Details

analyze255.0ms (3.1%)

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)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify28.0ms (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

prune4.0ms (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

14.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.5b	(neg.f64 (.f64 (.f64 (*.f64 a a) b) b))

Compiler

Compiled 38 to 20 computations (47.4% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.9b	(.f64 (.f64 (*.f64 a a) b) b)
✓	8.0b	(.f64 (.f64 a a) b)

series41.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(.f64 (.f64 (*.f64 a a) b) b)
19.0ms	(.f64 (.f64 a a) b)

rewrite25.0ms (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:

11.0ms	(.f64 (.f64 (*.f64 a a) b) b)
9.0ms	(.f64 (.f64 a a) b)

simplify125.0ms (1.5%)

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

prune105.0ms (1.3%)

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
	25.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	18.7b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
▶	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	22.3b	(neg.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 6)))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
	6.2b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	22.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	14.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a a) b)) (cbrt.f64 (.f64 (.f64 a a) b))) (cbrt.f64 (.f64 (*.f64 a a) b))) b))

Compiler

Compiled 940 to 336 computations (64.3% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series26.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

25.0ms

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

rewrite13.0ms (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:

9.0ms

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

simplify110.0ms (1.3%)

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

prune53.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	32	10	42

Error

0.0b

Counts

42 → 10

Alt Table

Status	Error	Program
	12.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) 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))))
	6.2b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) b))
	25.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	18.7b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	22.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	14.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a a) b)) (cbrt.f64 (.f64 (.f64 a a) b))) (cbrt.f64 (.f64 (*.f64 a a) b))) b))

Compiler

Compiled 694 to 294 computations (57.6% saved)

localize15.0ms (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)))
✓	23.8b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.8s (21.8%)

Counts

4 → 96

Calls

4 calls:

906.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))
879.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
21.0ms	(.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)))
12.0ms	(pow.f64 (*.f64 a b) 2)

rewrite51.0ms (0.6%)

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:

16.0ms	(.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)))
12.0ms	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
4.0ms	(pow.f64 (*.f64 a b) 2)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

simplify241.0ms (2.9%)

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

prune648.0ms (7.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	302	3	305
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	302	13	315

Error

0.0b

Counts

315 → 13

Alt Table

Status	Error	Program
	12.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
▶	0.8b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
	6.2b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) 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))))
	34.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (.f64 a b) 2/3)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	22.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	25.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	18.7b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	18.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 a 2)) (.f64 (cbrt.f64 (pow.f64 b 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	14.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a a) b)) (cbrt.f64 (.f64 (.f64 a a) b))) (cbrt.f64 (.f64 (*.f64 a a) b))) b))

Compiler

Compiled 8372 to 5022 computations (40% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
✓	0.5b	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
✓	2.1b	(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))
	23.8b	(cbrt.f64 (pow.f64 (*.f64 a b) 2))

series1.4s (17%)

Counts

2 → 48

Calls

2 calls:

891.0ms	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
533.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`cbrt-prod_binary64`
87×	`sqrt-prod_binary64`
72×	`add-sqr-sqrt_binary64`
44×	`rem-sqrt-square_binary64`
26×	`sqr-pow_binary64`

Counts

2 → 138

Calls

2 calls:

17.0ms	(.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
3.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2)))

simplify257.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
389×	`unswap-sqr_binary64`
337×	`exp-prod_binary64`
289×	`fma-def_binary64`
275×	`associate-l_binary64`

Counts

186 → 166

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	171	3453
1	262	3242
2	585	2802
3	1549	2500
4	4205	2476
5	4907	2476
6	4968	2476

prune1.3s (15.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	427	0	427
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	427	13	440

Error

0.0b

Counts

440 → 13

Alt Table

Status	Error	Program
	12.9b	(neg.f64 (.f64 a (.f64 a (*.f64 b b))))
	24.2b	(neg.f64 (.f64 (.f64 (.f64 a (.f64 a (sqrt.f64 b))) (sqrt.f64 b)) b))
✓	0.8b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2))) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 a b) 2))))))
	6.2b	(neg.f64 (.f64 (.f64 a (*.f64 a b)) 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))))
	34.6b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 a b) 2)) (.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (.f64 a b) 4))) (cbrt.f64 (pow.f64 (.f64 a b) 2/3)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	22.3b	(neg.f64 (.f64 (.f64 (.f64 a (sqrt.f64 b)) (.f64 a (sqrt.f64 b))) b))
	25.4b	(neg.f64 (.f64 (.f64 a (*.f64 a (pow.f64 b 3/2))) (sqrt.f64 b)))
	18.7b	(neg.f64 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	0.3b	(neg.f64 (.f64 (.f64 a b) (*.f64 a b)))
	18.9b	(neg.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 a 2)) (.f64 (cbrt.f64 (pow.f64 b 2)) (cbrt.f64 (pow.f64 (.f64 a b) 2)))) (cbrt.f64 (pow.f64 (*.f64 a b) 2))))
	4.6b	(neg.f64 (.f64 a (.f64 b (*.f64 a b))))
	14.9b	(neg.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a a) b)) (cbrt.f64 (.f64 (.f64 a a) b))) (cbrt.f64 (.f64 (*.f64 a a) b))) b))

Compiler

Compiled 15415 to 9540 computations (38.1% saved)

regimes527.0ms (6.3%)

Accuracy

Total 0.3b remaining (86.3%)

Threshold costs 0.3b (86.3%)

Counts

61 → 1

Compiler

Compiled 6404 to 4099 computations (36% saved)

simplify5.0ms (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

end12.0ms (0.1%)

Remove: (sort a b)
Compiler: Compiled 30 to 15 computations (50% saved)

sample1.2s (14.1%)

Algorithm

1×

intervals

Results

509.0ms	8000×	body	128	valid
8.0ms	131×	body	128	invalid

Compiler

Compiled 251 to 153 computations (39% 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

analyze255.0ms (3.1%)

sample45.0ms (0.5%)

simplify28.0ms (0.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series41.0ms (0.5%)

rewrite25.0ms (0.3%)

simplify125.0ms (1.5%)

prune105.0ms (1.3%)

localize9.0ms (0.1%)

series26.0ms (0.3%)

rewrite13.0ms (0.2%)

simplify110.0ms (1.3%)

prune53.0ms (0.6%)

localize15.0ms (0.2%)

series1.8s (21.8%)

rewrite51.0ms (0.6%)

simplify241.0ms (2.9%)

prune648.0ms (7.7%)

localize16.0ms (0.2%)

series1.4s (17%)

rewrite48.0ms (0.6%)

simplify257.0ms (3.1%)

prune1.3s (15.1%)

regimes527.0ms (6.3%)

simplify5.0ms (0.1%)

end12.0ms (0.1%)

sample1.2s (14.1%)

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