Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (38.9%)

Results

624.0ms	2146×	body	1024	valid
442.0ms	4364×	body	128	valid
217.0ms	1021×	body	512	valid
79.0ms	223×	body	2048	valid
70.0ms	502×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (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

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (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)
✓	2.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series51.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

36.0ms	(cbrt.f64 x)
11.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite18.0ms (0.5%)

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:

7.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

simplify116.0ms (3.1%)

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

prune188.0ms (5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	9	182

Error

8.5b

Counts

182 → 9

Alt Table

Status	Error	Program
	29.8b	(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)))
	33.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	29.5b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
	29.5b	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
	29.8b	(+.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)))
	29.6b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))
	32.1b	(-.f64 (fma.f64 x 1/3 1) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
▶	29.5b	(/.f64 (-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))

Compiler

Compiled 4024 to 2335 computations (42% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	1.9b	(-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))

series49.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
13.0ms	(-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 59

Calls

2 calls:

8.0ms	(-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

simplify89.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
484×	`associate-l_binary64`
406×	`associate-r_binary64`
402×	`fma-def_binary64`
256×	`cancel-sign-sub-inv_binary64`

Counts

83 → 109

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	1433
1	326	1122
2	911	1057
3	3616	1037
4	4265	976
5	4869	976

prune254.0ms (6.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	306	7	313

Error

0.4b

Counts

313 → 7

Alt Table

Status	Error	Program
	33.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	29.5b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
▶	29.5b	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
	32.6b	(/.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) -1/9 (*.f64 2/3 (cbrt.f64 (/.f64 1 x)))) (+.f64 (cbrt.f64 (+.f64 x 1)) (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)))
	32.1b	(-.f64 (fma.f64 x 1/3 1) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
✓	29.5b	(/.f64 (-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))

Compiler

Compiled 9379 to 5917 computations (36.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
✓	0.3b	(cbrt.f64 (+.f64 1 x))
	0.6b	(cbrt.f64 x)
✓	2.0b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))

series24.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
9.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
5.0ms	(cbrt.f64 (+.f64 1 x))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`cbrt-prod_binary64`
74×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`

Counts

3 → 130

Calls

3 calls:

9.0ms	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
7.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify180.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

687×	`fma-neg_binary64`
367×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
348×	`times-frac_binary64`
283×	`cancel-sign-sub-inv_binary64`

Counts

166 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	4872
1	567	3650
2	1733	3089
3	4381	2991
4	4945	2991
5	4997	2991
6	4821	2991

prune197.0ms (5.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	197	8	205

Error

0.4b

Counts

205 → 8

Alt Table

Status	Error	Program
	33.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
▶	29.5b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
✓	29.5b	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
	32.6b	(/.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) -1/9 (*.f64 2/3 (cbrt.f64 (/.f64 1 x)))) (+.f64 (cbrt.f64 (+.f64 x 1)) (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)))
	48.3b	(cbrt.f64 (pow.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)) 3))
	32.1b	(-.f64 (fma.f64 x 1/3 1) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
✓	29.5b	(/.f64 (-.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (+.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x)))

Compiler

Compiled 4922 to 3168 computations (35.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
	0.3b	(cbrt.f64 (+.f64 x 1))
	0.6b	(cbrt.f64 x)
	2.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series10.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64`
40×	`cbrt-prod_binary64`
19×	`swap-sqr_binary64`

Counts

1 → 86

Calls

1 calls:

18.0ms

(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))

simplify107.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
502×	`associate-l_binary64`
497×	`unswap-sqr_binary64`
355×	`fma-def_binary64`
224×	`sub-neg_binary64`

Counts

98 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2341
1	384	2138
2	1150	1950
3	3522	1856
4	4941	1856
5	4912	1856

prune372.0ms (9.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	1	4	5
Picked	0	1	1
Done	1	1	2
Total	491	7	498

Error

0.4b

Counts

498 → 7

Alt Table

Status	Error	Program
✓	29.5b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
	32.1b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
	33.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
✓	29.5b	(cbrt.f64 (pow.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x)) 3))
	32.6b	(/.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 4))) -1/9 (*.f64 2/3 (cbrt.f64 (/.f64 1 x)))) (+.f64 (cbrt.f64 (+.f64 x 1)) (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)))
	48.3b	(cbrt.f64 (pow.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)) 3))

Compiler

Compiled 14301 to 9005 computations (37% saved)

regimes352.0ms (9.3%)

Accuracy

Total 0.2b remaining (30.8%)

Threshold costs 0.2b (30.8%)

Counts

128 → 3

Compiler

Compiled 4787 to 3306 computations (30.9% saved)

bsearch31.0ms (0.8%)

Steps

Iters	Range		Point
6	81675.73502467913	366203.29729405977	87181.48070041489
10	-179997.72783292492	-7.665848459642672e-11	-59070.69068753034

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	95
1	35	95
2	39	95
3	41	95
4	42	95
5	41	95

end149.0ms (3.9%)

Compiler: Compiled 252 to 199 computations (21% 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

analyze1.0ms (0%)

sample1.5s (38.9%)

simplify11.0ms (0.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series51.0ms (1.4%)

rewrite18.0ms (0.5%)

simplify116.0ms (3.1%)

prune188.0ms (5%)

localize9.0ms (0.2%)

series49.0ms (1.3%)

rewrite14.0ms (0.4%)

simplify89.0ms (2.4%)

prune254.0ms (6.7%)

localize7.0ms (0.2%)

series24.0ms (0.6%)

rewrite27.0ms (0.7%)

simplify180.0ms (4.8%)

prune197.0ms (5.2%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite32.0ms (0.8%)

simplify107.0ms (2.8%)

prune372.0ms (9.9%)

regimes352.0ms (9.3%)

bsearch31.0ms (0.8%)

simplify4.0ms (0.1%)

end149.0ms (3.9%)

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