Details

analyze540.0ms (19.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample990.0ms (35.7%)

Results

866.0ms	8256×	body	128	valid
109.0ms	1028×	body	128	invalid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess31.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

830×	`fma-def_binary64`
737×	`times-frac_binary64`
438×	`distribute-rgt-in_binary64`
262×	`div-sub_binary64`
251×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	75	44
2	183	44
3	723	44
4	2221	44
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify24.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
407×	`fma-def_binary64`
279×	`cancel-sign-sub-inv_binary64`
251×	`times-frac_binary64`
245×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	56	11
3	175	11
4	443	11
5	1025	11
6	2797	11

Stop Event

1×	node limit

Counts

1 → 2

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

3.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.6b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
▶	3.6b	(-.f64 (/.f64 (fma.f64 x y x) z) x)

Compiler

Compiled 66 to 39 computations (40.9% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 (fma.f64 x y x) z)

series14.0ms (0.5%)

Counts

1 → 36

Calls

9 calls:

3.0ms	(/.f64 (fma.f64 x y x) z)	y	inf
2.0ms	(/.f64 (fma.f64 x y x) z)	x	-inf
2.0ms	(/.f64 (fma.f64 x y x) z)	x	inf
2.0ms	(/.f64 (fma.f64 x y x) z)	x	0
1.0ms	(/.f64 (fma.f64 x y x) z)	z	-inf

rewrite35.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
322×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1634	8

Stop Event

1×	node limit

Counts

1 → 36

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

37×	`fma-def_binary64`
15×	`associate-/r/_binary64`
14×	`associate-/l*_binary64`
13×	`associate-r_binary64`
9×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	282
1	32	282
2	41	282
3	85	282
4	123	282
5	157	282
6	175	282
7	178	282

Stop Event

1×

saturated

Counts

72 → 43

prune36.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	41	4	45

Error

0.0b

Counts

45 → 4

Alt Table

Status	Error	Program
	32.4b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x y x)) (.f64 (sqrt.f64 (fma.f64 x y x)) (/.f64 1 z))) x)
	4.2b	(-.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 x y x) z)) 2)) x)
	18.0b	(-.f64 (*.f64 x (/.f64 y z)) x)
▶	3.6b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)

Compiler

Compiled 700 to 256 computations (63.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))
✓	7.9b	(/.f64 (*.f64 y x) z)

series29.0ms (1%)

Counts

2 → 27

Calls

18 calls:

4.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))	x	inf
3.0ms	(/.f64 (*.f64 y x) z)	y	0
2.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))	x	-inf
2.0ms	(+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z))	x	0
2.0ms	(/.f64 (*.f64 y x) z)	x	-inf

rewrite59.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`fma-def_binary64`
237×	`fma-neg_binary64`
218×	`log-div_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	183	20
2	2994	18

Stop Event

1×	node limit

Counts

2 → 148

simplify20.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
16×	`associate-l_binary64`
15×	`associate-r_binary64`
12×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	330
1	25	330
2	39	330
3	58	282
4	74	210
5	138	210
6	177	210
7	190	210

Stop Event

1×

saturated

Counts

175 → 154

prune89.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	154	4	158

Error

Counts

158 → 4

Alt Table

Status	Error	Program
	32.4b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x y x)) (.f64 (sqrt.f64 (fma.f64 x y x)) (/.f64 1 z))) x)
	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
✓	3.6b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
▶	1.6b	(-.f64 (+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z)) x)

Compiler

Compiled 2712 to 930 computations (65.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z))
✓	3.1b	(*.f64 y (/.f64 x z))

series28.0ms (1%)

Counts

2 → 72

Calls

18 calls:

3.0ms	(+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z))	x	inf
2.0ms	(+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z))	x	-inf
2.0ms	(+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z))	x	0
2.0ms	(*.f64 y (/.f64 x z))	z	-inf
2.0ms	(+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z))	z	inf

rewrite48.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

915×	`log1p-expm1-u_binary64`
915×	`expm1-log1p-u_binary64`
83×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`
77×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	159	17
2	2421	17

Stop Event

1×	node limit

Counts

2 → 76

simplify34.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

42×	`fma-def_binary64`
16×	`associate-l_binary64`
15×	`associate-r_binary64`
12×	`associate-/l*_binary64`
9×	`+-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	699
1	27	699
2	43	633
3	65	633
4	80	534
5	144	534
6	183	534
7	196	534

Stop Event

1×

saturated

Counts

148 → 82

prune55.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	82	4	86

Error

Counts

86 → 4

Alt Table

Status	Error	Program
	32.4b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x y x)) (.f64 (sqrt.f64 (fma.f64 x y x)) (/.f64 1 z))) x)
▶	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
✓	3.6b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	1.6b	(-.f64 (+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z)) x)

Compiler

Compiled 1373 to 551 computations (59.9% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(fma.f64 (/.f64 y z) x (/.f64 x z))

series18.0ms (0.6%)

Counts

1 → 36

Calls

9 calls:

5.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))	x	-inf
3.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))	x	inf
2.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))	x	0
2.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))	y	-inf
2.0ms	(fma.f64 (/.f64 y z) x (/.f64 x z))	y	inf

rewrite36.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
243×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
71×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	148	11
2	2037	11

Stop Event

1×	node limit

Counts

1 → 23

simplify20.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

42×	`fma-def_binary64`
16×	`associate-l_binary64`
15×	`associate-r_binary64`
12×	`associate-/l*_binary64`
9×	`+-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	447
1	27	447
2	43	381
3	65	381
4	80	282
5	144	282
6	183	282
7	196	282

Stop Event

1×

saturated

Counts

59 → 30

prune16.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	30	4	34

Error

Counts

34 → 4

Alt Table

Status	Error	Program
	32.4b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x y x)) (.f64 (sqrt.f64 (fma.f64 x y x)) (/.f64 1 z))) x)
✓	2.8b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)
✓	3.6b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
✓	1.6b	(-.f64 (+.f64 (*.f64 y (/.f64 x z)) (/.f64 x z)) x)

Compiler

Compiled 488 to 149 computations (69.5% saved)

regimes532.0ms (19.2%)

Accuracy

Total 0.5b remaining (95.6%)

Threshold costs 0.5b (95.6%)

Counts

42 → 3

Compiler

Compiled 2336 to 1390 computations (40.5% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
0.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Steps

Iters	Point		Range
1.7476870974454313e-157	∈ [	1.7476870974454313e-157	,	8.76772401716374e-154	]
-0.0033332639133751216	∈ [	-0.0033332639133751216	,	-0.0022455170037508194	]

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	82
1	40	82
2	49	82
3	53	82
4	55	82

Stop Event

1×

saturated

end73.0ms (2.6%)

Stop Event

1×

fuel

Compiler

Compiled 179 to 90 computations (49.7% saved)

Details

analyze540.0ms (19.5%)

sample990.0ms (35.7%)

preprocess31.0ms (1.1%)

simplify24.0ms (0.9%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite35.0ms (1.2%)

simplify17.0ms (0.6%)

prune36.0ms (1.3%)

localize6.0ms (0.2%)

series29.0ms (1%)

rewrite59.0ms (2.1%)

simplify20.0ms (0.7%)

prune89.0ms (3.2%)

localize7.0ms (0.2%)

series28.0ms (1%)

rewrite48.0ms (1.7%)

simplify34.0ms (1.2%)

prune55.0ms (2%)

localize6.0ms (0.2%)

series18.0ms (0.6%)

rewrite36.0ms (1.3%)

simplify20.0ms (0.7%)

prune16.0ms (0.6%)

regimes532.0ms (19.2%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end73.0ms (2.6%)

Profiling