Details

analyze105.0ms (2%)

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
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.3s (25.8%)

Results

787.0ms	6517×	body	128	valid
179.0ms	583×	body	1024	valid
159.0ms	713×	body	512	valid
72.0ms	438×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify199.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

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

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	14.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	14.4b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series18.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

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

rewrite84.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

439×	`log-prod_binary64`
270×	`prod-diff_binary64`
215×	`fma-def_binary64`
172×	`expm1-udef_binary64`
172×	`log1p-udef_binary64`

Counts

2 → 67

Calls

2 calls:

83.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
83.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	193	24
2	2481	24
3	4892	24
4	5106	24
0	0	0
1	0	0

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
486×	`associate--l+_binary64`
453×	`times-frac_binary64`
420×	`associate--r+_binary64`
353×	`associate-+l+_binary64`

Counts

115 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1015
1	233	980
2	818	936
3	3450	893
4	4788	893
5	5485	893

prune82.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	4	108

Error

0.0b

Counts

108 → 4

Alt Table

Status	Error	Program
▶	14.7b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)
	27.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
	23.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	14.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 1865 to 1310 computations (29.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 y 1))
✓	0.4b	(cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1)))
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3)
✓	14.2b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)

series866.0ms (16.8%)

Counts

4 → 96

Calls

4 calls:

409.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3)
406.0ms	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)
40.0ms	(cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1)))
10.0ms	(/.f64 (+.f64 x -1) (+.f64 y 1))

rewrite80.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
200×	`log1p-udef_binary64`
199×	`expm1-udef_binary64`
197×	`fma-def_binary64`
170×	`log-pow_binary64`

Counts

4 → 165

Calls

4 calls:

76.0ms	(/.f64 (+.f64 x -1) (+.f64 y 1))
76.0ms	(cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1)))
76.0ms	(pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3)
76.0ms	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	242	46
2	2906	46
3	5339	46
0	0	0
1	0	0

simplify135.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
404×	`times-frac_binary64`
364×	`associate-/l*_binary64`
326×	`associate-/r*_binary64`
188×	`+-commutative_binary64`

Counts

261 → 260

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	535	7446
1	1917	7002
2	5078	7002

prune292.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	260	4	264

Error

0.0b

Counts

264 → 4

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)
	27.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
▶	23.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	14.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 11405 to 8734 computations (23.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) y)
✓	2.5b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	8.4b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

series23.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

11.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
8.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
4.0ms	(*.f64 (-.f64 1 x) y)

rewrite134.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

676×	`prod-diff_binary64`
541×	`fma-udef_binary64`
306×	`fma-def_binary64`
220×	`fma-neg_binary64`
189×	`expm1-udef_binary64`

Counts

3 → 127

Calls

3 calls:

132.0ms	(*.f64 (-.f64 1 x) y)
132.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
132.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	208	36
2	2931	36
3	4795	36
4	4817	36
5	5156	36
0	0	0
1	0	0

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-neg_binary64`
474×	`associate--l+_binary64`
408×	`associate--r+_binary64`
345×	`associate-+l+_binary64`
329×	`fma-def_binary64`

Counts

187 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1079
1	253	1058
2	858	1031
3	3665	1018
4	4771	1018
5	4968	1018

prune106.0ms (2.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Error

0.0b

Counts

175 → 4

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)
▶	27.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	23.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	14.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 3016 to 2105 computations (30.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (*.f64 y y))
✓	3.1b	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
✓	6.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	7.8b	(/.f64 x (*.f64 y y))

series74.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

28.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
25.0ms	(/.f64 x (*.f64 y y))
19.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
2.0ms	(/.f64 1 (*.f64 y y))

rewrite116.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

281×	`log1p-udef_binary64`
172×	`egg-rr`
158×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Counts

4 → 172

Calls

4 calls:

111.0ms	(/.f64 1 (*.f64 y y))
111.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
111.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
111.0ms	(/.f64 x (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	312	47
2	4739	47
3	5147	47
0	0	0
1	0	0

simplify188.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

608×	`div-sub_binary64`
541×	`times-frac_binary64`
517×	`unsub-neg_binary64`
383×	`neg-mul-1_binary64`
365×	`sub-neg_binary64`

Counts

256 → 197

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	1218
1	91	1062
2	224	1014
3	530	1008
4	1534	960
5	3793	960
6	4876	960
7	4938	960
8	4107	960
9	4670	960
10	4878	960
11	4952	960

prune140.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	196	5	201

Error

Counts

201 → 5

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 y (pow.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 y 1))) 3) 1)
✓	27.7b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	23.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
	53.1b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 y (.f64 (*.f64 y y) (+.f64 x -1))) (pow.f64 y 3)))
✓	14.3b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 5321 to 2894 computations (45.6% saved)

regimes856.0ms (16.6%)

Accuracy

Total 0.6b remaining (91%)

Threshold costs 0.6b (91%)

Counts

84 → 3

Compiler

Compiled 7760 to 5191 computations (33.1% saved)

bsearch42.0ms (0.8%)

Steps

Iters	Range		Point
10	9.808657792857068e-5	113005705.18286242	435.2526031412426
10	-846804759810.2698	-15.848058786683511	-396.1505766906375

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	75
1	31	75
2	34	75
3	36	75
4	37	75
5	36	75

end105.0ms (2%)

Compiler: Compiled 192 to 120 computations (37.5% saved)

Details

analyze105.0ms (2%)

sample1.3s (25.8%)

simplify199.0ms (3.8%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series18.0ms (0.3%)

rewrite84.0ms (1.6%)

simplify69.0ms (1.3%)

prune82.0ms (1.6%)

localize9.0ms (0.2%)

series866.0ms (16.8%)

rewrite80.0ms (1.5%)

simplify135.0ms (2.6%)

prune292.0ms (5.7%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite134.0ms (2.6%)

simplify77.0ms (1.5%)

prune106.0ms (2.1%)

localize11.0ms (0.2%)

series74.0ms (1.4%)

rewrite116.0ms (2.2%)

simplify188.0ms (3.6%)

prune140.0ms (2.7%)

regimes856.0ms (16.6%)

bsearch42.0ms (0.8%)

simplify4.0ms (0.1%)

end105.0ms (2%)

Profiling