Details

analyze1.6s (24%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.8%	98%	0.3%	13
2.4%	97.3%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample92.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
10.0ms	141×	body	128	invalid

Compiler

Compiled 49 to 33 computations (32.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

prune3.0ms (0.1%)

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
	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	4.6b	(.f64 (.f64 a z) b)

series51.0ms (0.7%)

Counts

4 → 204

Calls

4 calls:

26.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
11.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
8.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
5.0ms	(.f64 (.f64 a z) b)
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
2.0ms	(+.f64 x (*.f64 y z))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
720×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
194×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`

Counts

277 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2855
1	406	2550
2	1474	2538
3	5045	2538

prune86.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Error

0.0b

Counts

136 → 4

Alt Table

Status	Error	Program
	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
▶	2.8b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))

Compiler

Compiled 2852 to 546 computations (80.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z y (fma.f64 a t x))
✓	0.0b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))
	4.6b	(.f64 (.f64 a z) b)

series43.0ms (0.6%)

Counts

2 → 132

Calls

2 calls:

26.0ms	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))
17.0ms	(fma.f64 z y (fma.f64 a t x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))
0.0ms	(fma.f64 z y (fma.f64 a t x))

simplify96.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-neg_binary64`
542×	`associate-l_binary64`
508×	`cancel-sign-sub-inv_binary64`
504×	`distribute-rgt-in_binary64`
491×	`distribute-lft-in_binary64`

Counts

159 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	1876
1	173	1700
2	671	1693
3	3803	1693
4	4939	1693
5	5001	1693

prune60.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Error

0.0b

Counts

96 → 4

Alt Table

Status	Error	Program
▶	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.3b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))
✓	2.8b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))

Compiler

Compiled 1684 to 327 computations (80.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.9b	(fma.f64 a (fma.f64 z b t) x)

series41.0ms (0.6%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
18.0ms	(fma.f64 a (fma.f64 z b t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 a (fma.f64 z b t) x)
0.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
732×	`associate-+r+_binary64`
701×	`fma-def_binary64`
559×	`associate-l_binary64`
480×	`associate-r_binary64`

Counts

152 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	1737
1	97	1579
2	249	1579
3	1063	1579
4	5721	1579

prune38.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Error

0.0b

Counts

70 → 4

Alt Table

Status	Error	Program
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	3.3b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))
✓	2.8b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))

Compiler

Compiled 988 to 224 computations (77.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
✓	5.0b	(.f64 a (.f64 z b))
✓	15.0b	(cbrt.f64 (.f64 a (.f64 z b)))

series2.2s (31.5%)

Counts

4 → 124

Calls

4 calls:

1.4s	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
692.0ms	(cbrt.f64 (.f64 a (.f64 z b)))
47.0ms	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
8.0ms	(.f64 a (.f64 z b))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`pow1/3_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`pow-prod-up_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b))))
6.0ms	(.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (*.f64 z b))))
4.0ms	(.f64 a (.f64 z b))
2.0ms	(cbrt.f64 (.f64 a (.f64 z b)))

simplify173.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

540×	`exp-prod_binary64`
427×	`exp-diff_binary64`
393×	`fma-neg_binary64`
361×	`*-commutative_binary64`
355×	`exp-sum_binary64`

Counts

223 → 134

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	196	3303
1	429	3058
2	1055	2635
3	2674	2383
4	4449	2227
5	4869	2227
6	4323	2220
7	5087	2220

prune176.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	229	5	234

Error

0.0b

Counts

234 → 5

Alt Table

Status	Error	Program
✓	3.1b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.2b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 (cbrt.f64 a) (.f64 (cbrt.f64 (.f64 z b)) (cbrt.f64 (.f64 a (.f64 z b))))) (cbrt.f64 (.f64 a (.f64 z b)))))
✓	3.3b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 (cbrt.f64 (.f64 a (.f64 z b))) (cbrt.f64 (.f64 a (.f64 z b)))) (cbrt.f64 (.f64 a (.f64 z b)))))
✓	2.8b	(+.f64 (fma.f64 z y (fma.f64 a t x)) (.f64 (.f64 a z) b))

Compiler

Compiled 7653 to 1346 computations (82.4% saved)

regimes545.0ms (8%)

Accuracy

Total 0.3b remaining (97.8%)

Threshold costs 0.3b (97.8%)

Counts

53 → 3

Compiler

Compiled 6398 to 3948 computations (38.3% saved)

bsearch27.0ms (0.4%)

Steps

Iters	Range		Point
2	2.452103175727309e-64	1.1857666162924109e-63	8.306771119277255e-64
6	-5.4920249900663e+27	-6.2996241607061116e+25	-2.0887889302975253e+26

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	65
1	35	65
2	35	65

end1.0ms (0%)

Compiler: Compiled 52 to 25 computations (51.9% saved)

sample1.4s (20.1%)

Algorithm

1×

intervals

Results

508.0ms	8000×	body	128	valid
231.0ms	3834×	body	128	invalid

Compiler

Compiled 200 to 105 computations (47.5% saved)

Details

analyze1.6s (24%)

sample92.0ms (1.3%)

simplify9.0ms (0.1%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

series51.0ms (0.7%)

rewrite21.0ms (0.3%)

simplify73.0ms (1.1%)

prune86.0ms (1.3%)

localize9.0ms (0.1%)

series43.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify96.0ms (1.4%)

prune60.0ms (0.9%)

localize8.0ms (0.1%)

series41.0ms (0.6%)

rewrite1.0ms (0%)

simplify57.0ms (0.8%)

prune38.0ms (0.6%)

localize13.0ms (0.2%)

series2.2s (31.5%)

rewrite24.0ms (0.3%)

simplify173.0ms (2.5%)

prune176.0ms (2.6%)

regimes545.0ms (8%)

bsearch27.0ms (0.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.4s (20.1%)

Profiling