Details

analyze3.4s (11.6%)

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
0.6%	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)

sample62.0ms (0.2%)

Algorithm

1×

intervals

Results

30.0ms	256×	body	128	valid
2.0ms	19×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify97.0ms (0.3%)

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

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

24.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	24.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

Compiler

Compiled 80 to 41 computations (48.8% saved)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (-.f64 t a))
✓	1.0b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	23.7b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))

series451.0ms (1.5%)

Counts

3 → 168

Calls

3 calls:

406.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
31.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))
13.0ms	(*.f64 z (-.f64 t a))

rewrite31.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 89

Calls

3 calls:

14.0ms	(*.f64 z (-.f64 t a))
4.0ms	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
1.0ms	(fma.f64 x y (*.f64 z (-.f64 t a)))

simplify272.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

257 → 217

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	765	9527
1	2314	8862
2	5234	8862

prune412.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	209	8	217
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	209	9	218

Error

0.2b

Counts

218 → 9

Alt Table

Status	Error	Program
✓	24.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	47.6b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (pow.f64 t 3) (pow.f64 a 3))) (+.f64 (.f64 t t) (+.f64 (.f64 a a) (.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	33.5b	(/.f64 (-.f64 t a) (-.f64 b y))
	41.4b	(/.f64 x (-.f64 1 z))
	39.9b	(/.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))
	24.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
▶	24.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.9b	(-.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)))))
	29.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 11284 to 4290 computations (62% saved)

localize22.0ms (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)))))
	1.0b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	23.7b	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

series1.5s (5.1%)

Counts

2 → 144

Calls

2 calls:

1.1s	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))
420.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))

rewrite39.0ms (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:

8.0ms	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
5.0ms	(/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a))))

simplify597.0ms (2%)

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

prune906.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	391	9	400

Error

0.2b

Counts

400 → 9

Alt Table

Status	Error	Program
✓	24.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
	47.6b	(/.f64 (fma.f64 x y (/.f64 (.f64 z (-.f64 (pow.f64 t 3) (pow.f64 a 3))) (+.f64 (.f64 t t) (+.f64 (.f64 a a) (.f64 t a))))) (fma.f64 z (-.f64 b y) y))
	33.5b	(/.f64 (-.f64 t a) (-.f64 b y))
	41.4b	(/.f64 x (-.f64 1 z))
	39.9b	(/.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))
▶	24.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	24.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	27.9b	(-.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)))))
	29.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 29220 to 12139 computations (58.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 z (-.f64 t a))
✓	0.7b	(/.f64 1 (fma.f64 z (-.f64 b y) y))
	1.0b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	23.5b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))

series462.0ms (1.6%)

Counts

2 → 108

Calls

2 calls:

384.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
78.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

rewrite29.0ms (0.1%)

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:

15.0ms	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
4.0ms	(/.f64 1 (fma.f64 z (-.f64 b y) y))

simplify281.0ms (1%)

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

prune550.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	322	1	323
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	324	8	332

Error

0.2b

Counts

332 → 8

Alt Table

Status	Error	Program
▶	25.0b	(.f64 (.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))
	27.9b	(-.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)))))
	33.5b	(/.f64 (-.f64 t a) (-.f64 b y))
	41.4b	(/.f64 x (-.f64 1 z))
✓	24.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
✓	24.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	24.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	29.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 15345 to 6219 computations (59.5% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(fma.f64 x y (*.f64 z (-.f64 t a)))
✓	2.6b	(.f64 (.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))
✓	13.6b	(cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	16.5b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))

series11.8s (39.9%)

Counts

3 → 180

Calls

3 calls:

11.1s

(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))

420.0ms

(*.f64 (*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))

257.0ms

(cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))

rewrite73.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

3 → 91

Calls

3 calls:

29.0ms

(*.f64 (*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))

17.0ms

(*.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (*.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))))

3.0ms

(cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y)))

simplify1.5s (5%)

Algorithm

1×	egg-herbie

Rules

1094×	`fma-def_binary64`
2×	`fma-neg_binary64`
2×	`fma-udef_binary64`

Counts

271 → 289

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4714	67486
1	5811	67486

prune2.2s (7.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	488	0	488
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	488	8	496

Error

0.2b

Counts

496 → 8

Alt Table

Status	Error	Program
✓	25.0b	(.f64 (.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (.f64 (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))) (cbrt.f64 (/.f64 1 (fma.f64 z (-.f64 b y) y))))
	27.9b	(-.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)))))
	33.5b	(/.f64 (-.f64 t a) (-.f64 b y))
	41.4b	(/.f64 x (-.f64 1 z))
✓	24.4b	(/.f64 (fma.f64 x y (*.f64 z (-.f64 t a))) (fma.f64 z (-.f64 b y) y))
✓	24.4b	(.f64 (fma.f64 x y (.f64 z (-.f64 t a))) (/.f64 1 (fma.f64 z (-.f64 b y) y)))
✓	24.4b	(/.f64 1 (/.f64 (fma.f64 z (-.f64 b y) y) (fma.f64 x y (*.f64 z (-.f64 t a)))))
	29.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 b y)) (/.f64 x z) (fma.f64 (/.f64 a (pow.f64 (-.f64 b y) 2)) (/.f64 y z) (/.f64 t (-.f64 b y)))) (fma.f64 (/.f64 y (pow.f64 (-.f64 b y) 2)) (/.f64 t z) (/.f64 a (-.f64 b y))))

Compiler

Compiled 102717 to 69807 computations (32% saved)

regimes3.7s (12.5%)

Accuracy

Total 5.1b remaining (96.7%)

Threshold costs 0b (0%)

Counts

135 → 5

Compiler

Compiled 32791 to 18583 computations (43.3% saved)

bsearch5.0ms (0%)

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

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
14×	`*-commutative_binary64`
13×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	272
1	88	272
2	111	272
3	129	272
4	137	272
5	138	272
6	137	272

end1.0ms (0%)

Compiler: Compiled 190 to 60 computations (68.4% saved)

sample1.0s (3.6%)

Algorithm

1×

intervals

Results

524.0ms	8000×	body	128	valid
26.0ms	428×	body	128	invalid

Compiler

Compiled 451 to 206 computations (54.3% saved)

Details

analyze3.4s (11.6%)

sample62.0ms (0.2%)

simplify97.0ms (0.3%)

prune6.0ms (0%)

localize21.0ms (0.1%)

series451.0ms (1.5%)

rewrite31.0ms (0.1%)

simplify272.0ms (0.9%)

prune412.0ms (1.4%)

localize22.0ms (0.1%)

series1.5s (5.1%)

rewrite39.0ms (0.1%)

simplify597.0ms (2%)

prune906.0ms (3.1%)

localize24.0ms (0.1%)

series462.0ms (1.6%)

rewrite29.0ms (0.1%)

simplify281.0ms (1%)

prune550.0ms (1.9%)

localize32.0ms (0.1%)

series11.8s (39.9%)

rewrite73.0ms (0.2%)

simplify1.5s (5%)

prune2.2s (7.5%)

regimes3.7s (12.5%)

bsearch5.0ms (0%)

simplify13.0ms (0%)

end1.0ms (0%)

sample1.0s (3.6%)

Profiling