Details

analyze1.5s (16.8%)

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)

sample5.6s (61.4%)

Results

1.4s	2030×	body	1024	invalid
1.3s	1612×	body	1024	valid
857.0ms	4667×	body	128	valid
579.0ms	1203×	body	512	valid
452.0ms	2591×	body	128	invalid
449.0ms	1025×	body	512	invalid
218.0ms	711×	body	256	valid
168.0ms	526×	body	256	invalid
80.0ms	63×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify68.0ms (0.7%)

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

prune4.0ms (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

15.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.9b	(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 (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 l)
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	4.7b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

36.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(*.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)

rewrite22.0ms (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))))
6.0ms	(-.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)

simplify200.0ms (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

prune139.0ms (1.5%)

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
▶	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4881 to 1856 computations (62% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series92.0ms (1%)

Counts

2 → 72

Calls

2 calls:

63.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
29.0ms	(.f64 J (.f64 2 (sinh.f64 l)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

2 → 31

Calls

2 calls:

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)

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Rules

741×	`associate-r_binary64`
645×	`fma-def_binary64`
610×	`fma-neg_binary64`
259×	`associate-+l+_binary64`
224×	`associate--l+_binary64`

Counts

103 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2370
1	434	2263
2	1382	1966
3	4510	1966
4	5048	1966

prune50.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	69	2	71

Error

0.0b

Counts

71 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	0.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)

Compiler

Compiled 1531 to 894 computations (41.6% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))
✓	0.0b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series69.0ms (0.8%)

Counts

3 → 76

Calls

3 calls:

55.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
11.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
3.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))

rewrite7.0ms (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))

simplify107.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

116 → 98

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

prune86.0ms (1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	97	3	100

Error

0.0b

Counts

100 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
▶	45.4b	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)

Compiler

Compiled 2386 to 1681 computations (29.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series113.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

68.0ms	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)
20.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))
16.0ms	(.f64 (pow.f64 l 3) (cos.f64 (.f64 1/2 K)))
9.0ms	(.f64 l (cos.f64 (.f64 1/2 K)))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
23×	`add-exp-log_binary64`
21×	`associate-l_binary64`
15×	`add-cbrt-cube_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 96

Calls

4 calls:

7.0ms	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)
5.0ms	(.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))
5.0ms	(.f64 (pow.f64 l 3) (cos.f64 (.f64 1/2 K)))
3.0ms	(.f64 l (cos.f64 (.f64 1/2 K)))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
494×	`fma-neg_binary64`
434×	`associate-r_binary64`
394×	`associate-l_binary64`
257×	`distribute-rgt-neg-in_binary64`

Counts

132 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	3205
1	587	2586
2	2550	2567
3	4635	2565
4	4948	2565

prune147.0ms (1.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	45.4b	(.f64 (+.f64 (.f64 2 (.f64 l (cos.f64 (.f64 1/2 K)))) (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (*.f64 1/2 K))))) J)
	53.9b	(.f64 (.f64 (.f64 (cos.f64 (.f64 K 1/2)) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3)))) (sqrt.f64 J)) (sqrt.f64 J))

Compiler

Compiled 5566 to 4214 computations (24.3% saved)

regimes459.0ms (5.1%)

Accuracy

Total 0.4b remaining (90.4%)

Threshold costs 0.4b (90.4%)

Counts

44 → 1

Compiler

Compiled 8499 to 6373 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	30
1	21	30
2	21	30

end89.0ms (1%)

Compiler: Compiled 134 to 102 computations (23.9% saved)

Details

analyze1.5s (16.8%)

sample5.6s (61.4%)

simplify68.0ms (0.7%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series49.0ms (0.5%)

rewrite22.0ms (0.2%)

simplify200.0ms (2.2%)

prune139.0ms (1.5%)

localize9.0ms (0.1%)

series92.0ms (1%)

rewrite6.0ms (0.1%)

simplify86.0ms (1%)

prune50.0ms (0.6%)

localize12.0ms (0.1%)

series69.0ms (0.8%)

rewrite7.0ms (0.1%)

simplify107.0ms (1.2%)

prune86.0ms (1%)

localize12.0ms (0.1%)

series113.0ms (1.2%)

rewrite25.0ms (0.3%)

simplify115.0ms (1.3%)

prune147.0ms (1.6%)

regimes459.0ms (5.1%)

simplify2.0ms (0%)

end89.0ms (1%)

Profiling