Details

analyze133.0ms (3.1%)

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
50%	50%	0.1%	6
62.4%	31.2%	6.3%	7
71.8%	21.9%	6.3%	8
76.5%	14%	9.5%	9
80.4%	10.1%	9.5%	10
82.3%	6.6%	11%	11
84.1%	4.9%	11%	12
85%	3.2%	11.8%	13
85.8%	2.4%	11.8%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample1.9s (44.7%)

Results

1.8s	8256×	body	128	valid
15.0ms	82×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
13×	`distribute-lft-in_binary64`
13×	`distribute-rgt-in_binary64`
10×	`*-commutative_binary64`
9×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	32	8
3	56	8
4	68	8
5	74	8
6	66	8

prune7.0ms (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 3 -12/29)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)

series16.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

13.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
3.0ms	(fma.f64 x 3 -12/29)

rewrite89.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

583×	`log1p-expm1-u_binary64`
583×	`expm1-log1p-u_binary64`
287×	`log-prod_binary64`
246×	`fma-def_binary64`
190×	`pow2_binary64`

Counts

2 → 50

Calls

2 calls:

88.0ms	(fma.f64 x 3 -12/29)
87.0ms	(*.f64 (fma.f64 x 3 -12/29) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	141	13
2	1513	13
3	4944	13
4	5079	13
0	0	0
1	0	0

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
170×	`fma-neg_binary64`
59×	`cancel-sign-sub-inv_binary64`
48×	`distribute-rgt-neg-in_binary64`
29×	`distribute-rgt-in_binary64`

Counts

86 → 59

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	345
1	29	240
2	44	240
3	61	240
4	99	240
5	148	240
6	266	240
7	409	240
8	492	240
9	545	240
10	547	240
11	476	240

prune88.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	50	9	59
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	51	10	61

Error

0.0b

Counts

61 → 10

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	0.2b	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
	47.7b	(cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 3 -12/29) 3) (pow.f64 y 3)))
	36.6b	(cbrt.f64 (pow.f64 (*.f64 (fma.f64 x 3 -12/29) y) 3))
	19.5b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	50.9b	(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) 2) y)
	0.7b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 x 3 -12/29)) 3) y)
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)

Compiler

Compiled 782 to 606 computations (22.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
✓	0.1b	(*.f64 12/29 y)
✓	0.2b	(.f64 3 (.f64 y x))

series24.0ms (0.6%)

Counts

3 → 15

Calls

3 calls:

11.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
10.0ms	(.f64 3 (.f64 y x))
3.0ms	(*.f64 12/29 y)

rewrite116.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

495×	`log-prod_binary64`
410×	`fma-def_binary64`
219×	`egg-rr`
202×	`fma-neg_binary64`
178×	`pow1/3_binary64`

Counts

3 → 219

Calls

3 calls:

107.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
107.0ms	(*.f64 12/29 y)
107.0ms	(.f64 3 (.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	201	22
2	2449	22
3	4942	22
0	0	0
1	0	0

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

176×	`fma-def_binary64`
142×	`fma-neg_binary64`
49×	`associate-r_binary64`
48×	`associate-l_binary64`
36×	`cancel-sign-sub-inv_binary64`

Counts

234 → 226

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	114
1	37	114
2	74	114
3	155	114
4	248	114
5	374	114
6	468	114
7	541	114
8	470	114

prune319.0ms (7.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	6	2	8
Picked	1	0	1
Done	0	1	1
Total	231	5	236

Error

Counts

236 → 5

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
▶	0.2b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)

Compiler

Compiled 4283 to 2697 computations (37% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y -12/29)
✓	0.1b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))

series15.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

12.0ms	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
3.0ms	(*.f64 y -12/29)

rewrite121.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

668×	`log1p-expm1-u_binary64`
668×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`

Counts

2 → 41

Calls

2 calls:

118.0ms	(*.f64 y -12/29)
118.0ms	(fma.f64 x (.f64 3 y) (.f64 y -12/29))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	161	15
2	1748	15
3	4878	15
4	4946	15
5	4911	15
0	0	0
1	0	0

simplify50.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
135×	`fma-neg_binary64`
52×	`cancel-sign-sub-inv_binary64`
46×	`associate-r_binary64`
45×	`associate-l_binary64`

Counts

77 → 47

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	339
1	44	234
2	82	234
3	171	234
4	271	234
5	392	234
6	470	234
7	541	234
8	470	234

prune57.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	47	5	52

Error

Counts

52 → 5

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
✓	0.2b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)

Compiler

Compiled 672 to 483 computations (28.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y -12/29 (fma.f64 y -12/29 (*.f64 y 12/29)))
✓	0.1b	(*.f64 y 12/29)
✓	0.1b	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
✓	60.5b	(fma.f64 y -12/29 (*.f64 y 12/29))

series32.0ms (0.8%)

Counts

4 → 60

Calls

4 calls:

15.0ms	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
9.0ms	(fma.f64 y -12/29 (*.f64 y 12/29))
5.0ms	(fma.f64 y -12/29 (fma.f64 y -12/29 (*.f64 y 12/29)))
4.0ms	(*.f64 y 12/29)

rewrite91.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

463×	`log-prod_binary64`
298×	`pow2_binary64`
218×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`

Counts

4 → 106

Calls

4 calls:

87.0ms	(fma.f64 y -12/29 (fma.f64 y -12/29 (*.f64 y 12/29)))
87.0ms	(*.f64 y 12/29)
87.0ms	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
87.0ms	(fma.f64 y -12/29 (*.f64 y 12/29))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	222	31
2	2383	31
3	4923	31
0	0	0
1	0	0

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

203×	`fma-def_binary64`
135×	`fma-neg_binary64`
52×	`cancel-sign-sub-inv_binary64`
46×	`associate-r_binary64`
45×	`associate-l_binary64`

Counts

166 → 116

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	294
1	45	294
2	82	294
3	171	294
4	271	294
5	392	294
6	470	294
7	541	294
8	470	294

prune166.0ms (3.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 (.f64 y x) 3 (fma.f64 y -12/29 (fma.f64 y -12/29 (.f64 y 12/29))))
✓	0.2b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	1.3b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)

Compiler

Compiled 1944 to 1297 computations (33.3% saved)

regimes652.0ms (15.3%)

Accuracy

Total 0.2b remaining (94.3%)

Threshold costs 0.2b (94.3%)

Counts

76 → 1

Compiler

Compiled 4845 to 3621 computations (25.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	15
1	16	15
2	15	15

end147.0ms (3.4%)

Compiler: Compiled 82 to 60 computations (26.8% saved)

Iter	Nodes	Cost
0	14	345
1	29	240
2	44	240
3	61	240
4	99	240
5	148	240
6	266	240
7	409	240
8	492	240
9	545	240
10	547	240
11	476	240

Iter	Nodes	Cost
0	16	114
1	37	114
2	74	114
3	155	114
4	248	114
5	374	114
6	468	114
7	541	114
8	470	114

Iter	Nodes	Cost
0	18	339
1	44	234
2	82	234
3	171	234
4	271	234
5	392	234
6	470	234
7	541	234
8	470	234

Iter	Nodes	Cost
0	19	294
1	45	294
2	82	294
3	171	294
4	271	294
5	392	294
6	470	294
7	541	294
8	470	294

Iter	Nodes	Cost
0	14	345
1	29	240
2	44	240
3	61	240
4	99	240
5	148	240
6	266	240
7	409	240
8	492	240
9	545	240
10	547	240
11	476	240

Iter	Nodes	Cost
0	16	114
1	37	114
2	74	114
3	155	114
4	248	114
5	374	114
6	468	114
7	541	114
8	470	114

Iter	Nodes	Cost
0	18	339
1	44	234
2	82	234
3	171	234
4	271	234
5	392	234
6	470	234
7	541	234
8	470	234

Iter	Nodes	Cost
0	19	294
1	45	294
2	82	294
3	171	294
4	271	294
5	392	294
6	470	294
7	541	294
8	470	294

Details

analyze133.0ms (3.1%)

sample1.9s (44.7%)

simplify15.0ms (0.3%)

prune7.0ms (0.2%)

localize9.0ms (0.2%)

series16.0ms (0.4%)

rewrite89.0ms (2.1%)

simplify57.0ms (1.3%)

prune88.0ms (2.1%)

localize10.0ms (0.2%)

series24.0ms (0.6%)

rewrite116.0ms (2.7%)

simplify57.0ms (1.3%)

prune319.0ms (7.5%)

localize11.0ms (0.2%)

series15.0ms (0.3%)

rewrite121.0ms (2.8%)

simplify50.0ms (1.2%)

prune57.0ms (1.3%)

localize16.0ms (0.4%)

series32.0ms (0.8%)

rewrite91.0ms (2.1%)

simplify57.0ms (1.3%)

prune166.0ms (3.9%)

regimes652.0ms (15.3%)

simplify4.0ms (0.1%)

end147.0ms (3.4%)

Profiling

Iter	Nodes	Cost
0	14	345
1	29	240
2	44	240
3	61	240
4	99	240
5	148	240
6	266	240
7	409	240
8	492	240
9	545	240
10	547	240
11	476	240

Iter	Nodes	Cost
0	16	114
1	37	114
2	74	114
3	155	114
4	248	114
5	374	114
6	468	114
7	541	114
8	470	114

Iter	Nodes	Cost
0	18	339
1	44	234
2	82	234
3	171	234
4	271	234
5	392	234
6	470	234
7	541	234
8	470	234

Iter	Nodes	Cost
0	19	294
1	45	294
2	82	294
3	171	294
4	271	294
5	392	294
6	470	294
7	541	294
8	470	294