Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 20 to 15 computations (25% saved)

sample2.4s (52.8%)

Results

1.1s	1853×	body	1024	valid
694.0ms	4657×	body	128	valid
389.0ms	1108×	body	512	valid
148.0ms	605×	body	256	valid
31.0ms	33×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify73.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

8.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.9b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	2.7b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series45.0ms (1%)

Counts

2 → 56

Calls

2 calls:

42.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify138.0ms (3%)

Algorithm

1×	egg-herbie

Rules

447×	`sub-neg_binary64`
374×	`cancel-sign-sub-inv_binary64`
282×	`associate-+l+_binary64`
269×	`times-frac_binary64`
242×	`associate--l+_binary64`

Counts

97 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2515
1	456	2012
2	1638	1922
3	4312	1922
4	4861	1922
5	4993	1922
6	4843	1922

prune73.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	2	94

Error

0.0b

Counts

94 → 2

Alt Table

Status	Error	Program
	7.2b	(+.f64 U (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
▶	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2391 to 1045 computations (56.3% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series70.0ms (1.5%)

Counts

1 → 48

Calls

1 calls:

69.0ms

(fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

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 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify129.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
501×	`fma-def_binary64`
384×	`sub-neg_binary64`
373×	`associate-l_binary64`
303×	`associate-r_binary64`

Counts

58 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	126	1746
1	300	1690
2	954	1442
3	3386	1442
4	4872	1442
5	5039	1442

prune31.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Error

Counts

39 → 3

Alt Table

Status	Error	Program
	28.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	7.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)

Compiler

Compiled 1007 to 579 computations (42.5% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))
✓	1.7b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)

series80.0ms (1.7%)

Counts

3 → 76

Calls

3 calls:

66.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
10.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
4.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

3.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
0.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
0.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))

simplify112.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

765×	`fma-def_binary64`
366×	`cancel-sign-sub-inv_binary64`
352×	`sub-neg_binary64`
351×	`*-commutative_binary64`
334×	`distribute-rgt-neg-in_binary64`

Counts

116 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2609
1	351	2094
2	1262	2057
3	3893	2057
4	4829	2057
5	5024	2057

prune116.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
▶	28.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	7.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)

Compiler

Compiled 2232 to 1564 computations (29.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))
	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

series344.0ms (7.4%)

Counts

2 → 80

Calls

2 calls:

267.0ms

(sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))

76.0ms

(*.f64 (sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

6.0ms

(*.f64 (sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))

1.0ms

(sqrt.f64 (fma.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))

simplify140.0ms (3%)

Algorithm

1×	egg-herbie

Rules

436×	`associate-r_binary64`
333×	`associate-l_binary64`
307×	`fma-def_binary64`
279×	`unswap-sqr_binary64`
277×	`*-commutative_binary64`

Counts

148 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	376	6351
1	1029	6036
2	4141	5928
3	5203	5928

prune326.0ms (7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	258	0	258
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	258	3	261

Error

Counts

261 → 3

Alt Table

Status	Error	Program
✓	28.1b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	7.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)

Compiler

Compiled 14302 to 8154 computations (43% saved)

regimes346.0ms (7.5%)

Accuracy

Total 0.0b remaining (43.5%)

Threshold costs 0.0b (43.5%)

Counts

34 → 1

Compiler

Compiled 6969 to 5169 computations (25.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end88.0ms (1.9%)

Compiler: Compiled 99 to 73 computations (26.3% saved)

Details

analyze3.0ms (0.1%)

sample2.4s (52.8%)

simplify73.0ms (1.6%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series45.0ms (1%)

rewrite7.0ms (0.1%)

simplify138.0ms (3%)

prune73.0ms (1.6%)

localize9.0ms (0.2%)

series70.0ms (1.5%)

rewrite1.0ms (0%)

simplify129.0ms (2.8%)

prune31.0ms (0.7%)

localize13.0ms (0.3%)

series80.0ms (1.7%)

rewrite6.0ms (0.1%)

simplify112.0ms (2.4%)

prune116.0ms (2.5%)

localize11.0ms (0.2%)

series344.0ms (7.4%)

rewrite14.0ms (0.3%)

simplify140.0ms (3%)

prune326.0ms (7%)

regimes346.0ms (7.5%)

simplify2.0ms (0%)

end88.0ms (1.9%)

Profiling