Details

analyze1.7s (24.7%)

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
1.6%	98.1%	0.3%	13
2.3%	97.4%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.8s (26.4%)

Results

1.1s	8256×	body	128	valid
605.0ms	3925×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% 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

prune4.0ms (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
▶	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(fma.f64 a (fma.f64 z b t) x)

series15.0ms (0.2%)

Counts

1 → 60

Calls

1 calls:

15.0ms

(fma.f64 a (fma.f64 z b t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 a (fma.f64 z b t) x)

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

890×	`distribute-rgt-in_binary64`
886×	`distribute-lft-in_binary64`
636×	`unswap-sqr_binary64`
393×	`associate-l_binary64`
336×	`associate-r_binary64`

Counts

70 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	626
1	49	607
2	126	607
3	510	607
4	3225	607
5	3357	607
6	3579	607
7	3869	607
8	4363	607
9	4411	607
10	5048	607

prune25.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Error

0.0b

Counts

35 → 3

Alt Table

Status	Error	Program
▶	3.4b	(fma.f64 y z (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	3.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 553 to 159 computations (71.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))
✓	0.5b	(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))
	2.4b	(fma.f64 a (fma.f64 z b t) x)

series673.0ms (9.7%)

Counts

3 → 180

Calls

3 calls:

468.0ms

(*.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))

187.0ms

(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))

17.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)))

1.0ms

(cbrt.f64 (fma.f64 a (fma.f64 z b t) x))

simplify232.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

360×	`associate-r_binary64`
330×	`fma-def_binary64`
267×	`associate-+r+_binary64`
168×	`associate-*r/_binary64`
168×	`associate-/l*_binary64`

Counts

273 → 338

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1651	23216
1	5046	23216

prune902.0ms (13%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	689	0	689
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	689	3	692

Error

0.0b

Counts

692 → 3

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 y z (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	3.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 64520 to 29566 computations (54.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	5.2b	(.f64 (.f64 a z) b)

series54.0ms (0.8%)

Counts

4 → 204

Calls

4 calls:

25.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
12.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
11.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite19.0ms (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))
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify74.0ms (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

prune78.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	133	4	137

Error

0.0b

Counts

137 → 4

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 y z (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))))
▶	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 2722 to 498 computations (81.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series38.0ms (0.5%)

Counts

2 → 132

Calls

2 calls:

22.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
16.0ms	(fma.f64 z (fma.f64 a b y) 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 z (fma.f64 a b y) x)
0.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
520×	`associate-+r+_binary64`
505×	`associate-l_binary64`
470×	`associate-+l+_binary64`
444×	`associate-r_binary64`

Counts

152 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1796
1	103	1579
2	236	1579
3	906	1579
4	3548	1579
5	3771	1579
6	4661	1579
7	4888	1579
8	4888	1579

prune31.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	52	4	56

Error

0.0b

Counts

56 → 4

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 y z (.f64 (.f64 (cbrt.f64 (fma.f64 a (fma.f64 z b t) x)) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))) (cbrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	3.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.5b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	3.6b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 716 to 159 computations (77.8% saved)

regimes814.0ms (11.7%)

Accuracy

Total 0.4b remaining (98.2%)

Threshold costs 0.4b (98.2%)

Counts

65 → 3

Compiler

Compiled 8981 to 4984 computations (44.5% saved)

bsearch54.0ms (0.8%)

Steps

Iters	Range		Point
9	1.2471119665002397e-136	1.4864572606072702e-130	1.468672175698984e-130
6	-2.161682365781964e-36	-5.516854744360149e-38	-1.632405167082733e-37

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	23	40
2	23	40

end95.0ms (1.4%)

Compiler: Compiled 158 to 81 computations (48.7% saved)

Details

analyze1.7s (24.7%)

sample1.8s (26.4%)

simplify9.0ms (0.1%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series15.0ms (0.2%)

rewrite1.0ms (0%)

simplify108.0ms (1.6%)

prune25.0ms (0.4%)

localize14.0ms (0.2%)

series673.0ms (9.7%)

rewrite19.0ms (0.3%)

simplify232.0ms (3.3%)

prune902.0ms (13%)

localize10.0ms (0.1%)

series54.0ms (0.8%)

rewrite19.0ms (0.3%)

simplify74.0ms (1.1%)

prune78.0ms (1.1%)

localize8.0ms (0.1%)

series38.0ms (0.5%)

rewrite1.0ms (0%)

simplify107.0ms (1.5%)

prune31.0ms (0.4%)

regimes814.0ms (11.7%)

bsearch54.0ms (0.8%)

simplify3.0ms (0%)

end95.0ms (1.4%)

Profiling