Details

analyze71.0ms (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)

sample807.0ms (42.5%)

Results

767.0ms	8256×	body	128	valid
7.0ms	89×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify8.0ms (0.4%)

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`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	10
1	18	10
2	33	8
3	65	8
4	101	8
5	107	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 16 116))
✓	0.0b	(*.f64 (-.f64 x (/.f64 16 116)) 3)
✓	0.2b	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

series8.0ms (0.4%)

Counts

3 → 48

Calls

3 calls:

5.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)
1.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
1.0ms	(-.f64 x (/.f64 16 116))

rewrite50.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

539×	`unpow-prod-down_binary64`
423×	`log-prod_binary64`
258×	`pow2_binary64`
183×	`expm1-udef_binary64`
183×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	218	21
2	2459	17

Stop Event

1×	node limit

Counts

3 → 91

Calls

3 calls:

49.0ms	(-.f64 x (/.f64 16 116))
49.0ms	(*.f64 (-.f64 x (/.f64 16 116)) 3)
49.0ms	(.f64 (.f64 (-.f64 x (/.f64 16 116)) 3) y)

simplify36.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-def_binary64`
289×	`fma-neg_binary64`
103×	`cancel-sign-sub-inv_binary64`
71×	`distribute-rgt-neg-in_binary64`
65×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	384
1	39	279
2	78	279
3	126	279
4	173	279
5	259	279
6	422	279
7	737	279
8	1186	279
9	1862	279
10	1916	279

Stop Event

1×

saturated

Counts

139 → 103

prune68.0ms (3.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	99	6	105

Error

0.0b

Counts

105 → 6

Alt Table

Status	Error	Program
	17.0b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
▶	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
	19.3b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) -64/24389) (.f64 3 y)) (fma.f64 x x (fma.f64 x 4/29 16/841)))

Compiler

Compiled 1288 to 974 computations (24.4% saved)

localize4.0ms (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)

series7.0ms (0.4%)

Counts

2 → 36

Calls

2 calls:

5.0ms	(*.f64 (fma.f64 x 3 -12/29) y)
1.0ms	(fma.f64 x 3 -12/29)

rewrite36.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`log1p-expm1-u_binary64`
583×	`expm1-log1p-u_binary64`
287×	`log-prod_binary64`
173×	`pow2_binary64`
123×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	141	13
2	1561	13

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

35.0ms	(fma.f64 x 3 -12/29)
35.0ms	(*.f64 (fma.f64 x 3 -12/29) y)

simplify29.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	345
1	29	240
2	52	240
3	69	240
4	110	240
5	192	240
6	343	240
7	622	240
8	916	240
9	1021	240
10	1023	240

Stop Event

1×

saturated

Counts

86 → 60

prune35.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	60	6	66

Error

0.0b

Counts

66 → 6

Alt Table

Status	Error	Program
	17.0b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
▶	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
	33.8b	(pow.f64 (sqrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 2)
	19.3b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) -64/24389) (.f64 3 y)) (fma.f64 x x (fma.f64 x 4/29 16/841)))

Compiler

Compiled 709 to 541 computations (23.7% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x 4/29)
✓	0.1b	(*.f64 y (-.f64 x 4/29))
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))

series14.0ms (0.7%)

Counts

3 → 31

Calls

3 calls:

6.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))
4.0ms	(-.f64 x 4/29)
4.0ms	(*.f64 y (-.f64 x 4/29))

rewrite42.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

806×	`log1p-expm1-u_binary64`
806×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`
81×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	174	21
2	2111	21

Stop Event

1×	node limit

Counts

3 → 70

Calls

3 calls:

41.0ms	(-.f64 x 4/29)
41.0ms	(*.f64 y (-.f64 x 4/29))
41.0ms	(.f64 3 (.f64 y (-.f64 x 4/29)))

simplify38.0ms (2%)

Algorithm

1×	egg-herbie

Rules

444×	`fma-def_binary64`
244×	`fma-neg_binary64`
95×	`cancel-sign-sub-inv_binary64`
56×	`distribute-rgt-neg-in_binary64`
44×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	227
1	41	200
2	77	200
3	109	200
4	169	200
5	287	200
6	504	200
7	850	200
8	1265	200
9	1449	200
10	1453	200

Stop Event

1×

saturated

Counts

101 → 85

prune46.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	85	6	91

Error

0.0b

Counts

91 → 6

Alt Table

Status	Error	Program
	17.0b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
✓	0.3b	(.f64 3 (.f64 y (-.f64 x 4/29)))
▶	0.3b	(+.f64 (.f64 x (.f64 3 y)) (.f64 -4/29 (.f64 3 y)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	19.3b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) -64/24389) (.f64 3 y)) (fma.f64 x x (fma.f64 x 4/29 16/841)))

Compiler

Compiled 1007 to 752 computations (25.3% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x (.f64 3 y)) (.f64 -4/29 (.f64 3 y)))
✓	0.2b	(.f64 x (.f64 3 y))
✓	0.3b	(.f64 -4/29 (.f64 3 y))

series11.0ms (0.6%)

Counts

3 → 60

Calls

3 calls:

5.0ms	(+.f64 (.f64 x (.f64 3 y)) (.f64 -4/29 (.f64 3 y)))
4.0ms	(.f64 x (.f64 3 y))
1.0ms	(.f64 -4/29 (.f64 3 y))

rewrite48.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary64`
458×	`fma-def_binary64`
197×	`fma-neg_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	198	21
2	2591	19

Stop Event

1×	node limit

Counts

3 → 116

Calls

3 calls:

46.0ms	(+.f64 (.f64 x (.f64 3 y)) (.f64 -4/29 (.f64 3 y)))
46.0ms	(.f64 x (.f64 3 y))
46.0ms	(.f64 -4/29 (.f64 3 y))

simplify35.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	507
1	44	402
2	93	402
3	203	402
4	437	402
5	670	402
6	872	402
7	962	402

Stop Event

1×

saturated

Counts

176 → 121

prune89.0ms (4.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	120	7	127

Error

Counts

127 → 7

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 (.f64 x (.f64 3 y)) (.f64 -4/29 (.f64 3 y)))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 3 -12/29) y)) 3)
✓	0.2b	(*.f64 (fma.f64 x 3 -12/29) y)
	17.0b	(*.f64 (expm1.f64 (log1p.f64 (fma.f64 x 3 -12/29))) y)
	0.3b	(fma.f64 3 (.f64 y -4/29) (.f64 3 (*.f64 y x)))
	1.4b	(.f64 (pow.f64 (cbrt.f64 (.f64 3 y)) 2) (.f64 (cbrt.f64 (.f64 3 y)) (+.f64 -4/29 x)))
	19.3b	(/.f64 (.f64 (+.f64 (pow.f64 x 3) -64/24389) (.f64 3 y)) (fma.f64 x x (fma.f64 x 4/29 16/841)))

Compiler

Compiled 1783 to 1244 computations (30.2% saved)

regimes308.0ms (16.2%)

Accuracy

Total 0.2b remaining (93%)

Threshold costs 0.2b (93%)

Counts

73 → 1

Compiler

Compiled 4102 to 3172 computations (22.7% 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

Stop Event

1×

saturated

end87.0ms (4.6%)

Compiler: Compiled 110 to 84 computations (23.6% saved)

Details

analyze71.0ms (3.7%)

sample807.0ms (42.5%)

simplify8.0ms (0.4%)

prune3.0ms (0.2%)

localize9.0ms (0.5%)

series8.0ms (0.4%)

rewrite50.0ms (2.6%)

simplify36.0ms (1.9%)

prune68.0ms (3.6%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite36.0ms (1.9%)

simplify29.0ms (1.5%)

prune35.0ms (1.8%)

localize4.0ms (0.2%)

series14.0ms (0.7%)

rewrite42.0ms (2.2%)

simplify38.0ms (2%)

prune46.0ms (2.4%)

localize5.0ms (0.3%)

series11.0ms (0.6%)

rewrite48.0ms (2.5%)

simplify35.0ms (1.9%)

prune89.0ms (4.7%)

regimes308.0ms (16.2%)

simplify2.0ms (0.1%)

end87.0ms (4.6%)

Profiling