Details

analyze1.0ms (0%)

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)

sample813.0ms (37.5%)

Results

710.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify80.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
366×	`fma-neg_binary64`
277×	`*-commutative_binary64`
262×	`exp-prod_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	20	13
3	27	13
4	46	13
5	78	13
6	146	13
7	274	13
8	670	13
9	1896	13
10	2692	13
11	3535	13
12	4713	13
13	4865	13
14	4794	13

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

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)

localize6.0ms (0.3%)

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))))

series16.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 57

Calls

2 calls:

5.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
4.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify75.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
684×	`fma-def_binary64`
548×	`associate-l_binary64`
292×	`times-frac_binary64`
257×	`distribute-rgt-in_binary64`

Counts

73 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1210
1	248	1114
2	549	1101
3	1241	1099
4	4205	1099
5	4980	1099

prune63.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
▶	0.0b	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
	34.5b	(fma.f64 x (*.f64 x -1/2) (fma.f64 5/24 (pow.f64 x 4) 1))

Compiler

Compiled 1649 to 691 computations (58.1% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series41.0ms (1.9%)

Counts

2 → 24

Calls

2 calls:

21.0ms

(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

20.0ms

(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

rewrite136.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Rules

434×	`sqrt-prod_binary64`
376×	`times-frac_binary64`
354×	`add-sqr-sqrt_binary64`
292×	`*-un-lft-identity_binary64`
174×	`add-cube-cbrt_binary64`

Counts

2 → 345

Calls

2 calls:

53.0ms

(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

7.0ms

(/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

simplify345.0ms (15.9%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
480×	`associate-/r*_binary64`
438×	`associate-/r/_binary64`
290×	`associate-*l/_binary64`
286×	`associate-*r/_binary64`

Counts

369 → 332

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	16093
1	867	13574
2	2727	12897
3	4629	12897
4	5016	12897

prune358.0ms (16.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	493	0	493
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	493	3	496

Error

Counts

496 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.0b	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
▶	34.5b	(fma.f64 x (*.f64 x -1/2) (fma.f64 5/24 (pow.f64 x 4) 1))

Compiler

Compiled 15986 to 6668 computations (58.3% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 5/24 (pow.f64 x 4) 1)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 5/24 (pow.f64 x 4) 1)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 5/24 (pow.f64 x 4) 1)

simplify65.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1000×	`fma-def_binary64`
504×	`distribute-rgt-out_binary64`
362×	`distribute-rgt-in_binary64`
345×	`distribute-lft-in_binary64`
343×	`*-commutative_binary64`

Counts

22 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	214
1	27	196
2	60	196
3	155	196
4	604	196
5	2405	196
6	3070	196
7	4655	196
8	4944	196

prune12.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	15	3	18

Error

Counts

18 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
✓	0.0b	(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (/.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
✓	34.5b	(fma.f64 x (*.f64 x -1/2) (fma.f64 5/24 (pow.f64 x 4) 1))

Compiler

Compiled 261 to 198 computations (24.1% saved)

regimes67.0ms (3.1%)

Accuracy

Total 0.0b remaining (81.6%)

Threshold costs 0.0b (81.6%)

Counts

24 → 1

Compiler

Compiled 1020 to 759 computations (25.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	16	20
2	18	20
3	19	20
4	19	20

end60.0ms (2.8%)

Compiler: Compiled 69 to 49 computations (29% saved)

Details

analyze1.0ms (0%)

sample813.0ms (37.5%)

simplify80.0ms (3.7%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series16.0ms (0.7%)

rewrite12.0ms (0.5%)

simplify75.0ms (3.5%)

prune63.0ms (2.9%)

localize8.0ms (0.4%)

series41.0ms (1.9%)

rewrite136.0ms (6.3%)

simplify345.0ms (15.9%)

prune358.0ms (16.5%)

localize6.0ms (0.3%)

series3.0ms (0.2%)

rewrite1.0ms (0%)

simplify65.0ms (3%)

prune12.0ms (0.5%)

regimes67.0ms (3.1%)

simplify2.0ms (0.1%)

end60.0ms (2.8%)

Profiling