Details

analyze83.0ms (3.7%)

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)

sample926.0ms (41.6%)

Results

890.0ms	8256×	body	128	valid
6.0ms	68×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify7.0ms (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

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 55 to 43 computations (21.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

8.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
1.0ms	(fma.f64 x 3 -12/29)

rewrite119.0ms (5.4%)

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 → 52

Calls

2 calls:

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

simplify33.0ms (1.5%)

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

88 → 61

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

prune53.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	56	7	63

Error

0.0b

Counts

63 → 7

Alt Table

Status	Error	Program
	13.8b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	31.0b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
▶	0.2b	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x 3 -12/29) 3)) y)
	50.9b	(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) 2) y)

Compiler

Compiled 738 to 568 computations (23% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series8.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

6.0ms	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
1.0ms	(*.f64 y -12/29)

rewrite124.0ms (5.6%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

2 → 36

Calls

2 calls:

123.0ms	(*.f64 y -12/29)
123.0ms	(fma.f64 y (.f64 x 3) (.f64 y -12/29))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	161	14
2	1750	12
3	4912	12
4	4975	12
5	4995	12
6	4884	12
0	0	0
1	0	0

simplify29.0ms (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

72 → 43

Iterations

Useful iterations: 0 (0.0ms)

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

prune41.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	42	8	50

Error

0.0b

Counts

50 → 8

Alt Table

Status	Error	Program
	13.8b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	31.0b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
▶	0.2b	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
	1.4b	(.f64 (cbrt.f64 (.f64 y (fma.f64 x 3 -12/29))) (pow.f64 (cbrt.f64 (*.f64 y (fma.f64 x 3 -12/29))) 2))
✓	0.2b	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x 3 -12/29) 3)) y)
	50.9b	(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) 2) y)

Compiler

Compiled 630 to 466 computations (26% saved)

localize7.0ms (0.3%)

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)
✓	0.3b	(.f64 3 (.f64 y x))

series11.0ms (0.5%)

Counts

3 → 15

Calls

3 calls:

6.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
4.0ms	(.f64 3 (.f64 y x))
1.0ms	(*.f64 12/29 y)

rewrite77.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 221

Calls

3 calls:

73.0ms	(-.f64 (.f64 3 (.f64 y x)) (*.f64 12/29 y))
73.0ms	(*.f64 12/29 y)
73.0ms	(.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

simplify26.0ms (1.2%)

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

236 → 227

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

prune179.0ms (8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	224	3	227
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	228	7	235

Error

Counts

235 → 7

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x 3 -12/29) 3)) y)
▶	0.2b	(fma.f64 y -12/29 (.f64 3 (.f64 y x)))
✓	0.2b	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
	13.8b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	0.6b	(fma.f64 (cbrt.f64 (.f64 3 (.f64 y x))) (pow.f64 (cbrt.f64 (.f64 3 (.f64 y x))) 2) (*.f64 y -12/29))
	50.9b	(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x 3 -12/29)) 2) y)

Compiler

Compiled 4342 to 2750 computations (36.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y -12/29 (.f64 3 (.f64 y x)))
	0.3b	(.f64 3 (.f64 y x))

series10.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite43.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
158×	`prod-diff_binary64`
143×	`expm1-udef_binary64`
143×	`log1p-udef_binary64`

Counts

1 → 24

Calls

1 calls:

41.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	163	11
2	1792	11
3	4923	11
0	0	0
1	0	0

simplify28.0ms (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

48 → 32

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	186
1	44	186
2	82	186
3	171	186
4	271	186
5	392	186
6	470	186
7	541	186
8	470	186

prune38.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	48	7	55

Error

Counts

55 → 7

Alt Table

Status	Error	Program
	0.6b	(fma.f64 y -12/29 (pow.f64 (cbrt.f64 (.f64 3 (.f64 y x))) 3))
✓	0.2b	(fma.f64 y (.f64 x 3) (.f64 y -12/29))
	0.2b	(fma.f64 x (.f64 3 y) (.f64 y -12/29))
	14.4b	(*.f64 (cbrt.f64 (pow.f64 (fma.f64 x 3 -12/29) 3)) y)
✓	0.2b	(fma.f64 y -12/29 (.f64 3 (.f64 y x)))
	13.8b	(*.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)

Compiler

Compiled 637 to 408 computations (35.9% saved)

regimes251.0ms (11.3%)

Accuracy

Total 0.2b remaining (90.7%)

Threshold costs 0.2b (90.7%)

Counts

50 → 1

Compiler

Compiled 3005 to 2306 computations (23.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end106.0ms (4.7%)

Compiler: Compiled 95 to 71 computations (25.3% 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	18	234
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	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	186
1	44	186
2	82	186
3	171	186
4	271	186
5	392	186
6	470	186
7	541	186
8	470	186

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	18	234
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	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	186
1	44	186
2	82	186
3	171	186
4	271	186
5	392	186
6	470	186
7	541	186
8	470	186

Details

analyze83.0ms (3.7%)

sample926.0ms (41.6%)

simplify7.0ms (0.3%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite119.0ms (5.4%)

simplify33.0ms (1.5%)

prune53.0ms (2.4%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite124.0ms (5.6%)

simplify29.0ms (1.3%)

prune41.0ms (1.9%)

localize7.0ms (0.3%)

series11.0ms (0.5%)

rewrite77.0ms (3.5%)

simplify26.0ms (1.2%)

prune179.0ms (8%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite43.0ms (1.9%)

simplify28.0ms (1.2%)

prune38.0ms (1.7%)

regimes251.0ms (11.3%)

simplify2.0ms (0.1%)

end106.0ms (4.7%)

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	18	234
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	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	186
1	44	186
2	82	186
3	171	186
4	271	186
5	392	186
6	470	186
7	541	186
8	470	186