Details

analyze19.0ms (0.7%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample23.0ms (0.9%)

Algorithm

1×

intervals

Results

8.0ms	52×	body	1024	valid
4.0ms	148×	body	128	valid
3.0ms	36×	body	512	valid
1.0ms	15×	body	256	valid
1.0ms	5×	body	2048	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

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

26.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	26.5b	(-.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:

0.2b	(cbrt.f64 (+.f64 x 1))
0.5b	(cbrt.f64 x)
1.9b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

rewrite59.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

25.9b

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:

7.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
3.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 648 to 401 computations (38.1% saved)

series51.0ms (2%)

Error

14.1b

Counts

3 → 21

Calls

3 calls:

16.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
11.0ms	(cbrt.f64 x)
10.0ms	(cbrt.f64 (+.f64 x 1))

Compiler

Compiled 784 to 656 computations (16.3% saved)

simplify88.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

411×	`associate-l_binary64`
406×	`associate-r_binary64`
279×	`distribute-rgt-out_binary64`
240×	`distribute-rgt-neg-in_binary64`
223×	`distribute-lft-neg-in_binary64`

Counts

70 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1027
1	326	992
2	809	958
3	2743	954
4	4599	940
5	4794	940

prune45.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	6	57

Error

7.2b

Counts

57 → 6

Alt Table

Status	Error	Program
	28.2b	(+.f64 (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/9))) (-.f64 1 (cbrt.f64 x))) (*.f64 5/81 (pow.f64 x 3)))
▶	26.5b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
	48.2b	(+.f64 (-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8)))))
	26.5b	(-.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))
	46.3b	(*.f64 (+.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))))
	34.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 882 to 630 computations (28.6% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(cbrt.f64 (+.f64 1 x))
0.5b	(cbrt.f64 x)
1.9b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))

rewrite51.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

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:

8.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 1 x))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 648 to 401 computations (38.1% saved)

series49.0ms (1.9%)

Error

7.2b

Counts

3 → 21

Calls

3 calls:

15.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
12.0ms	(cbrt.f64 x)
9.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 784 to 656 computations (16.3% saved)

simplify90.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

463×	`associate-l_binary64`
431×	`associate-r_binary64`
283×	`distribute-rgt-out_binary64`
215×	`distribute-rgt-neg-in_binary64`
215×	`sub-neg_binary64`

Counts

70 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1027
1	328	992
2	819	958
3	2786	954
4	4577	940
5	4769	940

prune24.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	42	6	48

Error

7.2b

Counts

48 → 6

Alt Table

Status	Error	Program
	28.2b	(+.f64 (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/9))) (-.f64 1 (cbrt.f64 x))) (*.f64 5/81 (pow.f64 x 3)))
✓	26.5b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
	48.2b	(+.f64 (-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8)))))
▶	26.5b	(-.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))
	46.3b	(*.f64 (+.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))))
	34.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 692 to 501 computations (27.6% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.5b	(cbrt.f64 x)
8.2b	(-.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))

rewrite108.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

24×	`cbrt-div_binary64`
18×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 62

Calls

4 calls:

11.0ms	(-.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))
6.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1824 to 1355 computations (25.7% saved)

series80.0ms (3.1%)

Error

7.2b

Counts

4 → 33

Calls

4 calls:

16.0ms	(-.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))
16.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
14.0ms	(cbrt.f64 x)
12.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))

Compiler

Compiled 1589 to 1317 computations (17.1% saved)

simplify131.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

415×	`cancel-sign-sub-inv_binary64`
323×	`distribute-rgt-in_binary64`
286×	`*-commutative_binary64`
249×	`sub-neg_binary64`
246×	`unswap-sqr_binary64`

Counts

95 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	229	2094
1	512	2012
2	1297	1875
3	2472	1615
4	4195	1590
5	4924	1590
6	4813	1590

prune50.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	68	7	75

Error

7.2b

Counts

75 → 7

Alt Table

Status	Error	Program
	28.2b	(+.f64 (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/9))) (-.f64 1 (cbrt.f64 x))) (*.f64 5/81 (pow.f64 x 3)))
✓	26.5b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
	48.2b	(+.f64 (-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8)))))
	26.7b	(-.f64 (.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
▶	26.6b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	46.3b	(*.f64 (+.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))))
	34.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 1457 to 1096 computations (24.8% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.5b	(cbrt.f64 x)
0.6b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
19.7b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

rewrite129.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

7.2b

Rules

28×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
8.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1707 to 1326 computations (22.3% saved)

series83.0ms (3.2%)

Error

7.2b

Counts

4 → 30

Calls

4 calls:

17.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
16.0ms	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
14.0ms	(cbrt.f64 x)
12.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))

Compiler

Compiled 1482 to 1247 computations (15.9% saved)

simplify125.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

447×	`cancel-sign-sub-inv_binary64`
294×	`*-commutative_binary64`
271×	`log-prod_binary64`
270×	`exp-prod_binary64`
256×	`sqr-pow_binary64`

Counts

100 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	222	1922
1	534	1760
2	1383	1581
3	2988	1340
4	4208	1333
5	4984	1333
6	4847	1333

prune49.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	74	8	82

Error

7.2b

Counts

82 → 8

Alt Table

Status	Error	Program
	28.2b	(+.f64 (+.f64 (.f64 x (+.f64 1/3 (.f64 x -1/9))) (-.f64 1 (cbrt.f64 x))) (*.f64 5/81 (pow.f64 x 3)))
	26.5b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
	48.2b	(+.f64 (-.f64 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))) (.f64 1/9 (cbrt.f64 (/.f64 1 (pow.f64 x 5))))) (.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8)))))
	26.7b	(-.f64 (.f64 (.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 2))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	26.6b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	27.3b	(-.f64 (.f64 (cbrt.f64 (+.f64 1 (.f64 x 2/3))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	46.3b	(*.f64 (+.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 x))))
	34.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 1163 to 895 computations (23% saved)

regimes440.0ms (17%)

Accuracy

Total 0.4b remaining (4.8%)

Threshold costs 0.4b (4.8%)

Compiler

Compiled 5849 to 4568 computations (21.9% saved)

bsearch19.0ms (0.7%)

Steps

Iters	Range		Point
1	0.00013490107833346115	470.63808702969595	0.24647122882296646
9	-9751410.36484379	-0.07246764283249982	-0.9915729690158178

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
7×	`*-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	40	92
1	58	92
2	68	92
3	74	92
4	78	92
5	79	92
6	77	92

end1.0ms (0.1%)

Compiler: Compiled 61 to 48 computations (21.3% saved)

sample830.0ms (32%)

Algorithm

1×

intervals

Results

227.0ms	1983×	body	1024	valid
130.0ms	4308×	body	128	valid
87.0ms	1013×	body	512	valid
33.0ms	222×	body	2048	valid
26.0ms	474×	body	256	valid

Compiler

Compiled 234 to 188 computations (19.7% 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 (0.7%)

sample23.0ms (0.9%)

simplify12.0ms (0.5%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite59.0ms (2.3%)

series51.0ms (2%)

simplify88.0ms (3.4%)

prune45.0ms (1.7%)

localize5.0ms (0.2%)

rewrite51.0ms (2%)

series49.0ms (1.9%)

simplify90.0ms (3.5%)

prune24.0ms (0.9%)

localize10.0ms (0.4%)

rewrite108.0ms (4.2%)

series80.0ms (3.1%)

simplify131.0ms (5.1%)

prune50.0ms (1.9%)

localize12.0ms (0.5%)

rewrite129.0ms (5%)

series83.0ms (3.2%)

simplify125.0ms (4.8%)

prune49.0ms (1.9%)

regimes440.0ms (17%)

bsearch19.0ms (0.7%)

simplify6.0ms (0.2%)

end1.0ms (0.1%)

sample830.0ms (32%)

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