Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample955.0ms (37.4%)

Results

855.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	11	9
3	11	9

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

35.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	35.0b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 21 to 15 computations (28.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	33.6b	(sqrt.f64 (.f64 2 (.f64 x x)))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
2.0ms	(.f64 2 (.f64 x x))

rewrite85.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`log1p-udef_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`
449×	`unpow-prod-down_binary64`
268×	`log-prod_binary64`

Counts

2 → 72

Calls

2 calls:

84.0ms	(.f64 2 (.f64 x x))
84.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	121	13
2	1257	13
3	4991	13
4	6461	13

simplify107.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`fma-neg_binary64`
569×	`neg-mul-1_binary64`
441×	`fabs-mul_binary64`
416×	`distribute-rgt-neg-out_binary64`

Counts

96 → 75

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	41	164
3	76	164
4	160	164
5	416	164
6	614	164
7	992	164
8	1262	164
9	1713	164
10	2084	164
11	2649	164
12	2932	164
13	4196	164
14	4917	164
15	4747	164

prune153.0ms (6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Error

0.2b

Counts

76 → 8

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.2b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
▶	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 2 (.f64 x x)))
	43.2b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))

Compiler

Compiled 918 to 700 computations (23.7% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 (sqrt.f64 2) x)

rewrite74.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

711×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
336×	`pow1_binary64`
245×	`unpow-prod-down_binary64`

Counts

1 → 38

Calls

1 calls:

74.0ms

(*.f64 (sqrt.f64 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune22.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	37	9	46

Error

0.2b

Counts

46 → 9

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.2b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
✓	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	31.0b	(neg.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
	43.2b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))

Compiler

Compiled 524 to 441 computations (15.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(cbrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.8b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)

series540.0ms (21.2%)

Counts

2 → 24

Calls

2 calls:

354.0ms	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
185.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite52.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
488×	`unpow-prod-down_binary64`
278×	`log-prod_binary64`
155×	`pow2_binary64`

Counts

2 → 113

Calls

2 calls:

50.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) x))
50.0ms	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	147	14
2	1449	14
3	5269	14

simplify71.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
425×	`fma-def_binary64`
408×	`unswap-sqr_binary64`
277×	`associate-+l+_binary64`
236×	`associate-+r+_binary64`

Counts

137 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	448
1	74	448
2	133	424
3	382	220
4	1233	220
5	3771	220
6	4972	220
7	4921	220

prune83.0ms (3.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	157	11	168

Error

0.0b

Counts

168 → 11

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.2b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	31.0b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2))))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
✓	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	30.5b	(neg.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
✓	31.0b	(neg.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
	43.2b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))

Compiler

Compiled 2369 to 1960 computations (17.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (pow.f64 2 1/4) x)
✓	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

series33.0ms (1.3%)

Counts

2 → 12

Calls

2 calls:

27.0ms	(*.f64 (pow.f64 2 1/4) x)
5.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite42.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
392×	`unpow-prod-down_binary64`
310×	`log-prod_binary64`
168×	`pow2_binary64`

Counts

2 → 36

Calls

2 calls:

41.0ms	(*.f64 (pow.f64 2 1/4) x)
41.0ms	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1523	13
3	5396	13

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

48 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72
2	6	72

prune28.0ms (1.1%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	37	11	48

Error

0.0b

Counts

48 → 11

Alt Table

Status	Error	Program
	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	33.2b	(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
	31.0b	(neg.f64 (.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2))))
	35.0b	(.f64 (sqrt.f64 (sqrt.f64 2)) (pow.f64 (.f64 x (*.f64 x (sqrt.f64 2))) 1/2))
✓	30.6b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	32.5b	(*.f64 (sqrt.f64 2) x)
✓	35.0b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	30.5b	(neg.f64 (.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x)))
✓	31.0b	(neg.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3))
	43.2b	(.f64 (pow.f64 (.f64 (*.f64 2 x) (sqrt.f64 x)) 1/2) (sqrt.f64 (sqrt.f64 x)))
	33.2b	(.f64 (pow.f64 (.f64 (*.f64 x (sqrt.f64 2)) (sqrt.f64 2)) 1/2) (sqrt.f64 x))

Compiler

Compiled 515 to 447 computations (13.2% saved)

regimes111.0ms (4.3%)

Accuracy

Total 0.4b remaining (89.6%)

Threshold costs 0.4b (89.6%)

Counts

18 → 2

Compiler

Compiled 774 to 632 computations (18.3% saved)

bsearch17.0ms (0.7%)

Steps

Iters	Range		Point
9	-5.0244719348910686e-303	1.998438837190896e-307	-1.04069420257774e-310

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	25	27
2	38	27
3	45	27
4	49	27
5	50	27
6	50	27

end121.0ms (4.7%)

Compiler: Compiled 143 to 117 computations (18.2% saved)

Details

analyze4.0ms (0.2%)

sample955.0ms (37.4%)

simplify6.0ms (0.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite85.0ms (3.3%)

simplify107.0ms (4.2%)

prune153.0ms (6%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite74.0ms (2.9%)

simplify7.0ms (0.3%)

prune22.0ms (0.9%)

localize6.0ms (0.2%)

series540.0ms (21.2%)

rewrite52.0ms (2.1%)

simplify71.0ms (2.8%)

prune83.0ms (3.2%)

localize5.0ms (0.2%)

series33.0ms (1.3%)

rewrite42.0ms (1.6%)

simplify7.0ms (0.3%)

prune28.0ms (1.1%)

regimes111.0ms (4.3%)

bsearch17.0ms (0.7%)

simplify3.0ms (0.1%)

end121.0ms (4.7%)

Profiling