Details

analyze787.0ms (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
25%	74.9%	0.2%	5
37.4%	62.4%	0.2%	6
37.4%	62.4%	0.2%	7
37.4%	62.4%	0.2%	8
40.5%	59.3%	0.2%	9
49.1%	50.7%	0.2%	10
49.1%	50.7%	0.2%	11
54.2%	45.6%	0.2%	12
61.4%	38.4%	0.2%	13
70.5%	29.3%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.6s (22.1%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify128.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

5.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.9b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.8b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series170.0ms (2.3%)

Counts

3 → 105

Calls

3 calls:

109.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
50.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
10.0ms	(-.f64 (*.f64 y z) x)

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

3 → 97

Calls

3 calls:

14.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
12.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)

simplify179.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

202 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	400	8046
1	1239	7625
2	4866	7623
3	5312	7623

prune642.0ms (8.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	233	5	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	234	5	239

Error

0.0b

Counts

239 → 5

Alt Table

Status	Error	Program
	6.0b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	5.9b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	26.3b	(-.f64 1 (/.f64 (.f64 z y) (+.f64 x (.f64 x x))))
▶	1.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	23.2b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))

Compiler

Compiled 8748 to 3324 computations (62% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	2.5b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.0b	(/.f64 z (-.f64 (*.f64 t z) x))

series257.0ms (3.5%)

Counts

4 → 144

Calls

4 calls:

168.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
42.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
27.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
19.0ms	(/.f64 y (+.f64 x 1))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
8.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
6.0ms	(/.f64 y (+.f64 x 1))
1.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify254.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

408×	`times-frac_binary64`
329×	`associate-/l*_binary64`
276×	`fma-neg_binary64`
255×	`associate-/r*_binary64`
250×	`+-commutative_binary64`

Counts

251 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7626
1	1119	7175
2	4600	7050
3	4982	7050

prune289.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	263	5	268

Error

Counts

268 → 5

Alt Table

Status	Error	Program
	6.0b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	5.9b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	26.3b	(-.f64 1 (/.f64 (.f64 z y) (+.f64 x (.f64 x x))))
▶	1.9b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
	17.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 10234 to 3922 computations (61.7% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
✓	0.3b	(/.f64 1 (fma.f64 (/.f64 t x) z -1))
✓	3.3b	(fma.f64 (/.f64 t x) z -1)
	8.0b	(/.f64 z (-.f64 (*.f64 t z) x))

series218.0ms (2.9%)

Counts

3 → 120

Calls

3 calls:

151.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
45.0ms	(/.f64 1 (fma.f64 (/.f64 t x) z -1))
21.0ms	(fma.f64 (/.f64 t x) z -1)

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-exp-log_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(/.f64 1 (fma.f64 (/.f64 t x) z -1))
1.0ms	(fma.f64 (/.f64 t x) z -1)
1.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))

simplify213.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

625×	`cancel-sign-sub-inv_binary64`
311×	`times-frac_binary64`
278×	`sub-neg_binary64`
233×	`associate-/l*_binary64`
222×	`associate-+r+_binary64`

Counts

173 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	5659
1	793	5329
2	3495	5247
3	4942	5247
4	4997	5247
5	4967	5247

prune297.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	222	5	227

Error

Counts

227 → 5

Alt Table

Status	Error	Program
	6.0b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
▶	5.9b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	26.3b	(-.f64 1 (/.f64 (.f64 z y) (+.f64 x (.f64 x x))))
✓	1.9b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
	17.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 8953 to 4367 computations (51.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	0.5b	(/.f64 1 (-.f64 (*.f64 t z) x))
✓	9.4b	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))

series235.0ms (3.2%)

Counts

3 → 132

Calls

3 calls:

113.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
86.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
34.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 116

Calls

3 calls:

16.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
6.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

simplify431.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
423×	`fma-neg_binary64`
326×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
243×	`associate-+l+_binary64`

Counts

248 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	9431
1	1270	8756
2	4988	8754
3	5353	8754

prune572.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	301	5	306

Error

Counts

306 → 5

Alt Table

Status	Error	Program
	6.0b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
✓	5.9b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	26.3b	(-.f64 1 (/.f64 (.f64 z y) (+.f64 x (.f64 x x))))
✓	1.9b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (*.f64 t z) x)) (/.f64 (-.f64 x (/.f64 1 (fma.f64 (/.f64 t x) z -1))) (+.f64 x 1)))
	17.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 10672 to 4471 computations (58.1% saved)

regimes725.0ms (9.8%)

Accuracy

Total 1.8b remaining (98.9%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 11423 to 6957 computations (39.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	23	38
2	31	38
3	35	38
4	37	38
5	36	38

end177.0ms (2.4%)

Compiler: Compiled 169 to 104 computations (38.5% saved)

Details

analyze787.0ms (10.6%)

sample1.6s (22.1%)

simplify128.0ms (1.7%)

prune2.0ms (0%)

localize11.0ms (0.1%)

series170.0ms (2.3%)

rewrite36.0ms (0.5%)

simplify179.0ms (2.4%)

prune642.0ms (8.7%)

localize13.0ms (0.2%)

series257.0ms (3.5%)

rewrite32.0ms (0.4%)

simplify254.0ms (3.4%)

prune289.0ms (3.9%)

localize26.0ms (0.4%)

series218.0ms (2.9%)

rewrite10.0ms (0.1%)

simplify213.0ms (2.9%)

prune297.0ms (4%)

localize17.0ms (0.2%)

series235.0ms (3.2%)

rewrite37.0ms (0.5%)

simplify431.0ms (5.8%)

prune572.0ms (7.7%)

regimes725.0ms (9.8%)

simplify6.0ms (0.1%)

end177.0ms (2.4%)

Profiling