Details

analyze450.0ms (14.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56.4%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample19.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	30×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify372.0ms (11.8%)

Algorithm

1×	egg-herbie

Rules

1012×	`div-sub_binary64`
942×	`associate-/l/_binary64`
633×	`neg-mul-1_binary64`
604×	`sub-neg_binary64`
568×	`neg-sub0_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	13
2	48	13
3	148	13
4	286	13
5	523	13
6	1428	13
7	3183	13
8	2963	13
9	3619	13
10	3647	13
11	3663	13
12	3712	13
13	4265	13
14	4242	13
15	4544	13
16	4576	13
17	4596	13
18	4597	13
19	4609	13
20	4609	13
21	4621	13
22	5152	13

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

13.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	13.1b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (+.f64 (-.f64 y z) 1))
12.3b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

rewrite66.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`associate-r_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
9.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

Compiler

Compiled 729 to 365 computations (49.9% saved)

series75.0ms (2.4%)

Error

1.4b

Counts

2 → 30

Calls

2 calls:

38.0ms	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
28.0ms	(*.f64 x (+.f64 (-.f64 y z) 1))

Compiler

Compiled 658 to 393 computations (40.3% saved)

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-/l*_binary64`
493×	`distribute-rgt-in_binary64`
477×	`distribute-lft-in_binary64`
465×	`times-frac_binary64`
367×	`div-sub_binary64`

Counts

77 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1057
1	273	934
2	934	929
3	4096	929
4	5150	929

prune38.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Error

Counts

62 → 4

Alt Table

Status	Error	Program
▶	1.3b	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
	13.1b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
	2.2b	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))
	13.3b	(/.f64 1 (/.f64 z (*.f64 x (-.f64 (+.f64 y 1) z))))

Compiler

Compiled 644 to 357 computations (44.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
0.0b	(+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y))
4.0b	(*.f64 (/.f64 x z) y)

rewrite67.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-l_binary64`
12×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `times-frac_binary64`

Counts

3 → 62

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
7.0ms	(*.f64 (/.f64 x z) y)
6.0ms	(+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y))

Compiler

Compiled 1164 to 276 computations (76.3% saved)

series105.0ms (3.3%)

Error

Counts

3 → 36

Calls

3 calls:

37.0ms	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
34.0ms	(+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y))
25.0ms	(*.f64 (/.f64 x z) y)

Compiler

Compiled 916 to 534 computations (41.7% saved)

simplify99.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

694×	`associate-/l/_binary64`
288×	`associate-*l/_binary64`
258×	`associate-/l*_binary64`
211×	`associate-*r/_binary64`
207×	`distribute-rgt-out_binary64`

Counts

98 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	1364
1	332	1169
2	915	1145
3	3056	1145
4	4994	1145
5	4979	1145

prune39.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	70	4	74

Error

Counts

74 → 4

Alt Table

Status	Error	Program
✓	1.3b	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
	13.1b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
▶	2.2b	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))
	13.3b	(/.f64 1 (/.f64 z (*.f64 x (-.f64 (+.f64 y 1) z))))

Compiler

Compiled 837 to 358 computations (57.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 z (-.f64 (+.f64 y 1) z))
2.1b	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))

rewrite131.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

162×	`times-frac_binary64`
158×	`*-un-lft-identity_binary64`
110×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out--_binary64`

Counts

2 → 155

Calls

2 calls:

11.0ms	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))
7.0ms	(/.f64 z (-.f64 (+.f64 y 1) z))

Compiler

Compiled 2669 to 1511 computations (43.4% saved)

series100.0ms (3.2%)

Error

Counts

2 → 37

Calls

2 calls:

41.0ms	(/.f64 z (-.f64 (+.f64 y 1) z))
38.0ms	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))

Compiler

Compiled 1442 to 998 computations (30.8% saved)

simplify145.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

768×	`times-frac_binary64`
713×	`distribute-rgt-in_binary64`
196×	`associate-/r/_binary64`
172×	`associate-/l/_binary64`
138×	`associate-*l/_binary64`

Counts

192 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	4908
1	729	4764
2	2857	4658
3	5411	4658

prune62.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	1.3b	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
▶	13.1b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
✓	2.2b	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))
	13.3b	(/.f64 1 (/.f64 z (*.f64 x (-.f64 (+.f64 y 1) z))))

Compiler

Compiled 1732 to 922 computations (46.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 x (-.f64 y z))
0.0b	(+.f64 (*.f64 x (-.f64 y z)) x)
12.3b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)

rewrite72.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
12×	`cancel-sign-sub-inv_binary64`
9×	`times-frac_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
7.0ms	(+.f64 (*.f64 x (-.f64 y z)) x)
7.0ms	(*.f64 x (-.f64 y z))

Compiler

Compiled 1314 to 315 computations (76% saved)

series105.0ms (3.3%)

Error

Counts

3 → 45

Calls

3 calls:

41.0ms	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
27.0ms	(+.f64 (*.f64 x (-.f64 y z)) x)
27.0ms	(*.f64 x (-.f64 y z))

Compiler

Compiled 1023 to 597 computations (41.6% saved)

simplify97.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

527×	`distribute-rgt-in_binary64`
502×	`distribute-lft-in_binary64`
355×	`times-frac_binary64`
217×	`associate-/l*_binary64`
208×	`exp-prod_binary64`

Counts

123 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1634
1	347	1550
2	1105	1539
3	4502	1539
4	4975	1539

prune35.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
	1.3b	(-.f64 (+.f64 (/.f64 x z) (*.f64 (/.f64 x z) y)) x)
	13.1b	(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
	2.2b	(/.f64 x (/.f64 z (-.f64 (+.f64 y 1) z)))
	13.3b	(/.f64 1 (/.f64 z (*.f64 x (-.f64 (+.f64 y 1) z))))

Compiler

Compiled 797 to 397 computations (50.2% saved)

regimes301.0ms (9.5%)

Accuracy

Total 0.2b remaining (93.3%)

Threshold costs 0.2b (93.3%)

Compiler

Compiled 3256 to 2062 computations (36.7% saved)

bsearch11.0ms (0.3%)

Steps

Iters	Range		Point
3	4.6244826487412726e-11	4.6176019111166864e-10	3.6297350233992166e-10
2	-6.093513248310074e+52	-6.434249444301938e+40	-6.190203082263542e+49

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	51
1	34	51
2	42	51
3	46	51
4	48	51
5	47	51

end1.0ms (0%)

Compiler: Compiled 38 to 23 computations (39.5% saved)

sample662.0ms (20.9%)

Algorithm

1×

intervals

Results

242.0ms	8000×	body	128	valid
38.0ms	1027×	body	128	invalid

Compiler

Compiled 106 to 67 computations (36.8% saved)

Details

analyze450.0ms (14.3%)

sample19.0ms (0.6%)

simplify372.0ms (11.8%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite66.0ms (2.1%)

series75.0ms (2.4%)

simplify77.0ms (2.4%)

prune38.0ms (1.2%)

localize6.0ms (0.2%)

rewrite67.0ms (2.1%)

series105.0ms (3.3%)

simplify99.0ms (3.1%)

prune39.0ms (1.2%)

localize6.0ms (0.2%)

rewrite131.0ms (4.1%)

series100.0ms (3.2%)

simplify145.0ms (4.6%)

prune62.0ms (2%)

localize7.0ms (0.2%)

rewrite72.0ms (2.3%)

series105.0ms (3.3%)

simplify97.0ms (3.1%)

prune35.0ms (1.1%)

regimes301.0ms (9.5%)

bsearch11.0ms (0.3%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample662.0ms (20.9%)

Profiling