Details

analyze1.6s (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample5.5s (61.3%)

Results

1.4s	1801×	body	1024	valid
1.3s	2050×	body	1024	invalid
806.0ms	4501×	body	128	valid
585.0ms	1214×	body	512	valid
453.0ms	2602×	body	128	invalid
436.0ms	1022×	body	512	invalid
228.0ms	681×	body	256	valid
168.0ms	534×	body	256	invalid
67.0ms	59×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify73.0ms (0.8%)

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%)

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

18.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.1b	(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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 l)
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	5.9b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series48.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

35.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(exp.f64 l)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 105

Calls

4 calls:

7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(exp.f64 l)
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify195.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
339×	`cancel-sign-sub-inv_binary64`
337×	`fma-neg_binary64`
285×	`associate-r_binary64`
283×	`associate-l_binary64`

Counts

189 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	4064
1	608	3368
2	2159	3145
3	4420	3145
4	4807	3145
5	4992	3145
6	5000	3145
7	4858	3145

prune129.0ms (1.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	190	2	192

Error

0.0b

Counts

192 → 2

Alt Table

Status	Error	Program
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4881 to 1856 computations (62% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 (/.f64 K 2))
✓	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series88.0ms (1%)

Counts

3 → 84

Calls

3 calls:

60.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
27.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
2.0ms	(cos.f64 (/.f64 K 2))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 40

Calls

3 calls:

7.0ms	(cos.f64 (/.f64 K 2))
4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify102.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

706×	`fma-def_binary64`
638×	`fma-neg_binary64`
413×	`*-commutative_binary64`
266×	`associate-+l+_binary64`
235×	`associate--l+_binary64`

Counts

124 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2566
1	471	2444
2	1471	2145
3	4173	2145
4	4996	2145
5	5018	2145

prune72.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	83	6	89

Error

0.0b

Counts

89 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
	37.6b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2031 to 1239 computations (39% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3))
✓	0.4b	(pow.f64 (cos.f64 (/.f64 K 2)) 3)

series77.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

68.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
6.0ms	(pow.f64 (cos.f64 (/.f64 K 2)) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

3 → 58

Calls

3 calls:

2.0ms	(pow.f64 (cos.f64 (/.f64 K 2)) 3)
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
617×	`fma-def_binary64`
332×	`*-commutative_binary64`
252×	`associate-+l+_binary64`
246×	`associate--l+_binary64`

Counts

130 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2572
1	437	2451
2	1374	2181
3	3945	2181
4	4874	2181
5	4966	2181

prune151.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 2 (sinh.f64 l)) (cbrt.f64 J))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3441 to 2281 computations (33.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.1b	(exp.f64 (cos.f64 (/.f64 K 2)))
✓	0.3b	(log.f64 (exp.f64 (cos.f64 (/.f64 K 2))))

series64.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

60.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
3.0ms	(exp.f64 (cos.f64 (/.f64 K 2)))
2.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 K 2))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`exp-prod_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

3 → 40

Calls

3 calls:

2.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 K 2))))
2.0ms	(exp.f64 (cos.f64 (/.f64 K 2)))
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)

simplify119.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
465×	`sub-neg_binary64`
452×	`associate-l_binary64`
361×	`associate-r_binary64`
291×	`distribute-rgt-neg-in_binary64`

Counts

112 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2332
1	407	2237
2	1214	1979
3	4124	1979
4	4983	1979
5	4999	1979
6	4953	1979

prune143.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	138	6	144

Error

0.0b

Counts

144 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (log.f64 (exp.f64 (cos.f64 (/.f64 K 2)))) U)
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 2 (sinh.f64 l)) (cbrt.f64 J))) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 K 2)) 3)) U)
	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U))) (cbrt.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3025 to 1949 computations (35.6% saved)

regimes379.0ms (4.2%)

Accuracy

Total 0.0b remaining (49.9%)

Threshold costs 0.0b (49.9%)

Counts

39 → 1

Compiler

Compiled 8139 to 5959 computations (26.8% 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

end111.0ms (1.2%)

Compiler: Compiled 171 to 125 computations (26.9% saved)

Details

analyze1.6s (17.2%)

sample5.5s (61.3%)

simplify73.0ms (0.8%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series48.0ms (0.5%)

rewrite21.0ms (0.2%)

simplify195.0ms (2.2%)

prune129.0ms (1.4%)

localize9.0ms (0.1%)

series88.0ms (1%)

rewrite13.0ms (0.1%)

simplify102.0ms (1.1%)

prune72.0ms (0.8%)

localize11.0ms (0.1%)

series77.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify100.0ms (1.1%)

prune151.0ms (1.7%)

localize11.0ms (0.1%)

series64.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify119.0ms (1.3%)

prune143.0ms (1.6%)

regimes379.0ms (4.2%)

simplify2.0ms (0%)

end111.0ms (1.2%)

Profiling