Details

analyze1.8s (11.3%)

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
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

Compiler

Compiled 24 to 15 computations (37.5% saved)

sample1.4s (8.6%)

Results

1.2s	8256×	body	128	valid
70.0ms	416×	body	128	invalid

Compiler

Compiled 71 to 44 computations (38% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
593×	`fma-def_binary64`
507×	`div-sub_binary64`
484×	`sub-neg_binary64`
470×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	23
1	25	21
2	50	21
3	93	21
4	157	21
5	270	21
6	423	21
7	724	21
8	1341	21
9	3898	21
10	4400	21
11	4952	21

prune3.0ms (0%)

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

25.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	25.3b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
▶	25.3b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 126 to 69 computations (45.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 b y) y)
✓	0.0b	(*.f64 z (-.f64 t a))
✓	0.5b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	24.5b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series164.0ms (1%)

Counts

4 → 204

Calls

4 calls:

136.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
14.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))
8.0ms	(fma.f64 z (-.f64 b y) y)
6.0ms	(*.f64 z (-.f64 t a))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(*.f64 z (-.f64 t a))
2.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
0.0ms	(fma.f64 z (-.f64 b y) y)
0.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))

simplify145.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

911×	`associate-/l*_binary64`
492×	`fma-def_binary64`
260×	`+-commutative_binary64`
206×	`associate-+r+_binary64`
153×	`*-commutative_binary64`

Counts

303 → 243

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	773	10057
1	2327	9294
2	5266	9294

prune252.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	236	7	243
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	238	7	245

Error

0.0b

Counts

245 → 7

Alt Table

Status	Error	Program
	26.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	32.4b	(/.f64 (-.f64 t a) (-.f64 b y))
	42.7b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (.f64 t t) (*.f64 a a))) (+.f64 t a))) (fma.f64 z (-.f64 b y) y))
▶	25.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
	25.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	35.7b	(-.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y (-.f64 1 z))) (/.f64 x (-.f64 1 z))) (+.f64 (/.f64 (.f64 z (.f64 b x)) (.f64 y (pow.f64 (-.f64 1 z) 2))) (/.f64 (.f64 a z) (*.f64 y (-.f64 1 z)))))
	42.2b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 11623 to 4309 computations (62.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
	0.5b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	0.6b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
✓	24.3b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series166.0ms (1.1%)

Counts

2 → 108

Calls

2 calls:

140.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
26.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite158.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 71

Calls

2 calls:

151.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
2.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

simplify306.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

788×	`associate-/l*_binary64`
519×	`fma-def_binary64`
318×	`+-commutative_binary64`
239×	`associate-+r+_binary64`
177×	`sub-neg_binary64`

Counts

179 → 236

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	812	10485
1	2614	9766
2	5311	9766

prune337.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	323	7	330

Error

0.0b

Counts

330 → 7

Alt Table

Status	Error	Program
	26.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
	32.4b	(/.f64 (-.f64 t a) (-.f64 b y))
	42.7b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (.f64 t t) (*.f64 a a))) (+.f64 t a))) (fma.f64 z (-.f64 b y) y))
✓	25.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
▶	25.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	35.7b	(-.f64 (+.f64 (/.f64 (.f64 t z) (.f64 y (-.f64 1 z))) (/.f64 x (-.f64 1 z))) (+.f64 (/.f64 (.f64 z (.f64 b x)) (.f64 y (pow.f64 (-.f64 1 z) 2))) (/.f64 (.f64 a z) (*.f64 y (-.f64 1 z)))))
	42.2b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 15311 to 6221 computations (59.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	0.5b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	24.5b	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

series437.0ms (2.8%)

Counts

2 → 144

Calls

2 calls:

296.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))
140.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
2.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

simplify234.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

656×	`+-commutative_binary64`
547×	`associate-+r+_binary64`
293×	`associate-/l*_binary64`
280×	`*-commutative_binary64`
202×	`associate-/r*_binary64`

Counts

251 → 304

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1525	24218
1	5092	24218

prune446.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	389	2	391
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	390	8	398

Error

0.0b

Counts

398 → 8

Alt Table

Status	Error	Program
	32.5b	(/.f64 1 (/.f64 (-.f64 b y) (-.f64 t a)))
	26.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
✓	25.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
▶	25.4b	(+.f64 (/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y))) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y))))
	32.4b	(/.f64 (-.f64 t a) (-.f64 b y))
	42.7b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (.f64 t t) (*.f64 a a))) (+.f64 t a))) (fma.f64 z (-.f64 b y) y))
✓	25.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	42.2b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 29110 to 12079 computations (58.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(-.f64 (.f64 x y) (.f64 z a))
✓	1.9b	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))
✓	13.6b	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
✓	22.1b	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))

series173.0ms (1.1%)

Counts

4 → 192

Calls

4 calls:

96.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))
62.0ms	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
8.0ms	(-.f64 (.f64 x y) (.f64 z a))
7.0ms	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 97

Calls

4 calls:

8.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y)))
6.0ms	(/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y)))
5.0ms	(-.f64 (+.f64 (.f64 z b) y) (.f64 z y))
2.0ms	(-.f64 (.f64 x y) (.f64 z a))

simplify139.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

873×	`times-frac_binary64`
455×	`fma-def_binary64`
208×	`+-commutative_binary64`
189×	`sub-neg_binary64`
158×	`associate-/l*_binary64`

Counts

289 → 319

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	749	9848
1	2320	9173
2	5001	9173

prune307.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	365	8	373

Error

0.0b

Counts

373 → 8

Alt Table

Status	Error	Program
	32.5b	(/.f64 1 (/.f64 (-.f64 b y) (-.f64 t a)))
	26.7b	(-.f64 (fma.f64 (/.f64 y z) (/.f64 a (pow.f64 (-.f64 y b) 2)) (/.f64 a (-.f64 y b))) (fma.f64 (/.f64 y z) (/.f64 x (-.f64 y b)) (fma.f64 (/.f64 y z) (/.f64 t (pow.f64 (-.f64 y b) 2)) (/.f64 t (-.f64 y b)))))
✓	25.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	25.4b	(+.f64 (/.f64 (.f64 z t) (-.f64 (+.f64 (.f64 z b) y) (.f64 z y))) (/.f64 (-.f64 (.f64 x y) (.f64 z a)) (-.f64 (+.f64 (.f64 z b) y) (*.f64 z y))))
	32.4b	(/.f64 (-.f64 t a) (-.f64 b y))
	42.7b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (.f64 t t) (*.f64 a a))) (+.f64 t a))) (fma.f64 z (-.f64 b y) y))
✓	25.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	42.2b	(/.f64 x (-.f64 1 z))

Compiler

Compiled 18794 to 4709 computations (74.9% saved)

regimes9.0s (57%)

Accuracy

Total 5.6b remaining (97%)

Threshold costs 0b (0%)

Counts

246 → 5

Compiler

Compiled 58961 to 33204 computations (43.7% saved)

bsearch10.0ms (0.1%)

Compiler: Compiled 23 to 14 computations (39.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
16×	`*-commutative_binary64`
15×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	367
1	100	367
2	128	367
3	144	367
4	152	367
5	151	367

end167.0ms (1.1%)

Compiler: Compiled 711 to 269 computations (62.2% saved)

Details

analyze1.8s (11.3%)

sample1.4s (8.6%)

simplify70.0ms (0.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series164.0ms (1%)

rewrite13.0ms (0.1%)

simplify145.0ms (0.9%)

prune252.0ms (1.6%)

localize11.0ms (0.1%)

series166.0ms (1.1%)

rewrite158.0ms (1%)

simplify306.0ms (1.9%)

prune337.0ms (2.1%)

localize13.0ms (0.1%)

series437.0ms (2.8%)

rewrite20.0ms (0.1%)

simplify234.0ms (1.5%)

prune446.0ms (2.8%)

localize14.0ms (0.1%)

series173.0ms (1.1%)

rewrite27.0ms (0.2%)

simplify139.0ms (0.9%)

prune307.0ms (2%)

regimes9.0s (57%)

bsearch10.0ms (0.1%)

simplify10.0ms (0.1%)

end167.0ms (1.1%)

Profiling