Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample711.0ms (49.7%)

Results

663.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify27.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
366×	`fma-def_binary64`
257×	`associate-/l*_binary64`
247×	`*-commutative_binary64`
242×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	21	13
3	28	13
4	47	13
5	87	13
6	184	13
7	419	13
8	1133	13
9	3111	13
10	4302	13

Stop Event

1×	node limit

Counts

1 → 1

prune3.0ms (0.2%)

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series14.0ms (1%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite70.0ms (4.9%)

Algorithm

4×	egg-rewrite
1×	batch-egg-rewrite

Rules

88×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`
85×	`expm1-log1p-u_binary64`
83×	`add-cbrt-cube_binary64`
83×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	176	18
2	2796	18
0	8	9
1	176	9
2	2796	9
0	8	9
0	6	6
1	129	6
2	2130	6
0	6	6

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 22

Calls

2 calls:

69.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
69.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

simplify25.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-neg_binary64`
391×	`distribute-rgt-neg-in_binary64`
370×	`fma-def_binary64`
346×	`distribute-lft-neg-in_binary64`
330×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	187
1	89	183
2	217	177
3	655	175
4	2761	175

Stop Event

1×	node limit

Counts

38 → 40

prune28.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
	29.6b	(fma.f64 x (*.f64 x -1/2) (fma.f64 5/24 (pow.f64 x 4) 1))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 521 to 367 computations (29.6% saved)

localize5.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (*.f64 2 (cosh.f64 x)))
✓	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

series42.0ms (2.9%)

Counts

2 → 24

Calls

2 calls:

21.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))
21.0ms	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

rewrite37.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

639×	`log1p-expm1-u_binary64`
639×	`expm1-log1p-u_binary64`
333×	`log-prod_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	174	12
2	1835	12

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

36.0ms	(/.f64 2 (*.f64 2 (cosh.f64 x)))
36.0ms	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))

simplify26.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

981×	`fma-neg_binary64`
391×	`distribute-rgt-neg-in_binary64`
343×	`distribute-lft-neg-in_binary64`
285×	`unswap-sqr_binary64`
230×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	312
1	61	312
2	145	304
3	463	300
4	2007	300

Stop Event

1×	node limit

Counts

88 → 53

prune48.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	66	2	68

Error

Counts

68 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
▶	0.0b	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))

Compiler

Compiled 891 to 607 computations (31.9% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
✓	0.0b	(pow.f64 (cosh.f64 x) 2)
✓	0.0b	(/.f64 1 (pow.f64 (cosh.f64 x) 2))

series72.0ms (5.1%)

Counts

3 → 36

Calls

3 calls:

41.0ms	(/.f64 1 (pow.f64 (cosh.f64 x) 2))
20.0ms	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
11.0ms	(pow.f64 (cosh.f64 x) 2)

rewrite52.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
302×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	168	18
2	1847	18

Stop Event

1×	node limit

Counts

3 → 95

Calls

3 calls:

51.0ms	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))
51.0ms	(pow.f64 (cosh.f64 x) 2)
51.0ms	(/.f64 1 (pow.f64 (cosh.f64 x) 2))

simplify37.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

554×	`fma-def_binary64`
505×	`associate-l_binary64`
428×	`associate-r_binary64`
309×	`unswap-sqr_binary64`
297×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	498
1	118	494
2	315	488
3	1023	486
4	4502	486

Stop Event

1×	node limit

Counts

131 → 120

prune74.0ms (5.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	120	2	122

Error

Counts

122 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (/.f64 2 (.f64 2 (cosh.f64 x)))) (sqrt.f64 (/.f64 2 (*.f64 2 (cosh.f64 x)))))
✓	0.0b	(sqrt.f64 (/.f64 1 (pow.f64 (cosh.f64 x) 2)))

Compiler

Compiled 1259 to 870 computations (30.9% saved)

regimes101.0ms (7%)

Accuracy

Total 0.0b remaining (74.6%)

Threshold costs 0.0b (74.6%)

Counts

49 → 1

Compiler

Compiled 1349 to 1099 computations (18.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14

Stop Event

1×

saturated

end46.0ms (3.2%)

Compiler: Compiled 44 to 38 computations (13.6% saved)

Details

analyze1.0ms (0.1%)

sample711.0ms (49.7%)

simplify27.0ms (1.9%)

prune3.0ms (0.2%)

localize5.0ms (0.4%)

series14.0ms (1%)

rewrite70.0ms (4.9%)

simplify25.0ms (1.8%)

prune28.0ms (2%)

localize5.0ms (0.4%)

series42.0ms (2.9%)

rewrite37.0ms (2.6%)

simplify26.0ms (1.8%)

prune48.0ms (3.4%)

localize5.0ms (0.4%)

series72.0ms (5.1%)

rewrite52.0ms (3.6%)

simplify37.0ms (2.6%)

prune74.0ms (5.2%)

regimes101.0ms (7%)

simplify2.0ms (0.1%)

end46.0ms (3.2%)

Profiling