Details

analyze92.0ms (2.3%)

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)

sample779.0ms (19.2%)

Symmetry

(sort a b)

Results

727.0ms	8256×	body	128	valid
12.0ms	147×	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

prune3.0ms (0.1%)

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

16.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.1b	(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
✓	5.6b	(.f64 (.f64 (*.f64 a a) b) b)
✓	9.5b	(.f64 (.f64 a a) b)

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (.f64 (*.f64 a a) b) b)
8.0ms	(.f64 (.f64 a a) b)

rewrite13.0ms (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:

6.0ms	(.f64 (.f64 a a) b)
5.0ms	(.f64 (.f64 (*.f64 a a) b) b)

simplify78.0ms (1.9%)

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 (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	11	57

Error

0.1b

Counts

57 → 11

Alt Table

Status	Error	Program
	25.8b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	22.2b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
▶	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	16.5b	(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))))
	25.4b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	31.5b	(neg.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (.f64 a a) b) b) (.f64 (.f64 (.f64 a a) b) b)) (.f64 (.f64 (*.f64 a a) b) b))))
	26.0b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	16.5b	(neg.f64 (.f64 (.f64 (.f64 (.f64 a a) (*.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)) b))
	5.9b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	20.8b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))

Compiler

Compiled 1046 to 378 computations (63.9% 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))

series12.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

12.0ms

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

rewrite7.0ms (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))

simplify77.0ms (1.9%)

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

prune32.0ms (0.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	36	9	45

Error

0.0b

Counts

45 → 9

Alt Table

Status	Error	Program
	16.4b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	20.8b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	25.8b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	26.0b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	5.9b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	5.4b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
▶	0.9b	(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))))

Compiler

Compiled 634 to 266 computations (58% saved)

localize9.0ms (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)))
✓	19.2b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.2s (30.4%)

Counts

4 → 96

Calls

4 calls:

652.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
558.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))
14.0ms	(.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)))
8.0ms	(pow.f64 (*.f64 a b) 2)

rewrite31.0ms (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:

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	(.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))

simplify174.0ms (4.3%)

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 → 193

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	184	3987
1	321	3345
2	776	2770
3	1650	2453
4	3874	2219
5	4832	2215
6	4391	2210
7	5217	2210

prune331.0ms (8.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	300	5	305
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	303	11	314

Error

0.0b

Counts

314 → 11

Alt Table

Status	Error	Program
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	0.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (.f64 a b))) (cbrt.f64 (*.f64 a b))))
	26.0b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	20.0b	(neg.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 a b)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
▶	0.9b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	5.9b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	16.4b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	5.4b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	1.1b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))))) (cbrt.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))))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	0.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (cbrt.f64 (.f64 a b)) (cbrt.f64 (*.f64 a b)))))

Compiler

Compiled 8333 to 4995 computations (40.1% saved)

localize7.0ms (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)
	19.2b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series568.0ms (14%)

Counts

1 → 24

Calls

1 calls:

568.0ms

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

rewrite4.0ms (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)

simplify60.0ms (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	749
3	2801	588
4	5144	588

prune110.0ms (2.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	104	11	115

Error

0.0b

Counts

115 → 11

Alt Table

Status	Error	Program
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	0.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (cbrt.f64 (.f64 a b))) (cbrt.f64 (*.f64 a b))))
	26.0b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	20.0b	(neg.f64 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 a b)) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
✓	0.9b	(neg.f64 (pow.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)) 3))
	5.9b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	16.4b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	5.4b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	1.1b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))))) (cbrt.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))))
✓	16.1b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))
	0.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (cbrt.f64 (.f64 a b)) (cbrt.f64 (*.f64 a b)))))

Compiler

Compiled 1664 to 1145 computations (31.2% saved)

regimes213.0ms (5.3%)

Accuracy

Total 0.3b remaining (87.9%)

Threshold costs 0.3b (87.9%)

Counts

47 → 1

Compiler

Compiled 5324 to 3239 computations (39.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	14	12
2	24	12
3	31	12
4	36	12
5	38	12
6	38	12

end134.0ms (3.3%)

Remove: (sort a b)
Compiler: Compiled 242 to 141 computations (41.7% 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

analyze92.0ms (2.3%)

sample779.0ms (19.2%)

simplify13.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series19.0ms (0.5%)

rewrite13.0ms (0.3%)

simplify78.0ms (1.9%)

prune46.0ms (1.1%)

localize4.0ms (0.1%)

series12.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify77.0ms (1.9%)

prune32.0ms (0.8%)

localize9.0ms (0.2%)

series1.2s (30.4%)

rewrite31.0ms (0.8%)

simplify174.0ms (4.3%)

prune331.0ms (8.2%)

localize7.0ms (0.2%)

series568.0ms (14%)

rewrite4.0ms (0.1%)

simplify60.0ms (1.5%)

prune110.0ms (2.7%)

regimes213.0ms (5.3%)

simplify2.0ms (0.1%)

end134.0ms (3.3%)

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