Details

analyze1.5s (40.3%)

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
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.3s (34.9%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 44 to 30 computations (31.8% saved)

preprocess16.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

7×	`fma-neg_binary64`
7×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	175
1	60	175
2	67	175
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 21 to 14 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`fma-neg_binary64`
1×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	16	25
2	17	25

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

10.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 80 to 51 computations (36.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 y 2) z)
✓	0.9b	(-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))
✓	19.3b	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))

series44.0ms (1.2%)

Counts

3 → 96

Calls

24 calls:

4.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	t	-inf
4.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	y	inf
3.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	z	0
3.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	z	-inf
3.0ms	(/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t)))	y	-inf

rewrite46.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`pow2_binary64`
325×	`log-prod_binary64`
236×	`pow1/3_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	235	42
2	2577	42

Stop Event

1×	node limit

Counts

3 → 76

simplify380.0ms (10.3%)

Algorithm

1×	egg-herbie

Rules

1667×	`sqr-pow_binary64`
783×	`pow-sqr_binary64`
96×	`cube-prod_binary64`
96×	`cube-mult_binary64`
96×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	1769
1	121	1769
2	153	1769
3	190	1769
4	243	1769
5	300	1769
6	366	1769
7	437	1769
8	518	1769
9	604	1769
10	700	1769
11	801	1769
12	912	1769
13	1028	1769
14	1154	1769
15	1285	1769
16	1426	1769
17	1572	1769
18	1728	1769
19	1889	1769
20	2060	1769
21	2236	1769
22	2284	1769
23	2290	1769
24	2290	1769
25	2465	1769
26	2651	1769
27	2848	1769
28	3055	1769
29	3267	1769
30	3489	1769
31	3716	1769
32	3953	1769
33	4195	1769
34	4207	1769
35	4213	1769
36	4213	1769
37	4462	1769
38	4713	1769
39	4980	1769

Stop Event

1×	node limit

Counts

172 → 96

prune57.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	3	97

Error

Counts

97 → 3

Alt Table

Status	Error	Program
✓	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
▶	23.2b	(-.f64 x (*.f64 -2 (/.f64 z t)))
	25.6b	(-.f64 x (/.f64 y z))

Compiler

Compiled 2445 to 950 computations (61.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 -2 (/.f64 z t))

series6.0ms (0.2%)

Counts

1 → 0

Calls

6 calls:

1.0ms	(*.f64 -2 (/.f64 z t))	z	0
1.0ms	(*.f64 -2 (/.f64 z t))	z	-inf
1.0ms	(*.f64 -2 (/.f64 z t))	z	inf
1.0ms	(*.f64 -2 (/.f64 z t))	t	inf
1.0ms	(*.f64 -2 (/.f64 z t))	t	0

rewrite29.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

438×	`log1p-expm1-u_binary64`
438×	`expm1-log1p-u_binary64`
419×	`pow1_binary64`
157×	`unpow-prod-down_binary64`
145×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	111	7
2	1134	7

Stop Event

1×	node limit

Counts

1 → 23

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

23 → 23

prune15.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	23	3	26

Error

Counts

26 → 3

Alt Table

Status	Error	Program
✓	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	23.2b	(-.f64 x (*.f64 -2 (/.f64 z t)))
▶	25.6b	(-.f64 x (/.f64 y z))

Compiler

Compiled 333 to 214 computations (35.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 9

Calls

9 calls:

1.0ms	(-.f64 x (/.f64 y z))	x	0
1.0ms	(-.f64 x (/.f64 y z))	y	inf
1.0ms	(-.f64 x (/.f64 y z))	y	-inf
1.0ms	(-.f64 x (/.f64 y z))	x	-inf
1.0ms	(-.f64 x (/.f64 y z))	x	inf

rewrite33.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log1p-expm1-u_binary64`
523×	`expm1-log1p-u_binary64`
209×	`unpow-prod-down_binary64`
167×	`pow2_binary64`
161×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	117	7
2	1319	7

Stop Event

1×	node limit

Counts

1 → 33

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	33

Stop Event

1×

saturated

Counts

42 → 35

prune16.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Status	Error	Program
✓	10.5b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))
✓	23.2b	(-.f64 x (*.f64 -2 (/.f64 z t)))
✓	25.6b	(-.f64 x (/.f64 y z))

Compiler

Compiled 474 to 167 computations (64.8% saved)

regimes88.0ms (2.4%)

Accuracy

Total 3.4b remaining (96.3%)

Threshold costs 0b (0%)

Counts

4 → 5

Compiler

Compiled 460 to 322 computations (30% saved)

bsearch72.0ms (2%)

Algorithm

4×	binary-search

Calls

4 calls:

22.0ms	z
18.0ms	z
18.0ms	z
14.0ms	z

Steps

Iters	Point		Range
2.649674061790002e+68	∈ [	5.2215529413161436e+66	,	7.53454227364104e+68	]
1.7187323970340757e-115	∈ [	1.103121302603298e-115	,	7.771290074975882e-113	]
-6.317127196530134e-66	∈ [	-5.846067440850147e-61	,	-1.3246846198426114e-67	]
-5.481381047956685e+88	∈ [	-1.8238915567031067e+89	,	-1.4668873517803834e+88	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	98

Stop Event

1×

saturated

end71.0ms (1.9%)

Stop Event

1×

done

Compiler

Compiled 183 to 110 computations (39.9% saved)

Details

analyze1.5s (40.3%)

sample1.3s (34.9%)

preprocess16.0ms (0.4%)

simplify5.0ms (0.1%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series44.0ms (1.2%)

rewrite46.0ms (1.2%)

simplify380.0ms (10.3%)

prune57.0ms (1.5%)

localize5.0ms (0.1%)

series6.0ms (0.2%)

rewrite29.0ms (0.8%)

simplify4.0ms (0.1%)

prune15.0ms (0.4%)

localize3.0ms (0.1%)

series7.0ms (0.2%)

rewrite33.0ms (0.9%)

simplify5.0ms (0.1%)

prune16.0ms (0.4%)

regimes88.0ms (2.4%)

bsearch72.0ms (2%)

simplify2.0ms (0.1%)

end71.0ms (1.9%)

Profiling