Details

analyze1.8s (27.6%)

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)

sample2.1s (31.4%)

Results

1.4s	8256×	body	128	valid
602.0ms	3895×	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

prune370.0ms (5.6%)

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
▶	2.0b	(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)

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))
✓	2.0b	(fma.f64 a (fma.f64 z b t) x)

series45.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

29.0ms	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
16.0ms	(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))

simplify62.0ms (0.9%)

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

prune44.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Error

0.0b

Counts

68 → 4

Alt Table

Status	Error	Program
	31.9b	(fma.f64 y z (*.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) (sqrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	2.0b	(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))
▶	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 995 to 233 computations (76.6% 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))
✓	1.7b	(fma.f64 z (fma.f64 a b y) x)

series46.0ms (0.7%)

Counts

2 → 132

Calls

2 calls:

27.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
19.0ms	(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))

simplify115.0ms (1.7%)

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

prune34.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	52	4	56

Error

0.0b

Counts

56 → 4

Alt Table

Status	Error	Program
	31.9b	(fma.f64 y z (*.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) (sqrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	2.0b	(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))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 754 to 182 computations (75.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

series52.0ms (0.8%)

Counts

3 → 168

Calls

3 calls:

27.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
15.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
10.0ms	(.f64 (.f64 a z) b)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64`
9×	`sum-log_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`

Counts

3 → 57

Calls

3 calls:

9.0ms	(+.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)

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
704×	`fma-def_binary64`
676×	`distribute-lft-in_binary64`
542×	`fma-neg_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

225 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2565
1	340	2260
2	1287	2248
3	4764	2248
4	5136	2248

prune71.0ms (1.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	6	114

Error

Counts

114 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	34.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
	31.9b	(fma.f64 y z (*.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) (sqrt.f64 (fma.f64 a (fma.f64 z b t) x))))
▶	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
✓	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 2382 to 458 computations (80.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
✓	0.6b	(cbrt.f64 b)
✓	1.0b	(.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))
✓	3.9b	(.f64 (.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))

series807.0ms (12.2%)

Counts

4 → 96

Calls

4 calls:

709.0ms	(.f64 (.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))
40.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
33.0ms	(cbrt.f64 b)
25.0ms	(.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
36×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`pow-prod-down_binary64`
22×	`cbrt-prod_binary64`

Counts

4 → 111

Calls

4 calls:

10.0ms	(.f64 (.f64 a z) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))
9.0ms	(.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b))
4.0ms	(*.f64 (cbrt.f64 b) (cbrt.f64 b))
1.0ms	(cbrt.f64 b)

simplify134.0ms (2%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
709×	`unswap-sqr_binary64`
597×	`*-commutative_binary64`
434×	`log-prod_binary64`
299×	`associate-l_binary64`

Counts

207 → 154

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2286
1	259	1919
2	1085	1784
3	1812	1756
4	3905	1744
5	4893	1744
6	5017	1744

prune154.0ms (2.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	192	6	198

Error

Counts

198 → 6

Alt Table

Status	Error	Program
✓	2.0b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
	34.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (*.f64 a z) (sqrt.f64 b)) (sqrt.f64 b)))
	31.9b	(fma.f64 y z (*.f64 (sqrt.f64 (fma.f64 a (fma.f64 z b t) x)) (sqrt.f64 (fma.f64 a (fma.f64 z b t) x))))
✓	3.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 a z) (.f64 (cbrt.f64 b) (cbrt.f64 b))) (cbrt.f64 b)))
✓	2.8b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	1.8b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

Compiler

Compiled 5213 to 1102 computations (78.9% saved)

regimes478.0ms (7.2%)

Accuracy

Total 0.5b remaining (98.4%)

Threshold costs 0.5b (98.4%)

Counts

54 → 3

Compiler

Compiled 5817 to 3703 computations (36.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	97
1	39	97
2	39	97

end95.0ms (1.4%)

Compiler: Compiled 280 to 129 computations (53.9% saved)

Details

analyze1.8s (27.6%)

sample2.1s (31.4%)

simplify9.0ms (0.1%)

prune370.0ms (5.6%)

localize8.0ms (0.1%)

series45.0ms (0.7%)

rewrite1.0ms (0%)

simplify62.0ms (0.9%)

prune44.0ms (0.7%)

localize8.0ms (0.1%)

series46.0ms (0.7%)

rewrite1.0ms (0%)

simplify115.0ms (1.7%)

prune34.0ms (0.5%)

localize10.0ms (0.2%)

series52.0ms (0.8%)

rewrite20.0ms (0.3%)

simplify98.0ms (1.5%)

prune71.0ms (1.1%)

localize13.0ms (0.2%)

series807.0ms (12.2%)

rewrite31.0ms (0.5%)

simplify134.0ms (2%)

prune154.0ms (2.3%)

regimes478.0ms (7.2%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end95.0ms (1.4%)

Profiling