Details

analyze743.0ms (17%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
37.5%	62.5%	0%	6
40.6%	59.3%	0%	7
41.4%	58.6%	0%	8
41.8%	58.2%	0%	9
42%	58%	0%	10
42.1%	57.9%	0%	11
42.2%	57.7%	0%	12
42.3%	57.6%	0%	13
42.5%	57.4%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.4s (32.7%)

Results

608.0ms	2061×	body	1024	valid
394.0ms	4401×	body	128	valid
226.0ms	1039×	body	512	valid
92.0ms	249×	body	2048	valid
76.0ms	506×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify13.0ms (0.3%)

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

prune2.0ms (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

29.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.3b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.6b	(cbrt.f64 x)
✓	2.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series49.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

34.0ms	(cbrt.f64 x)
10.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
5.0ms	(cbrt.f64 (+.f64 x 1))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`cbrt-prod_binary64`
58×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

3 → 104

Calls

3 calls:

9.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

simplify122.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
417×	`associate-/r*_binary64`
348×	`times-frac_binary64`
258×	`cancel-sign-sub-inv_binary64`
133×	`associate--l+_binary64`

Counts

140 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3526
1	455	2550
2	1336	2116
3	3957	2052
4	4888	2052
5	4814	2052

prune182.0ms (4.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Error

8.0b

Counts

182 → 7

Alt Table

Status	Error	Program
▶	29.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	30.4b	(fma.f64 (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	29.5b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	48.0b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
	29.5b	(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	30.6b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
	33.1b	(/.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 3942 to 2281 computations (42.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.7b	(cbrt.f64 (cbrt.f64 x))
✓	10.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))

series559.0ms (12.8%)

Counts

3 → 36

Calls

3 calls:

296.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
252.0ms	(cbrt.f64 (cbrt.f64 x))
10.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`fma-neg_binary64`

Counts

3 → 55

Calls

3 calls:

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

simplify114.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
393×	`unswap-sqr_binary64`
338×	`fma-def_binary64`
268×	`associate-l_binary64`
252×	`associate-r_binary64`

Counts

91 → 113

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	2180
1	371	1804
2	952	1650
3	2923	1179
4	4059	1020
5	4962	1020
6	4735	1020

prune96.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	169	5	174

Error

0.2b

Counts

174 → 5

Alt Table

Status	Error	Program
	32.6b	(*.f64 (/.f64 (cbrt.f64 x) x) (-.f64 1/3 (/.f64 1/9 x)))
	48.0b	(fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))))))
	31.1b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
▶	30.6b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
	33.1b	(/.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 3550 to 1770 computations (50.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	1.2b	(pow.f64 (+.f64 x 1) 1/3)
✓	14.7b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))

series15.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
5.0ms	(pow.f64 (+.f64 x 1) 1/3)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64`
48×	`prod-diff_binary64`
46×	`add-sqr-sqrt_binary64`
36×	`add-cube-cbrt_binary64`
34×	`unpow-prod-down_binary64`

Counts

2 → 103

Calls

2 calls:

8.0ms	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
3.0ms	(pow.f64 (+.f64 x 1) 1/3)

simplify141.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-neg_binary64`
400×	`associate-/r*_binary64`
315×	`times-frac_binary64`
226×	`*-commutative_binary64`
216×	`cancel-sign-sub-inv_binary64`

Counts

127 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	2940
1	482	2480
2	1387	2008
3	3881	1944
4	4942	1944
5	5000	1944
6	4987	1944

prune120.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	195	1	196
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	196	5	201

Error

0.2b

Counts

201 → 5

Alt Table

Status	Error	Program
	32.6b	(*.f64 (/.f64 (cbrt.f64 x) x) (-.f64 1/3 (/.f64 1/9 x)))
	48.0b	(fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))))))
	31.1b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
✓	30.6b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
▶	30.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2/3)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (cbrt.f64 x))) 0)

Compiler

Compiled 4260 to 2506 computations (41.2% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
	0.6b	(cbrt.f64 x)
✓	1.5b	(pow.f64 (+.f64 1 x) 2/3)
✓	14.5b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2/3)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (cbrt.f64 x)))

series27.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

16.0ms	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2/3)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (cbrt.f64 x)))
7.0ms	(pow.f64 (+.f64 1 x) 2/3)
5.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
4×	`cbrt-div_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms	(pow.f64 (+.f64 1 x) 2/3)
3.0ms	(cbrt.f64 (cbrt.f64 (+.f64 1 x)))
0.0ms	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2/3)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (cbrt.f64 x)))

simplify82.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

876×	`fma-neg_binary64`
728×	`fma-def_binary64`
315×	`associate-r_binary64`
301×	`associate-l_binary64`
293×	`cancel-sign-sub-inv_binary64`

Counts

85 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	236	2015
1	605	1926
2	1551	1577
3	4654	1575
4	5278	1575

prune122.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Error

0.2b

Counts

151 → 5

Alt Table

Status	Error	Program
	32.6b	(*.f64 (/.f64 (cbrt.f64 x) x) (-.f64 1/3 (/.f64 1/9 x)))
	48.0b	(fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))))))
	31.1b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
✓	30.6b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
✓	30.6b	(+.f64 (fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) 2/3)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (cbrt.f64 x))) 0)

Compiler

Compiled 3879 to 2939 computations (24.2% saved)

regimes310.0ms (7.1%)

Accuracy

Total 0.1b remaining (25.5%)

Threshold costs 0.1b (25.5%)

Counts

117 → 3

Compiler

Compiled 4351 to 2861 computations (34.2% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
9	6.106237116231505	469705894.23956144	66997.7420196915
10	-14794194.672642631	-1.1510355055853714e-9	-1.0054654754205168

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	53
1	39	53
2	47	53
3	50	53
4	51	53
5	49	53

end105.0ms (2.4%)

Compiler: Compiled 145 to 112 computations (22.8% 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

analyze743.0ms (17%)

sample1.4s (32.7%)

simplify13.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series49.0ms (1.1%)

rewrite18.0ms (0.4%)

simplify122.0ms (2.8%)

prune182.0ms (4.2%)

localize10.0ms (0.2%)

series559.0ms (12.8%)

rewrite14.0ms (0.3%)

simplify114.0ms (2.6%)

prune96.0ms (2.2%)

localize6.0ms (0.1%)

series15.0ms (0.3%)

rewrite21.0ms (0.5%)

simplify141.0ms (3.2%)

prune120.0ms (2.8%)

localize12.0ms (0.3%)

series27.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify82.0ms (1.9%)

prune122.0ms (2.8%)

regimes310.0ms (7.1%)

bsearch41.0ms (0.9%)

simplify4.0ms (0.1%)

end105.0ms (2.4%)

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