Details

analyze2.0s (20.6%)

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
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)

sample60.0ms (0.6%)

Algorithm

1×

intervals

Results

39.0ms	256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify103.0ms (1.1%)

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

prune7.0ms (0.1%)

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

8.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.9b	(/.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)

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
✓	1.2b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series358.0ms (3.7%)

Counts

4 → 153

Calls

4 calls:

160.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
96.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
92.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
9.0ms	(-.f64 (*.f64 y z) x)

rewrite89.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

4 → 115

Calls

4 calls:

23.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
22.0ms	(+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x)))
17.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
13.0ms	(-.f64 (*.f64 y z) x)

simplify305.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
290×	`associate--l+_binary64`
201×	`fma-def_binary64`

Counts

268 → 300

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	10267
1	1359	9717
2	5100	9717

prune551.0ms (5.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	296	5	301

Error

0.0b

Counts

301 → 5

Alt Table

Status	Error	Program
	35.7b	(/.f64 (+.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 y z) x)) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 (-.f64 (*.f64 y z) x))))) (+.f64 x 1))
	8.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
▶	2.3b	(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)))
	8.9b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	19.3b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))

Compiler

Compiled 10772 to 3963 computations (63.2% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	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)))
✓	2.0b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	9.9b	(/.f64 z (-.f64 (*.f64 t z) x))

series257.0ms (2.7%)

Counts

4 → 129

Calls

4 calls:

169.0ms	(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)))
40.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
38.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
10.0ms	(-.f64 (*.f64 t z) x)

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 92

Calls

4 calls:

10.0ms	(-.f64 (*.f64 t z) x)
8.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
8.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
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)))

simplify321.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

534×	`times-frac_binary64`
407×	`associate-/l*_binary64`
309×	`fma-neg_binary64`
292×	`associate-/r*_binary64`
243×	`associate-+r+_binary64`

Counts

221 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	7137
1	1025	6709
2	4918	6705
3	5157	6705

prune668.0ms (6.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	277	6	283

Error

0.0b

Counts

283 → 6

Alt Table

Status	Error	Program
	35.7b	(/.f64 (+.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 y z) x)) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 (-.f64 (*.f64 y z) x))))) (+.f64 x 1))
	8.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.3b	(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)))
▶	2.3b	(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)))
	8.9b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	18.6b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))

Compiler

Compiled 10798 to 4109 computations (61.9% saved)

localize26.0ms (0.3%)

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)))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 (*.f64 t z) x) z))
	2.0b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	9.9b	(/.f64 (-.f64 (*.f64 t z) x) z)

series236.0ms (2.4%)

Counts

3 → 120

Calls

3 calls:

168.0ms

(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)))

46.0ms

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

21.0ms

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

rewrite47.0ms (0.5%)

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:

15.0ms

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

13.0ms

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

1.0ms

(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)))

simplify361.0ms (3.7%)

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

prune690.0ms (7.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	324	1	325
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	326	5	331

Error

Counts

331 → 5

Alt Table

Status	Error	Program
	35.7b	(/.f64 (+.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 y z) x)) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 (-.f64 (*.f64 y z) x))))) (+.f64 x 1))
	8.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.3b	(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)))
	8.9b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
▶	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)))))

Compiler

Compiled 13154 to 5069 computations (61.5% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (/.f64 x z))
✓	0.0b	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
✓	2.0b	(/.f64 x (-.f64 (*.f64 z t) x))
✓	4.2b	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))

series388.0ms (4%)

Counts

4 → 129

Calls

4 calls:

299.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
39.0ms	(/.f64 x (-.f64 (*.f64 z t) x))
33.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
14.0ms	(-.f64 t (/.f64 x z))

rewrite132.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`add-sqr-sqrt_binary64`
146×	`*-un-lft-identity_binary64`
140×	`add-cube-cbrt_binary64`
122×	`times-frac_binary64`
117×	`prod-diff_binary64`

Counts

4 → 271

Calls

4 calls:

26.0ms	(*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z)))
16.0ms	(/.f64 y (*.f64 (+.f64 x 1) (-.f64 t (/.f64 x z))))
13.0ms	(-.f64 t (/.f64 x z))
11.0ms	(/.f64 x (-.f64 (*.f64 z t) x))

simplify578.0ms (6%)

Algorithm

1×	egg-herbie

Rules

641×	`times-frac_binary64`
438×	`associate-/l*_binary64`
376×	`distribute-rgt-in_binary64`
288×	`fma-def_binary64`
270×	`distribute-lft-in_binary64`

Counts

400 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	642	15144
1	1926	11871
2	4894	11867
3	4989	11867
4	4970	11867

prune473.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	443	5	448

Error

Counts

448 → 5

Alt Table

Status	Error	Program
	35.7b	(/.f64 (+.f64 x (/.f64 (sqrt.f64 (-.f64 (.f64 y z) x)) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 (-.f64 (*.f64 y z) x))))) (+.f64 x 1))
	8.9b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))
✓	2.3b	(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)))
	8.9b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
✓	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)))))

Compiler

Compiled 20440 to 7275 computations (64.4% saved)

regimes888.0ms (9.2%)

Accuracy

Total 0.0b remaining (70.5%)

Threshold costs 0.0b (70.5%)

Counts

122 → 1

Compiler

Compiled 15331 to 9407 computations (38.6% saved)

simplify3.0ms (0%)

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)

sample984.0ms (10.2%)

Algorithm

1×

intervals

Results

539.0ms	8000×	body	128	valid
21.0ms	335×	body	128	invalid

Compiler

Compiled 191 to 117 computations (38.7% saved)

Details

analyze2.0s (20.6%)

sample60.0ms (0.6%)

simplify103.0ms (1.1%)

prune7.0ms (0.1%)

localize28.0ms (0.3%)

series358.0ms (3.7%)

rewrite89.0ms (0.9%)

simplify305.0ms (3.2%)

prune551.0ms (5.7%)

localize30.0ms (0.3%)

series257.0ms (2.7%)

rewrite35.0ms (0.4%)

simplify321.0ms (3.3%)

prune668.0ms (6.9%)

localize26.0ms (0.3%)

series236.0ms (2.4%)

rewrite47.0ms (0.5%)

simplify361.0ms (3.7%)

prune690.0ms (7.2%)

localize31.0ms (0.3%)

series388.0ms (4%)

rewrite132.0ms (1.4%)

simplify578.0ms (6%)

prune473.0ms (4.9%)

regimes888.0ms (9.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample984.0ms (10.2%)

Profiling