Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample801.0ms (49%)

Results

627.0ms	7531×	body	128	valid
95.0ms	393×	body	1024	valid
50.0ms	228×	body	512	valid
14.0ms	104×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess41.0ms (2.5%)

Algorithm

2×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
87×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	43	10
3	101	8
4	229	8
5	361	8
6	545	8
7	816	8
8	1369	8
9	1522	8
10	1835	8
11	2255	8
12	2364	8
13	2368	8
14	2368	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 8 computations (20% saved)

simplify32.0ms (2%)

Algorithm

1×	egg-herbie

Rules

927×	`fma-def_binary64`
405×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
87×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	43	10
3	101	8
4	229	8
5	361	8
6	545	8
7	816	8
8	1369	8
9	1522	8
10	1835	8
11	2255	8
12	2364	8
13	2368	8
14	2368	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 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
▶	0.2b	(*.f64 x (fma.f64 x -9 6))

Compiler

Compiled 50 to 38 computations (24% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -9 6)
✓	0.1b	(*.f64 x (fma.f64 x -9 6))

series4.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(*.f64 x (fma.f64 x -9 6))	x	-inf
1.0ms	(*.f64 x (fma.f64 x -9 6))	x	inf
1.0ms	(*.f64 x (fma.f64 x -9 6))	x	0
1.0ms	(fma.f64 x -9 6)	x	-inf
1.0ms	(fma.f64 x -9 6)	x	inf

rewrite36.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`log1p-expm1-u_binary64`
506×	`expm1-log1p-u_binary64`
285×	`unpow-prod-down_binary64`
243×	`log-prod_binary64`
147×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1346	13

Stop Event

1×	node limit

Counts

2 → 54

simplify50.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-neg_binary64`
474×	`fma-def_binary64`
450×	`cancel-sign-sub-inv_binary64`
315×	`associate-l_binary64`
255×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	207
1	32	189
2	61	144
3	132	144
4	424	144
5	1493	144
6	2879	144
7	4277	144

Stop Event

1×	node limit

Counts

78 → 64

prune50.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	6	64
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Error

0.0b

Counts

66 → 8

Alt Table

Status	Error	Program
	1.5b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
▶	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	40.6b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	44.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
✓	0.2b	(*.f64 x (fma.f64 x -9 6))
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	11.5b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))

Compiler

Compiled 815 to 637 computations (21.8% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (*.f64 x 3))
✓	0.1b	(.f64 3 (-.f64 2 (.f64 x 3)))
✓	0.1b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

series9.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(-.f64 2 (*.f64 x 3))	x	inf
1.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)	x	-inf
1.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)	x	inf
1.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)	x	0
1.0ms	(.f64 3 (-.f64 2 (.f64 x 3)))	x	-inf

rewrite54.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
121×	`prod-diff_binary64`
87×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	177	30
2	2207	30

Stop Event

1×	node limit

Counts

3 → 64

simplify40.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-neg_binary64`
532×	`fma-def_binary64`
368×	`associate-l_binary64`
280×	`distribute-rgt-neg-in_binary64`
257×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	279
1	43	261
2	78	198
3	168	198
4	517	198
5	1760	198
6	3269	198
7	4710	198

Stop Event

1×	node limit

Counts

100 → 79

prune58.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	6	6
Picked	0	1	1
Done	1	0	1
Total	79	8	87

Error

0.0b

Counts

87 → 8

Alt Table

Status	Error	Program
	1.5b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
✓	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	40.6b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	44.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	11.5b	(*.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -9 6)) 2))
	0.2b	(pow.f64 (.f64 (.f64 3 x) (+.f64 2 (*.f64 x -3))) 1)
▶	0.2b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))

Compiler

Compiled 1147 to 914 computations (20.3% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series7.0ms (0.4%)

Counts

2 → 3

Calls

6 calls:

3.0ms	(*.f64 9 (pow.f64 x 2))	x	0
1.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))	x	inf
1.0ms	(-.f64 (.f64 6 x) (.f64 9 (pow.f64 x 2)))	x	-inf
1.0ms	(*.f64 9 (pow.f64 x 2))	x	inf
1.0ms	(*.f64 9 (pow.f64 x 2))	x	-inf

rewrite47.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

893×	`log1p-expm1-u_binary64`
893×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`
92×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	208	18
2	2480	18

Stop Event

1×	node limit

Counts

2 → 63

simplify58.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

624×	`sqr-pow_binary64`
513×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
279×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	26	18
3	51	18
4	124	18
5	367	18
6	1383	18
7	2272	18
8	2436	18
9	2649	18
10	2869	18
11	3169	18
12	3569	18
13	4057	18
14	4618	18

Stop Event

1×	node limit

Counts

66 → 66

prune48.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	67	7	74

Error

0.0b

Counts

74 → 7

Alt Table

Status	Error	Program
	1.5b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
✓	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	40.6b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	44.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	0.2b	(pow.f64 (.f64 (.f64 3 x) (+.f64 2 (*.f64 x -3))) 1)
▶	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))

Compiler

Compiled 1328 to 800 computations (39.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 6 (.f64 (.f64 x x) -9))
✓	0.2b	(.f64 (.f64 x x) -9)

series5.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))	x	-inf
1.0ms	(fma.f64 x 6 (.f64 (.f64 x x) -9))	x	inf
1.0ms	(.f64 (.f64 x x) -9)	x	0
1.0ms	(.f64 (.f64 x x) -9)	x	inf
1.0ms	(.f64 (.f64 x x) -9)	x	-inf

rewrite37.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log1p-expm1-u_binary64`
577×	`expm1-log1p-u_binary64`
291×	`log-prod_binary64`
123×	`prod-diff_binary64`
120×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	144	17
2	1597	17

Stop Event

1×	node limit

Counts

2 → 46

simplify34.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-neg_binary64`
596×	`fma-def_binary64`
293×	`distribute-rgt-neg-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
251×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	219
1	24	201
2	50	192
3	134	174
4	402	174
5	1345	174
6	2596	174
7	4165	174

Stop Event

1×	node limit

Counts

70 → 52

prune31.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	52	7	59

Error

0.0b

Counts

59 → 7

Alt Table

Status	Error	Program
	1.5b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -9 6))) 3)
✓	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	40.6b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -9 6)) 3))
	44.2b	(pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -9 6))) 2)
	7.0b	(*.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -9 6) 3)))
	0.2b	(pow.f64 (.f64 (.f64 3 x) (+.f64 2 (*.f64 x -3))) 1)
✓	0.1b	(fma.f64 x 6 (.f64 (.f64 x x) -9))

Compiler

Compiled 703 to 524 computations (25.5% saved)

regimes75.0ms (4.6%)

Accuracy

Total 0.1b remaining (72.1%)

Threshold costs 0.1b (72.1%)

Counts

40 → 1

Compiler

Compiled 808 to 606 computations (25% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

end85.0ms (5.2%)

Stop Event

1×

fuel

Compiler

Compiled 89 to 68 computations (23.6% saved)

Details

analyze5.0ms (0.3%)

sample801.0ms (49%)

preprocess41.0ms (2.5%)

simplify32.0ms (2%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series4.0ms (0.3%)

rewrite36.0ms (2.2%)

simplify50.0ms (3.1%)

prune50.0ms (3%)

localize5.0ms (0.3%)

series9.0ms (0.6%)

rewrite54.0ms (3.3%)

simplify40.0ms (2.4%)

prune58.0ms (3.6%)

localize5.0ms (0.3%)

series7.0ms (0.4%)

rewrite47.0ms (2.9%)

simplify58.0ms (3.5%)

prune48.0ms (3%)

localize6.0ms (0.3%)

series5.0ms (0.3%)

rewrite37.0ms (2.2%)

simplify34.0ms (2.1%)

prune31.0ms (1.9%)

regimes75.0ms (4.6%)

simplify2.0ms (0.2%)

end85.0ms (5.2%)

Profiling