Details

analyze911.0ms (15.4%)

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
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample101.0ms (1.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify95.0ms (1.6%)

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

prune3.0ms (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

9.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.1b	(/.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)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	11.4b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series131.0ms (2.2%)

Counts

3 → 105

Calls

3 calls:

79.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
47.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)

rewrite34.0ms (0.6%)

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:

19.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
6.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
3.0ms	(-.f64 (*.f64 y z) x)

simplify159.0ms (2.7%)

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

prune241.0ms (4.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	232	6	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	233	6	239

Error

0.0b

Counts

239 → 6

Alt Table

Status	Error	Program
	20.0b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	20.9b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
▶	2.5b	(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)))
	28.9b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 8772 to 3342 computations (61.9% saved)

localize11.0ms (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)))
✓	3.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.4b	(/.f64 z (-.f64 (*.f64 t z) x))

series127.0ms (2.2%)

Counts

4 → 144

Calls

4 calls:

77.0ms	(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)))
21.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
19.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
9.0ms	(/.f64 y (+.f64 x 1))

rewrite22.0ms (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:

4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 y (+.f64 x 1))
0.0ms	(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)))

simplify160.0ms (2.7%)

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

prune311.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	261	8	269

Error

Counts

269 → 8

Alt Table

Status	Error	Program
▶	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	9.1b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	25.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (.f64 (sqrt.f64 (/.f64 z (-.f64 (.f64 t z) x))) (sqrt.f64 (/.f64 z (-.f64 (.f64 t z) x)))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	9.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	20.0b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	20.9b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
✓	2.5b	(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)))
	28.9b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 10390 to 4000 computations (61.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) z)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))
	3.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.4b	(/.f64 (-.f64 (*.f64 t z) x) z)

series110.0ms (1.9%)

Counts

3 → 120

Calls

3 calls:

80.0ms

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

21.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))

9.0ms

(/.f64 (-.f64 (*.f64 t z) x) z)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 120

Calls

3 calls:

5.0ms

(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))

5.0ms

(/.f64 (-.f64 (*.f64 t z) x) z)

0.0ms

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

simplify195.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

370×	`times-frac_binary64`
297×	`sub-neg_binary64`
279×	`associate-/l*_binary64`
261×	`fma-neg_binary64`
250×	`associate-/r*_binary64`

Counts

240 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	7319
1	951	6735
2	4112	6501
3	4862	6500
4	4966	6500

prune305.0ms (5.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	327	6	333

Error

Counts

333 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
	20.0b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	20.9b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))
	28.9b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 13166 to 5086 computations (61.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 z t) x))) (+.f64 x 1))
✓	0.1b	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
✓	3.2b	(/.f64 x (-.f64 (*.f64 z t) x))
✓	4.6b	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))

series205.0ms (3.5%)

Counts

4 → 156

Calls

4 calls:

140.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
30.0ms	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 z t) x))) (+.f64 x 1))
21.0ms	(/.f64 x (-.f64 (*.f64 z t) x))
13.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`add-sqr-sqrt_binary64`
138×	`*-un-lft-identity_binary64`
114×	`times-frac_binary64`
110×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

4 → 253

Calls

4 calls:

12.0ms	(/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 z t) x))) (+.f64 x 1))
11.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
10.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
4.0ms	(/.f64 x (-.f64 (*.f64 z t) x))

simplify304.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

848×	`times-frac_binary64`
404×	`distribute-rgt-in_binary64`
337×	`fma-def_binary64`
244×	`neg-mul-1_binary64`
171×	`*-commutative_binary64`

Counts

409 → 456

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	771	15785
1	2317	13441
2	4729	13347
3	5068	13347

prune455.0ms (7.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	455	1	456
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	456	6	462

Error

Counts

462 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 z t) x))) (+.f64 x 1)) (/.f64 y (.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))))
	20.0b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	9.1b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
	23.7b	(+.f64 (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 z t) x))) (+.f64 x 1)) (/.f64 y (/.f64 (fma.f64 -1 x -1) (/.f64 z x))))
	20.9b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x))) (+.f64 x 1)) 3))

Compiler

Compiled 20597 to 7721 computations (62.5% saved)

regimes662.0ms (11.2%)

Accuracy

Total 0.0b remaining (73.9%)

Threshold costs 0.0b (73.9%)

Counts

126 → 1

Compiler

Compiled 16570 to 10061 computations (39.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	37
1	29	37
2	41	37
3	47	37
4	50	37
5	49	37

end1.0ms (0%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

sample1.2s (20.9%)

Algorithm

1×

intervals

Results

710.0ms	8000×	body	128	valid
20.0ms	338×	body	128	invalid

Compiler

Compiled 195 to 127 computations (34.9% saved)

Details

analyze911.0ms (15.4%)

sample101.0ms (1.7%)

simplify95.0ms (1.6%)

prune3.0ms (0%)

localize10.0ms (0.2%)

series131.0ms (2.2%)

rewrite34.0ms (0.6%)

simplify159.0ms (2.7%)

prune241.0ms (4.1%)

localize11.0ms (0.2%)

series127.0ms (2.2%)

rewrite22.0ms (0.4%)

simplify160.0ms (2.7%)

prune311.0ms (5.3%)

localize13.0ms (0.2%)

series110.0ms (1.9%)

rewrite18.0ms (0.3%)

simplify195.0ms (3.3%)

prune305.0ms (5.2%)

localize18.0ms (0.3%)

series205.0ms (3.5%)

rewrite64.0ms (1.1%)

simplify304.0ms (5.1%)

prune455.0ms (7.7%)

regimes662.0ms (11.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (20.9%)

Profiling