Details

analyze1.5s (17.9%)

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 (64.3%)

Results

1.3s	1718×	body	1024	valid
1.3s	2097×	body	1024	invalid
780.0ms	4601×	body	128	valid
542.0ms	1193×	body	512	valid
444.0ms	2688×	body	128	invalid
442.0ms	1040×	body	512	invalid
274.0ms	691×	body	256	valid
154.0ms	498×	body	256	invalid
55.0ms	53×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify67.0ms (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

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

17.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.8b	(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 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)
✓	7.9b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series39.0ms (0.5%)

Counts

2 → 56

Calls

2 calls:

36.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite8.0ms (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:

6.0ms	(-.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)

simplify134.0ms (1.6%)

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

prune85.0ms (1%)

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
▶	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 2379 to 1035 computations (56.5% saved)

localize9.0ms (0.1%)

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)

series65.0ms (0.8%)

Counts

1 → 48

Calls

1 calls:

65.0ms

(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)

simplify82.0ms (1%)

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

prune33.0ms (0.4%)

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

0.0b

Counts

39 → 3

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	31.8b	(.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)))

Compiler

Compiled 1007 to 579 computations (42.5% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)))

series68.0ms (0.8%)

Counts

2 → 64

Calls

2 calls:

59.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
9.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 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)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

94 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2329
1	338	1837
2	1219	1800
3	3798	1800
4	4858	1800
5	4965	1800

prune74.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	76	4	80

Error

Counts

80 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
▶	31.0b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (cos.f64 (.f64 1/2 K)))) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	31.8b	(.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)))

Compiler

Compiled 2010 to 1402 computations (30.2% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (cos.f64 (.f64 1/2 K)))) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)) U)
✓	0.1b	(.f64 (sqrt.f64 J) (cos.f64 (.f64 1/2 K)))
✓	0.3b	(.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (cos.f64 (*.f64 1/2 K))))

series87.0ms (1%)

Counts

3 → 68

Calls

3 calls:

63.0ms

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

13.0ms

(*.f64 (sqrt.f64 J) (cos.f64 (*.f64 1/2 K)))

11.0ms

(*.f64 (sqrt.f64 J) (*.f64 (sqrt.f64 J) (cos.f64 (*.f64 1/2 K))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`

Counts

3 → 57

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 J) (*.f64 (sqrt.f64 J) (cos.f64 (*.f64 1/2 K))))

5.0ms

(*.f64 (sqrt.f64 J) (cos.f64 (*.f64 1/2 K)))

0.0ms

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

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-def_binary64`
442×	`cancel-sign-sub-inv_binary64`
420×	`sub-neg_binary64`
312×	`associate-+l+_binary64`
306×	`associate--l+_binary64`

Counts

125 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2751
1	429	2242
2	1558	2193
3	4573	2193
4	5122	2193

prune98.0ms (1.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	122	4	126

Error

Counts

126 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	31.0b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (cos.f64 (.f64 1/2 K)))) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	31.8b	(.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)))

Compiler

Compiled 3302 to 2101 computations (36.4% saved)

regimes312.0ms (3.7%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Counts

24 → 1

Compiler

Compiled 4938 to 3573 computations (27.6% 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

end93.0ms (1.1%)

Compiler: Compiled 123 to 90 computations (26.8% saved)

Details

analyze1.5s (17.9%)

sample5.5s (64.3%)

simplify67.0ms (0.8%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series39.0ms (0.5%)

rewrite8.0ms (0.1%)

simplify134.0ms (1.6%)

prune85.0ms (1%)

localize9.0ms (0.1%)

series65.0ms (0.8%)

rewrite1.0ms (0%)

simplify82.0ms (1%)

prune33.0ms (0.4%)

localize13.0ms (0.2%)

series68.0ms (0.8%)

rewrite5.0ms (0.1%)

simplify98.0ms (1.2%)

prune74.0ms (0.9%)

localize21.0ms (0.3%)

series87.0ms (1%)

rewrite15.0ms (0.2%)

simplify91.0ms (1.1%)

prune98.0ms (1.2%)

regimes312.0ms (3.7%)

simplify2.0ms (0%)

end93.0ms (1.1%)

Profiling