Details

analyze763.0ms (12.8%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (16.9%)

Results

911.0ms	8256×	body	128	valid
84.0ms	652×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess33.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

891×	`fma-def_binary64`
651×	`div-sub_binary64`
212×	`sub-neg_binary64`
202×	`distribute-rgt-in_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	91
1	62	91
2	162	91
3	399	91
4	919	91
5	2312	91
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

574×	`times-frac_binary64`
572×	`fma-def_binary64`
533×	`div-sub_binary64`
349×	`fma-neg_binary64`
190×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	77	13
4	173	13
5	318	13
6	711	13
7	2139	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	12.2b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 74 to 42 computations (43.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	2.5b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

series47.0ms (0.8%)

Counts

2 → 84

Calls

21 calls:

6.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))	t	-inf
3.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))	x	-inf
3.0ms	(/.f64 (-.f64 y z) (-.f64 t z))	t	-inf
2.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))	t	inf
2.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))	t	0

rewrite123.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
257×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	23
2	3217	23

Stop Event

1×	node limit

Counts

2 → 257

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-def_binary64`
656×	`times-frac_binary64`
500×	`cancel-sign-sub-inv_binary64`
337×	`sub-neg_binary64`
202×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	2603
1	499	2525
2	1839	2084

Stop Event

1×	node limit

Counts

341 → 327

prune227.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	322	5	327
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	323	6	329

Error

0.0b

Counts

329 → 6

Alt Table

Status	Error	Program
▶	2.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
✓	2.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	20.9b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 (-.f64 t z)) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (-.f64 t z))) (/.f64 (cbrt.f64 (.f64 z z)) 1) (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))))
	12.6b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
	34.9b	(/.f64 y (/.f64 (-.f64 t z) x))
	12.2b	(-.f64 (/.f64 (.f64 y x) (-.f64 t z)) (/.f64 (.f64 z x) (-.f64 t z)))

Compiler

Compiled 14515 to 4019 computations (72.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	2.5b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

series49.0ms (0.8%)

Counts

2 → 84

Calls

21 calls:

7.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))	t	0
3.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))	y	inf
3.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))	t	-inf
3.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))	t	inf
2.0ms	(/.f64 (-.f64 t z) (-.f64 y z))	y	-inf

rewrite122.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

979×	`prod-diff_binary64`
278×	`egg-rr`
115×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`
110×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	214	23
2	3470	23

Stop Event

1×	node limit

Counts

2 → 278

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

830×	`times-frac_binary64`
731×	`fma-def_binary64`
541×	`cancel-sign-sub-inv_binary64`
323×	`sub-neg_binary64`
210×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2597
1	492	2531
2	1898	2289

Stop Event

1×	node limit

Counts

362 → 349

prune234.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	347	2	349
Fresh	2	2	4
Picked	0	1	1
Done	1	0	1
Total	350	5	355

Error

Counts

355 → 5

Alt Table

Status	Error	Program
✓	2.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	20.9b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 (-.f64 t z)) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (-.f64 t z))) (/.f64 (cbrt.f64 (.f64 z z)) 1) (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))))
▶	10.5b	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))
	34.9b	(/.f64 y (/.f64 (-.f64 t z) x))
	12.3b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))

Compiler

Compiled 14969 to 4061 computations (72.9% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))
✓	0.0b	(/.f64 x (-.f64 t z))
✓	4.0b	(*.f64 y (/.f64 x (-.f64 t z)))
✓	8.4b	(*.f64 (neg.f64 z) (/.f64 x (-.f64 t z)))

series98.0ms (1.6%)

Counts

4 → 156

Calls

42 calls:

11.0ms	(*.f64 (neg.f64 z) (/.f64 x (-.f64 t z)))	x	0
4.0ms	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))	x	-inf
4.0ms	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))	x	inf
4.0ms	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))	x	0
3.0ms	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))	t	-inf

rewrite65.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

264×	`fma-neg_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
153×	`egg-rr`
133×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	255	40
2	4054	40

Stop Event

1×	node limit

Counts

4 → 153

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
644×	`times-frac_binary64`
497×	`associate-/l*_binary64`
366×	`cancel-sign-sub-inv_binary64`
189×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	4080
1	412	4026
2	1501	3483

Stop Event

1×	node limit

Counts

309 → 238

prune192.0ms (3.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	288	5	293

Error

Counts

293 → 5

Alt Table

Status	Error	Program
✓	2.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	20.9b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 (-.f64 t z)) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (-.f64 t z))) (/.f64 (cbrt.f64 (.f64 z z)) 1) (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))))
✓	10.5b	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))
	34.9b	(/.f64 y (/.f64 (-.f64 t z) x))
▶	12.3b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))

Compiler

Compiled 6819 to 1870 computations (72.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.2b	(/.f64 x (/.f64 1 (-.f64 y z)))
✓	11.6b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))

series49.0ms (0.8%)

Counts

4 → 132

Calls

33 calls:

3.0ms	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))	t	inf
3.0ms	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))	y	inf
3.0ms	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))	t	-inf
3.0ms	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))	t	0
2.0ms	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))	x	-inf

rewrite66.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`prod-diff_binary64`
139×	`add-sqr-sqrt_binary64`
137×	`egg-rr`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	274	34
2	4034	34

Stop Event

1×	node limit

Counts

4 → 137

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

679×	`times-frac_binary64`
586×	`fma-def_binary64`
544×	`associate-/l*_binary64`
302×	`cancel-sign-sub-inv_binary64`
170×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2737
1	411	2665
2	1497	2434

Stop Event

1×	node limit

Counts

269 → 206

prune141.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	206	5	211

Error

Counts

211 → 5

Alt Table

Status	Error	Program
✓	2.6b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	20.9b	(.f64 x (+.f64 (fma.f64 y (/.f64 1 (-.f64 t z)) (neg.f64 (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 z) (-.f64 t z))) (/.f64 (cbrt.f64 (.f64 z z)) 1) (.f64 (/.f64 (cbrt.f64 z) (-.f64 t z)) (/.f64 (cbrt.f64 (.f64 z z)) 1)))))
✓	10.5b	(+.f64 (.f64 y (/.f64 x (-.f64 t z))) (.f64 (neg.f64 z) (/.f64 x (-.f64 t z))))
✓	12.3b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
	10.7b	(/.f64 (-.f64 y z) (/.f64 (-.f64 t z) x))

Compiler

Compiled 3980 to 1735 computations (56.4% saved)

regimes2.3s (38.9%)

Accuracy

Total 2.7b remaining (99.2%)

Threshold costs 0b (0%)

Counts

260 → 3

Compiler

Compiled 26871 to 16358 computations (39.1% saved)

bsearch32.0ms (0.5%)

Algorithm

2×	binary-search

Calls

2 calls:

21.0ms	x
2.0ms	x

Steps

Iters	Point		Range
563.0956741630507	∈ [	0.5969984459439822	,	527221.6982317708	]
-1.1573558099256976e-117	∈ [	-3.491609924320744e-117	,	-7.35759892225056e-123	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

52×	`distribute-rgt-neg-in_binary64`
50×	`cancel-sign-sub-inv_binary64`
38×	`neg-sub0_binary64`
37×	`neg-mul-1_binary64`
36×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	75
1	51	72
2	84	72
3	128	68
4	175	66
5	224	66
6	302	66
7	377	66
8	424	66
9	453	66
10	461	66

Stop Event

1×

saturated

end81.0ms (1.4%)

Stop Event

1×

fuel

Compiler

Compiled 216 to 109 computations (49.5% saved)

Iter	Nodes	Cost
0	29	75
1	51	72
2	84	72
3	128	68
4	175	66
5	224	66
6	302	66
7	377	66
8	424	66
9	453	66
10	461	66

Iter	Nodes	Cost
0	29	75
1	51	72
2	84	72
3	128	68
4	175	66
5	224	66
6	302	66
7	377	66
8	424	66
9	453	66
10	461	66

Details

analyze763.0ms (12.8%)

sample1.0s (16.9%)

preprocess33.0ms (0.6%)

simplify23.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series47.0ms (0.8%)

rewrite123.0ms (2%)

simplify64.0ms (1.1%)

prune227.0ms (3.8%)

localize6.0ms (0.1%)

series49.0ms (0.8%)

rewrite122.0ms (2%)

simplify66.0ms (1.1%)

prune234.0ms (3.9%)

localize8.0ms (0.1%)

series98.0ms (1.6%)

rewrite65.0ms (1.1%)

simplify71.0ms (1.2%)

prune192.0ms (3.2%)

localize8.0ms (0.1%)

series49.0ms (0.8%)

rewrite66.0ms (1.1%)

simplify56.0ms (0.9%)

prune141.0ms (2.4%)

regimes2.3s (38.9%)

bsearch32.0ms (0.5%)

simplify10.0ms (0.2%)

end81.0ms (1.4%)

Profiling

Iter	Nodes	Cost
0	29	75
1	51	72
2	84	72
3	128	68
4	175	66
5	224	66
6	302	66
7	377	66
8	424	66
9	453	66
10	461	66