Details

analyze992.0ms (11.5%)

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%	74.9%	25.1%	8
6.2%	68.6%	25.1%	9
7.8%	67.1%	25.1%	10
10.1%	64.7%	25.1%	11
14.8%	47.6%	37.6%	12
15.8%	36.8%	47.4%	13
16.6%	35.1%	48.3%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample2.9s (33.3%)

Results

1.6s	10903×	body	128	invalid
1.3s	8256×	body	128	valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

preprocess53.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

519×	`associate-l_binary64`
472×	`fma-def_binary64`
412×	`associate-r_binary64`
243×	`*-commutative_binary64`
201×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	175
1	118	175
2	242	175
3	639	175
4	1663	175
5	3683	175
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 16 computations (23.8% saved)

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
314×	`associate-l_binary64`
304×	`*-commutative_binary64`
272×	`fma-neg_binary64`
248×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	25
2	52	25
3	116	25
4	286	25
5	632	25
6	1793	25
7	3725	25

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

Compiler

Compiled 77 to 57 computations (26% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
✓	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series255.0ms (3%)

Counts

3 → 52

Calls

21 calls:

42.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	y	0
36.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	t	inf
35.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	y	-inf
24.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	x	-inf
22.0ms	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	x	0

rewrite59.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	333	42
2	4103	42

Stop Event

1×	node limit

Counts

3 → 58

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
340×	`sub-neg_binary64`
303×	`*-commutative_binary64`
275×	`cancel-sign-sub-inv_binary64`
256×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1862
1	299	1740
2	1086	1549
3	3896	1541

Stop Event

1×	node limit

Counts

110 → 90

prune97.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	8	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Error

0.0b

Counts

91 → 9

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
▶	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
	0.9b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
	18.3b	(.f64 (-.f64 (.f64 x 1/2) y) (cbrt.f64 (.f64 (pow.f64 (.f64 z 2) 3/2) (pow.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) 3))))
	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))
	37.3b	(cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))
	50.4b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
	34.5b	(pow.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))) 2)

Compiler

Compiled 2404 to 1562 computations (35% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))
	0.0b	(sqrt.f64 (exp.f64 t))
✓	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
✓	0.4b	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))

series307.0ms (3.6%)

Counts

3 → 60

Calls

24 calls:

25.0ms	(.f64 (-.f64 (.f64 1/2 x) y) (*.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))	x	0
23.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))	x	-inf
22.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))	x	inf
21.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))	y	inf
21.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))	y	0

rewrite62.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
169×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
159×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	62
1	353	56
2	4333	56

Stop Event

1×	node limit

Counts

3 → 53

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

654×	`sub-neg_binary64`
508×	`cancel-sign-sub-inv_binary64`
306×	`*-commutative_binary64`
292×	`associate--r+_binary64`
288×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	2431
1	347	2267
2	1353	1627
3	4773	1627

Stop Event

1×	node limit

Counts

113 → 88

prune103.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	118	8	126

Error

0.0b

Counts

126 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))
	50.4b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
✓	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
	0.9b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
▶	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))
	37.3b	(cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))

Compiler

Compiled 3065 to 1963 computations (36% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
✓	0.6b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)

series1.6s (18.3%)

Counts

4 → 100

Calls

30 calls:

213.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)	z	0
164.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))	z	0
163.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)	z	inf
158.0ms	(sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t))))	z	inf
123.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2)	t	inf

rewrite66.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
161×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`
151×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	65
1	356	64
2	4088	64

Stop Event

1×	node limit

Counts

4 → 91

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

528×	`distribute-lft-out--_binary64`
386×	`*-commutative_binary64`
343×	`sub-neg_binary64`
262×	`cancel-sign-sub-inv_binary64`
250×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	2879
1	399	2745
2	1380	2120
3	3724	2076

Stop Event

1×	node limit

Counts

191 → 137

prune121.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	137	8	145

Error

0.0b

Counts

145 → 8

Alt Table

Status	Error	Program
▶	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))
	50.4b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
✓	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
	0.9b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
✓	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))
	37.3b	(cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))

Compiler

Compiled 3533 to 2259 computations (36.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 t) t)))
✓	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))
✓	0.4b	(.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 t) t)))) 2))
✓	1.0b	(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 t) t)))) 2)

series525.0ms (6.1%)

Counts

4 → 96

Calls

27 calls:

101.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 t) t)))) 2)	t	inf
100.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 2 (pow.f64 (exp.f64 t) t)))) 2)	t	-inf
38.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))	y	0
37.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))	x	inf
21.0ms	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))	y	-inf

rewrite71.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`prod-diff_binary64`
168×	`add-sqr-sqrt_binary64`
161×	`log1p-expm1-u_binary64`
161×	`expm1-log1p-u_binary64`
158×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	67
1	374	65
2	4293	65

Stop Event

1×	node limit

Counts

4 → 92

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

752×	`associate-l_binary64`
570×	`associate-r_binary64`
500×	`cancel-sign-sub-inv_binary64`
295×	`fma-neg_binary64`
269×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	3313
1	369	3235
2	1408	2248

Stop Event

1×	node limit

Counts

188 → 108

prune93.0ms (1.1%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	108	8	116

Error

0.0b

Counts

116 → 8

Alt Table

Status	Error	Program
✓	0.6b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (pow.f64 (exp.f64 t) t)))) 2)) (sqrt.f64 z))
	50.4b	(sqrt.f64 (.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)) (pow.f64 (-.f64 (.f64 x 1/2) y) 2)))
✓	0.3b	(.f64 (-.f64 (.f64 x 1/2) y) (.f64 (sqrt.f64 (.f64 z 2)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
✓	0.4b	(.f64 (.f64 (-.f64 (.f64 1/2 x) y) (.f64 (sqrt.f64 2) (pow.f64 (sqrt.f64 (exp.f64 t)) t))) (sqrt.f64 z))
	0.9b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 z) (-.f64 (*.f64 1/2 x) y)))
✓	0.6b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (sqrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 2))
	1.4b	(.f64 (-.f64 (.f64 x 1/2) y) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))
	37.3b	(cbrt.f64 (pow.f64 (.f64 (-.f64 (.f64 x 1/2) y) (sqrt.f64 (.f64 (.f64 z 2) (pow.f64 (exp.f64 t) t)))) 3))

Compiler

Compiled 2794 to 1788 computations (36% saved)

regimes891.0ms (10.3%)

Accuracy

Total 0.3b remaining (88.7%)

Threshold costs 0.3b (88.7%)

Counts

63 → 1

Compiler

Compiled 17593 to 13566 computations (22.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	22	25
2	27	25
3	29	25
4	30	25

Stop Event

1×

saturated

end133.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 206 to 158 computations (23.3% saved)

Details

analyze992.0ms (11.5%)

sample2.9s (33.3%)

preprocess53.0ms (0.6%)

simplify28.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series255.0ms (3%)

rewrite59.0ms (0.7%)

simplify60.0ms (0.7%)

prune97.0ms (1.1%)

localize12.0ms (0.1%)

series307.0ms (3.6%)

rewrite62.0ms (0.7%)

simplify68.0ms (0.8%)

prune103.0ms (1.2%)

localize14.0ms (0.2%)

series1.6s (18.3%)

rewrite66.0ms (0.8%)

simplify75.0ms (0.9%)

prune121.0ms (1.4%)

localize14.0ms (0.2%)

series525.0ms (6.1%)

rewrite71.0ms (0.8%)

simplify61.0ms (0.7%)

prune93.0ms (1.1%)

regimes891.0ms (10.3%)

simplify3.0ms (0%)

end133.0ms (1.5%)

Profiling