Details

analyze96.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	62.4%	12.6%	6
37.5%	43.7%	18.8%	7
50%	31.2%	18.8%	8
56.2%	20.3%	23.5%	9
61.7%	14.8%	23.5%	10
64.4%	9.8%	25.9%	11
66.9%	7.2%	25.9%	12
68.2%	4.8%	27%	13
69.4%	3.6%	27%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample807.0ms (20.4%)

Symmetry

(sort a b)

Results

751.0ms	8256×	body	128	valid
14.0ms	118×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

284×	`fma-def_binary64`
35×	`associate-l_binary64`
24×	`distribute-rgt-in_binary64`
24×	`sub-neg_binary64`
19×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 38 to 20 computations (47.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.6b	(.f64 (.f64 (*.f64 a a) b) b)
✓	11.0b	(.f64 (.f64 a a) b)

series50.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

42.0ms	(.f64 (.f64 (*.f64 a a) b) b)
8.0ms	(.f64 (.f64 a a) b)

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

5.0ms	(.f64 (.f64 (*.f64 a a) b) b)
4.0ms	(.f64 (.f64 a a) b)

simplify82.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
359×	`unswap-sqr_binary64`
354×	`associate-/l/_binary64`
272×	`sqr-pow_binary64`
262×	`associate-/r/_binary64`

Counts

92 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	983
1	142	854
2	480	830
3	782	812
4	1506	801
5	2460	801
6	4674	801
7	4916	801

prune46.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Error

0.1b

Counts

57 → 8

Alt Table

Status	Error	Program
▶	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	16.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 (.f64 a a) b) b)) (cbrt.f64 (.f64 (.f64 (.f64 a a) b) b))) (cbrt.f64 (.f64 (.f64 (*.f64 a a) b) b))))
	24.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	22.4b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	22.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	26.8b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	16.6b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	4.8b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 954 to 338 computations (64.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 a b) (*.f64 a b))

series10.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`pow1_binary64`
17×	`pow-prod-down_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
8×	`cbrt-unprod_binary64`

Counts

1 → 36

Calls

1 calls:

5.0ms

(*.f64 (*.f64 a b) (*.f64 a b))

simplify79.0ms (2%)

Algorithm

1×	egg-herbie

Rules

654×	`associate-l_binary64`
551×	`fma-def_binary64`
352×	`associate-r_binary64`
341×	`associate-/l*_binary64`
311×	`associate-/l/_binary64`

Counts

60 → 34

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	613
1	92	508
2	315	474
3	1009	474
4	1436	372
5	2353	372
6	4908	372
7	4999	372
8	4954	372

prune29.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	33	9	42

Error

0.0b

Counts

42 → 9

Alt Table

Status	Error	Program
	17.5b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	22.4b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	24.6b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	5.0b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
▶	0.8b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	22.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	16.6b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	4.8b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 642 to 274 computations (57.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	0.3b	(pow.f64 (*.f64 a b) 2)
✓	0.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	22.5b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.1s (27.6%)

Counts

4 → 96

Calls

4 calls:

544.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))
528.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
11.0ms	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
7.0ms	(pow.f64 (*.f64 a b) 2)

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`pow1_binary64`
20×	`unswap-sqr_binary64`
18×	`associate-r_binary64`

Counts

4 → 142

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
9.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
2.0ms	(pow.f64 (*.f64 a b) 2)
1.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify175.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

865×	`fma-def_binary64`
708×	`unswap-sqr_binary64`
612×	`exp-prod_binary64`
576×	`fma-neg_binary64`
540×	`log-prod_binary64`

Counts

238 → 183

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	184	3987
1	321	3345
2	776	2804
3	1650	2467
4	3874	2437
5	4832	2433
6	4391	2433
7	5217	2433

prune320.0ms (8.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	281	4	285
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	282	12	294

Error

0.0b

Counts

294 → 12

Alt Table

Status	Error	Program
	17.5b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	22.4b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	16.4b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (.f64 a b))) (cbrt.f64 (*.f64 a b))))
	5.0b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
▶	0.8b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	22.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	16.5b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
✓	0.8b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	16.3b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	16.6b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	4.8b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 7886 to 4750 computations (39.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (*.f64 a b) 2)
✓	0.4b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)
	22.5b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series561.0ms (14.2%)

Counts

1 → 24

Calls

1 calls:

560.0ms

(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`unpow-prod-down_binary64`
9×	`cube-prod_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`

Counts

1 → 38

Calls

1 calls:

3.0ms

(pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3)

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-def_binary64`
542×	`exp-prod_binary64`
538×	`associate-l_binary64`
439×	`associate-r_binary64`
409×	`log-prod_binary64`

Counts

62 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	1004
1	246	893
2	586	769
3	2801	618
4	5144	618

prune100.0ms (2.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	99	12	111

Error

0.0b

Counts

111 → 12

Alt Table

Status	Error	Program
	17.5b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	22.4b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	16.4b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (.f64 a b))) (cbrt.f64 (*.f64 a b))))
	5.0b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
✓	0.8b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	22.0b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
	16.5b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4))) (cbrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
✓	0.8b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	16.3b	(neg.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	16.6b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) b) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
	4.8b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))

Compiler

Compiled 1607 to 1112 computations (30.8% saved)

regimes211.0ms (5.3%)

Accuracy

Total 0.3b remaining (87.4%)

Threshold costs 0.3b (87.4%)

Counts

47 → 1

Compiler

Compiled 4410 to 2527 computations (42.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
2	14	9
3	15	9
4	15	9

end132.0ms (3.4%)

Remove: (sort a b)
Compiler: Compiled 214 to 137 computations (36% saved)

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12

Details

analyze96.0ms (2.4%)

sample807.0ms (20.4%)

simplify13.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series50.0ms (1.3%)

rewrite12.0ms (0.3%)

simplify82.0ms (2.1%)

prune46.0ms (1.2%)

localize4.0ms (0.1%)

series10.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify79.0ms (2%)

prune29.0ms (0.7%)

localize8.0ms (0.2%)

series1.1s (27.6%)

rewrite33.0ms (0.8%)

simplify175.0ms (4.4%)

prune320.0ms (8.1%)

localize6.0ms (0.2%)

series561.0ms (14.2%)

rewrite5.0ms (0.1%)

simplify61.0ms (1.5%)

prune100.0ms (2.5%)

regimes211.0ms (5.3%)

simplify2.0ms (0.1%)

end132.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	7	12
1	21	12
2	55	12
3	97	12
4	144	12
5	185	12
6	230	12
7	264	12
8	273	12
9	267	12
10	233	12