1	49	78
2	59	78
3	65	78
4	69	78
5	70	78
6	68	78

end1.0ms (0.1%)

Compiler: Compiled 52 to 40 computations (23.1% saved)

sample801.0ms (35%)

Algorithm

1×

intervals

Results

231.0ms	2043×	body	1024	valid
134.0ms	4312×	body	128	valid
84.0ms	972×	body	512	valid
33.0ms	227×	body	2048	valid
25.0ms	446×	body	256	valid

Compiler

Compiled 173 to 138 computations (20.2% 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

analyze19.0ms (0.8%)

sample24.0ms (1%)

simplify12.0ms (0.5%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite56.0ms (2.4%)

series39.0ms (1.7%)

simplify88.0ms (3.8%)

prune31.0ms (1.3%)

localize12.0ms (0.5%)

rewrite125.0ms (5.5%)

series59.0ms (2.6%)

simplify109.0ms (4.8%)

prune53.0ms (2.3%)

localize11.0ms (0.5%)

rewrite93.0ms (4.1%)

series59.0ms (2.6%)

simplify120.0ms (5.2%)

prune34.0ms (1.5%)

localize11.0ms (0.5%)

rewrite64.0ms (2.8%)

series40.0ms (1.7%)

simplify96.0ms (4.2%)

prune33.0ms (1.4%)

regimes269.0ms (11.7%)

bsearch19.0ms (0.8%)

simplify6.0ms (0.2%)

end1.0ms (0.1%)

sample801.0ms (35%)

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