Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

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

Compiler

Compiled 10 to 8 computations (20% saved)

sample767.0ms (42.9%)

Results

751.0ms	8253×	body	128	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 20 to 16 computations (20% saved)

preprocess18.0ms (1%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series35.0ms (2%)

Counts

3 → 12

Calls

9 calls:

12.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	inf
11.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	-inf
3.0ms	(sqrt.f64 (+.f64 x 1))	x	-inf
2.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))	x	-inf
2.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))	x	inf

rewrite48.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
424×	`prod-diff_binary64`
93×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	27
1	158	27
2	2207	27

Stop Event

1×	node limit

Counts

3 → 93

simplify29.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
361×	`distribute-rgt-neg-in_binary64`
306×	`distribute-lft-neg-in_binary64`
251×	`distribute-lft-out--_binary64`
235×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	158
1	91	142
2	232	130
3	812	109
4	2941	109

Stop Event

1×	node limit

Counts

105 → 114

prune79.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
	22.4b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
	21.5b	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 1545 to 1208 computations (21.8% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series45.0ms (2.5%)

Counts

2 → 8

Calls

6 calls:

12.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))	x	inf
11.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	-inf
11.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))	x	-inf
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	inf
1.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))	x	0

rewrite47.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`log1p-expm1-u_binary64`
853×	`expm1-log1p-u_binary64`
415×	`prod-diff_binary64`
85×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	180	24
2	2398	24

Stop Event

1×	node limit

Counts

2 → 51

simplify29.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

443×	`distribute-rgt-neg-in_binary64`
396×	`fma-def_binary64`
366×	`distribute-lft-neg-in_binary64`
291×	`cancel-sign-sub-inv_binary64`
287×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	111
1	86	103
2	241	90
3	824	74
4	2992	74

Stop Event

1×	node limit

Counts

59 → 65

prune91.0ms (5.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	137	4	141

Error

Counts

141 → 4

Alt Table

Status	Error	Program
	22.4b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶	21.5b	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 1922 to 1555 computations (19.1% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))

series3.0ms (0.2%)

Counts

1 → 3

Calls

3 calls:

1.0ms	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))	x	inf
1.0ms	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))	x	-inf
1.0ms	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))	x	0

rewrite44.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

878×	`log1p-expm1-u_binary64`
878×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
92×	`add-cbrt-cube_binary64`
90×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	204	11
2	2437	11

Stop Event

1×	node limit

Counts

1 → 50

simplify57.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

625×	`sqr-pow_binary64`
511×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
278×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	25	18
3	51	18
4	122	18
5	358	18
6	1370	18
7	2257	18
8	2421	18
9	2634	18
10	2854	18
11	3154	18
12	3554	18
13	4040	18
14	4599	18

Stop Event

1×	node limit

Counts

53 → 53

prune36.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	53	4	57

Error

Counts

57 → 4

Alt Table

Status	Error	Program
▶	22.4b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	21.5b	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 1110 to 693 computations (37.6% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series67.0ms (3.7%)

Counts

2 → 4

Calls

6 calls:

23.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	inf
14.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))	x	-inf
12.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	-inf
11.0ms	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))	x	inf
5.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))	x	0

rewrite53.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`prod-diff_binary64`
301×	`fma-def_binary64`
175×	`fma-neg_binary64`
166×	`log1p-udef_binary64`
165×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	230	26
2	2857	26

Stop Event

1×	node limit

Counts

2 → 81

simplify26.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

362×	`distribute-rgt-neg-in_binary64`
306×	`distribute-lft-neg-in_binary64`
287×	`*-commutative_binary64`
272×	`fma-def_binary64`
251×	`distribute-lft-out--_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	64
1	59	60
2	157	56
3	557	47
4	2224	47

Stop Event

1×	node limit

Counts

85 → 88

prune89.0ms (5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
✓	22.4b	(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓	21.5b	(-.f64 (.f64 1/2 x) (.f64 1/8 (pow.f64 x 2)))

Compiler

Compiled 2788 to 1979 computations (29% saved)

regimes129.0ms (7.2%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Counts

64 → 1

Compiler

Compiled 1524 to 1220 computations (19.9% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12

Stop Event

1×

saturated

end56.0ms (3.1%)

Stop Event

1×

done

Compiler

Compiled 63 to 49 computations (22.2% saved)

Details

analyze3.0ms (0.2%)

sample767.0ms (42.9%)

preprocess18.0ms (1%)

simplify6.0ms (0.4%)

prune1.0ms (0.1%)

localize6.0ms (0.3%)

series35.0ms (2%)

rewrite48.0ms (2.7%)

simplify29.0ms (1.6%)

prune79.0ms (4.4%)

localize7.0ms (0.4%)

series45.0ms (2.5%)

rewrite47.0ms (2.6%)

simplify29.0ms (1.6%)

prune91.0ms (5.1%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite44.0ms (2.4%)

simplify57.0ms (3.2%)

prune36.0ms (2%)

localize9.0ms (0.5%)

series67.0ms (3.7%)

rewrite53.0ms (3%)

simplify26.0ms (1.5%)

prune89.0ms (5%)

regimes129.0ms (7.2%)

simplify3.0ms (0.2%)

end56.0ms (3.1%)

Profiling