Details

analyze1.6s (24.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	96.7%	3.3%	10
0%	95.1%	4.9%	11
0%	93.7%	6.3%	12
0%	92.4%	7.6%	13
0.2%	86.5%	13.4%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample2.3s (34.4%)

Symmetry

(sort d2 d4)

Results

1.1s	8256×	body	128	valid
731.0ms	960×	body	8192	exit
188.0ms	1423×	body	128	invalid

Compiler

Compiled 39 to 23 computations (41% saved)

simplify95.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1400×	`fma-neg_binary64`
654×	`fma-def_binary64`
233×	`sub-neg_binary64`
210×	`unsub-neg_binary64`
158×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	32	14
2	94	13
3	263	13
4	655	13
5	1556	13
6	1691	13
7	1500	13
8	1500	13
9	2739	13
10	2707	13
11	2707	13
12	2632	13

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
	0.0b	(-.f64 (+.f64 (-.f64 (.f64 d1 d2) (.f64 d1 d3)) (.f64 d4 d1)) (.f64 d1 d1))

Compiler

Compiled 92 to 53 computations (42.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 d4 (-.f64 (-.f64 d2 d3) d1))
✓	0.0b	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

series28.0ms (0.4%)

Counts

2 → 96

Calls

2 calls:

21.0ms	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))
6.0ms	(+.f64 d4 (-.f64 (-.f64 d2 d3) d1))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64`
32×	`associate-+r+_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
21×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

18.0ms	(+.f64 d4 (-.f64 (-.f64 d2 d3) d1))
9.0ms	(*.f64 d1 (+.f64 d4 (-.f64 (-.f64 d2 d3) d1)))

simplify135.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1002×	`fma-neg_binary64`
693×	`fma-def_binary64`
566×	`exp-prod_binary64`
374×	`*-commutative_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

177 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2211
1	316	1984
2	1276	1866
3	3067	1866
4	4524	1866
5	4962	1866
6	4951	1866

prune111.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	141	3	144

Error

Counts

144 → 3

Alt Table

Status	Error	Program
	0.5b	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
	32.0b	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))
▶	0.0b	(+.f64 (.f64 d4 d1) (.f64 (-.f64 (-.f64 d2 d3) d1) d1))

Compiler

Compiled 2488 to 601 computations (75.8% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 (-.f64 d2 d3) d1) d1)

series12.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(*.f64 (-.f64 (-.f64 d2 d3) d1) d1)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`
3×	`associate-r_binary64`
3×	`distribute-lft-out--_binary64`

Counts

1 → 25

Calls

1 calls:

7.0ms

(*.f64 (-.f64 (-.f64 d2 d3) d1) d1)

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
455×	`unsub-neg_binary64`
420×	`fma-neg_binary64`
339×	`*-commutative_binary64`
234×	`exp-prod_binary64`

Counts

61 → 51

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	785
1	141	650
2	414	650
3	1574	650
4	3515	650
5	4959	650
6	4996	650

prune32.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	51	3	54

Error

Counts

54 → 3

Alt Table

Status	Error	Program
▶	0.5b	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
	32.0b	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))
✓	0.0b	(+.f64 (.f64 d4 d1) (.f64 (-.f64 (-.f64 d2 d3) d1) d1))

Compiler

Compiled 957 to 268 computations (72% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
✓	0.1b	(fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))
✓	0.5b	(*.f64 (cbrt.f64 d2) (cbrt.f64 d2))
✓	0.6b	(cbrt.f64 d2)

series720.0ms (10.9%)

Counts

4 → 96

Calls

4 calls:

436.0ms	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
205.0ms	(fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))
41.0ms	(cbrt.f64 d2)
38.0ms	(*.f64 (cbrt.f64 d2) (cbrt.f64 d2))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
15×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

4 → 97

Calls

4 calls:

13.0ms	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
4.0ms	(*.f64 (cbrt.f64 d2) (cbrt.f64 d2))
1.0ms	(cbrt.f64 d2)
0.0ms	(fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))

simplify121.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-neg_binary64`
376×	`associate-+l+_binary64`
341×	`associate-+r+_binary64`
334×	`unsub-neg_binary64`
236×	`+-commutative_binary64`

Counts

193 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	2634
1	478	2216
2	1887	1809
3	3600	1792
4	4911	1792
5	4883	1792

prune156.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	198	3	201

Error

Counts

201 → 3

Alt Table

Status	Error	Program
✓	0.5b	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
▶	32.0b	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))
✓	0.0b	(+.f64 (.f64 d4 d1) (.f64 (-.f64 (-.f64 d2 d3) d1) d1))

Compiler

Compiled 6520 to 3074 computations (52.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 d4 (+.f64 d3 d1))
✓	0.0b	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))
✓	0.3b	(pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3)
✓	30.5b	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))

series255.0ms (3.9%)

Counts

4 → 180

Calls

4 calls:

203.0ms	(pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3)
31.0ms	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))
16.0ms	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))
5.0ms	(-.f64 d4 (+.f64 d3 d1))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
9×	`distribute-lft-out_binary64`

Counts

4 → 111

Calls

4 calls:

9.0ms	(-.f64 d4 (+.f64 d3 d1))
8.0ms	(*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1))))
7.0ms	(pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))

simplify159.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-def_binary64`
560×	`associate-+r+_binary64`
361×	`associate-+l+_binary64`
334×	`associate-r_binary64`
311×	`associate-l_binary64`

Counts

291 → 197

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	421	10243
1	1245	9311
2	5606	9311

prune187.0ms (2.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	197	3	200

Error

Counts

200 → 3

Alt Table

Status	Error	Program
✓	0.5b	(.f64 d1 (+.f64 (+.f64 d4 (fma.f64 (.f64 (cbrt.f64 d2) (cbrt.f64 d2)) (cbrt.f64 d2) (neg.f64 (.f64 d3 1)))) (-.f64 (fma.f64 (neg.f64 d3) 1 (.f64 d3 1)) d1)))
✓	32.0b	(cbrt.f64 (pow.f64 (*.f64 d1 (+.f64 d2 (-.f64 d4 (+.f64 d3 d1)))) 3))
✓	0.0b	(+.f64 (.f64 d4 d1) (.f64 (-.f64 (-.f64 d2 d3) d1) d1))

Compiler

Compiled 7960 to 4446 computations (44.1% saved)

regimes394.0ms (6%)

Accuracy

Total 0.0b remaining (40.3%)

Threshold costs 0.0b (40.3%)

Counts

71 → 1

Compiler

Compiled 4978 to 3259 computations (34.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	16
2	25	16
3	29	16
4	31	16
5	31	16

end83.0ms (1.3%)

Compiler: Compiled 121 to 75 computations (38% saved)

Details

analyze1.6s (24.2%)

sample2.3s (34.4%)

simplify95.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series28.0ms (0.4%)

rewrite34.0ms (0.5%)

simplify135.0ms (2%)

prune111.0ms (1.7%)

localize7.0ms (0.1%)

series12.0ms (0.2%)

rewrite8.0ms (0.1%)

simplify104.0ms (1.6%)

prune32.0ms (0.5%)

localize16.0ms (0.2%)

series720.0ms (10.9%)

rewrite25.0ms (0.4%)

simplify121.0ms (1.8%)

prune156.0ms (2.4%)

localize9.0ms (0.1%)

series255.0ms (3.9%)

rewrite31.0ms (0.5%)

simplify159.0ms (2.4%)

prune187.0ms (2.8%)

regimes394.0ms (6%)

simplify4.0ms (0.1%)

end83.0ms (1.3%)

Profiling