Details

analyze1.3s (21.2%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (19.8%)

Results

1.0s	8255×	body	128	valid
93.0ms	718×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

2.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	2.1b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 88 to 49 computations (44.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.8b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series123.0ms (2%)

Counts

3 → 144

Calls

3 calls:

76.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
31.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
15.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite76.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`fma-def_binary64`
280×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

3 → 131

Calls

3 calls:

73.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
73.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
73.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	258	37
2	3854	37
3	5479	37
0	0	0
1	0	0

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
661×	`times-frac_binary64`
630×	`fma-neg_binary64`
450×	`sub-neg_binary64`
213×	`associate--l+_binary64`

Counts

275 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	4438
1	594	4195
2	2193	3525
3	4362	3513
4	5027	3513

prune190.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	234	6	240
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	235	7	242

Error

Counts

242 → 7

Alt Table

Status	Error	Program
	2.4b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) 2) (*.f64 (cbrt.f64 (/.f64 (-.f64 z t) (-.f64 z a))) y) x)
▶	1.7b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	2.4b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (-.f64 z a)) 2)) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))) x)
	12.6b	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))
	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	3.1b	(fma.f64 (-.f64 z t) (*.f64 (/.f64 1 (-.f64 z a)) y) x)
	32.8b	(+.f64 x (-.f64 (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 z t) a))) (/.f64 (*.f64 z y) a)))

Compiler

Compiled 5849 to 1958 computations (66.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	2.4b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series90.0ms (1.5%)

Counts

3 → 144

Calls

3 calls:

43.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
29.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))
18.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite81.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`fma-neg_binary64`
260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`

Counts

3 → 134

Calls

3 calls:

77.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
77.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
77.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	264	37
2	4092	37
3	5219	37
0	0	0
1	0	0

simplify115.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
711×	`cancel-sign-sub-inv_binary64`
596×	`fma-neg_binary64`
435×	`sub-neg_binary64`
210×	`associate--l+_binary64`

Counts

278 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	4438
1	619	4195
2	2299	4075
3	4938	4075
4	5336	4075

prune196.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Status	Error	Program
	12.6b	(+.f64 x (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 y (/.f64 1 (-.f64 z t)))))
	2.4b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (-.f64 z a)) 2)) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))) x)
	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	1.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))

Compiler

Compiled 6116 to 1976 computations (67.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))
	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1)
✓	2.4b	(/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y)

series217.0ms (3.6%)

Counts

3 → 156

Calls

3 calls:

103.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))
82.0ms	(pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1)
32.0ms	(/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y)

rewrite113.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

289×	`expm1-udef_binary64`
289×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`

Counts

3 → 130

Calls

3 calls:

110.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))
110.0ms	(pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1)
110.0ms	(/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	306	42
2	4481	42
3	4994	42
4	5312	42
0	0	0
1	0	0

simplify134.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
490×	`associate-/l*_binary64`
377×	`associate-/r*_binary64`
316×	`associate--l+_binary64`
229×	`associate-r_binary64`

Counts

286 → 260

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	485	8748
1	1500	8036
2	5205	8036

prune305.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	345	0	345
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	345	5	350

Error

Counts

350 → 5

Alt Table

Status	Error	Program
	12.6b	(+.f64 x (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 y (/.f64 1 (-.f64 z t)))))
	2.4b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (-.f64 z a)) 2)) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))) x)
	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
▶	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	1.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))

Compiler

Compiled 12547 to 5066 computations (59.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	2.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series36.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

36.0ms

(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

rewrite89.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Counts

1 → 27

Calls

1 calls:

88.0ms

(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	227	14
2	3258	14
3	4982	14
4	4996	14
0	0	0
1	0	0

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
509×	`associate--l+_binary64`
471×	`fma-def_binary64`
456×	`associate-/l*_binary64`
296×	`cancel-sign-sub-inv_binary64`

Counts

87 → 70

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1836
1	305	1836
2	1154	1335
3	5013	1335

prune112.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
	12.6b	(+.f64 x (*.f64 (/.f64 1 (-.f64 z a)) (/.f64 y (/.f64 1 (-.f64 z t)))))
	2.4b	(fma.f64 (/.f64 y (pow.f64 (cbrt.f64 (-.f64 z a)) 2)) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))) x)
	3.0b	(fma.f64 (/.f64 y (-.f64 z a)) (-.f64 z t) x)
✓	2.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	1.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 z a) (-.f64 z t)) y) -1))

Compiler

Compiled 3420 to 1138 computations (66.7% saved)

regimes1.3s (21%)

Accuracy

Total 1.2b remaining (99.1%)

Threshold costs 0b (0%)

Counts

132 → 3

Compiler

Compiled 18752 to 11873 computations (36.7% saved)

bsearch19.0ms (0.3%)

Steps

Iters	Range		Point
5	1.4971378104384128e-238	8.175234475707689e-230	4.435070156250409e-230
1	-4.5536670067674154e-116	-5.419612250897526e-120	-5.0433371292086095e-118

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
12×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`*-commutative_binary64`
10×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	75
1	44	75
2	66	73
3	94	71
4	116	71
5	123	71
6	119	71

end94.0ms (1.6%)

Compiler: Compiled 197 to 111 computations (43.7% saved)

Details

analyze1.3s (21.2%)

sample1.2s (19.8%)

simplify115.0ms (1.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series123.0ms (2%)

rewrite76.0ms (1.3%)

simplify111.0ms (1.8%)

prune190.0ms (3.1%)

localize9.0ms (0.1%)

series90.0ms (1.5%)

rewrite81.0ms (1.3%)

simplify115.0ms (1.9%)

prune196.0ms (3.2%)

localize9.0ms (0.1%)

series217.0ms (3.6%)

rewrite113.0ms (1.9%)

simplify134.0ms (2.2%)

prune305.0ms (5%)

localize7.0ms (0.1%)

series36.0ms (0.6%)

rewrite89.0ms (1.5%)

simplify47.0ms (0.8%)

prune112.0ms (1.8%)

regimes1.3s (21%)

bsearch19.0ms (0.3%)

simplify6.0ms (0.1%)

end94.0ms (1.6%)

Profiling