Details

analyze654.0ms (8.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample191.0ms (2.4%)

Algorithm

1×

intervals

Results

29.0ms	52×	body	1024	valid
19.0ms	46×	body	1024	invalid
15.0ms	55×	body	512	invalid
13.0ms	45×	body	512	valid
12.0ms	141×	body	128	valid
10.0ms	119×	body	128	invalid
3.0ms	4×	body	2048	valid
2.0ms	14×	body	256	valid
2.0ms	9×	body	256	invalid

Compiler

Compiled 43 to 33 computations (23.3% 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

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

19.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.0b	(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	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	4.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series13.0ms (0.2%)

Counts

2 → 32

Calls

2 calls:

11.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 82

Calls

2 calls:

8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify129.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-def_binary64`
405×	`fma-neg_binary64`
321×	`associate-/r*_binary64`
267×	`exp-prod_binary64`
250×	`neg-mul-1_binary64`

Counts

114 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2026
1	303	1740
2	954	1535
3	2479	1535
4	4342	1532
5	4908	1532
6	4751	1532

prune97.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Error

0.1b

Counts

125 → 2

Alt Table

Status	Error	Program
	19.0b	(fma.f64 (+.f64 (.f64 (fma.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 l)) (neg.f64 (.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l))))))) J) (.f64 (fma.f64 (neg.f64 (cbrt.f64 (exp.f64 (neg.f64 l)))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l)))) (.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l)))))) J)) (cos.f64 (/.f64 K 2)) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Status

Error

Program

19.0b

(fma.f64 (+.f64 (*.f64 (fma.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 l)) (neg.f64 (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l))))))) J) (*.f64 (fma.f64 (neg.f64 (cbrt.f64 (exp.f64 (neg.f64 l)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l)))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (*.f64 (cbrt.f64 (exp.f64 (neg.f64 l))) (cbrt.f64 (exp.f64 (neg.f64 l)))))) J)) (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 3478 to 1178 computations (66.1% 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)))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series94.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

65.0ms	(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 (1.1%)

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

prune65.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Error

0.0b

Counts

71 → 6

Alt Table

Status	Error	Program
	25.9b	(fma.f64 (.f64 (sqrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (sqrt.f64 (.f64 J (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	10.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (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)))
▶	0.1b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1769 to 1064 computations (39.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)))
✓	0.0b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series108.0ms (1.3%)

Counts

4 → 64

Calls

4 calls:

89.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))
10.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
4.0ms	(+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)))
3.0ms	(*.f64 1/60 (pow.f64 l 5))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`

Counts

4 → 86

Calls

4 calls:

7.0ms	(.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))
5.0ms	(*.f64 1/60 (pow.f64 l 5))
4.0ms	(+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)))
3.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

746×	`distribute-rgt-in_binary64`
491×	`cancel-sign-sub-inv_binary64`
365×	`associate-r_binary64`
352×	`associate-l_binary64`
212×	`fma-def_binary64`

Counts

150 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	4004
1	642	3228
2	2451	3178
3	5056	3178

prune279.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	158	7	165

Error

Counts

165 → 7

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
	0.4b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	10.9b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (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)))
✓	0.1b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
	21.7b	(+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) 3)) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
▶	0.1b	(+.f64 (.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))) U)

Compiler

Compiled 5622 to 4200 computations (25.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2)))
	0.0b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))))
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (.f64 l 2))))

series131.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

93.0ms

(*.f64 J (*.f64 (cos.f64 (*.f64 1/2 K)) (+.f64 (*.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))))

39.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (+.f64 (*.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 50

Calls

2 calls:

7.0ms

(*.f64 J (*.f64 (cos.f64 (*.f64 1/2 K)) (+.f64 (*.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))))

6.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (+.f64 (*.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))

simplify139.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

634×	`associate--l+_binary64`
591×	`cancel-sign-sub-inv_binary64`
349×	`associate-r_binary64`
322×	`associate-l_binary64`
254×	`fma-def_binary64`

Counts

110 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	4467
1	623	3569
2	2552	3492
3	4773	3492
4	4994	3492
5	4963	3492

prune299.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	184	5	189

Error

Counts

189 → 5

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))) (cbrt.f64 (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
	0.2b	(+.f64 (.f64 J (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 K))) (cbrt.f64 (cos.f64 (.f64 1/2 K)))) (.f64 (cbrt.f64 (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))))) U)
✓	0.1b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)))) U)
	32.5b	(+.f64 (.f64 (sqrt.f64 J) (.f64 (.f64 (fma.f64 2 l (fma.f64 1/60 (pow.f64 l 5) (.f64 1/3 (pow.f64 l 3)))) (cos.f64 (*.f64 K 1/2))) (sqrt.f64 J))) U)
✓	0.1b	(+.f64 (.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (+.f64 (.f64 1/60 (pow.f64 l 5)) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2))))) U)

Compiler

Compiled 6418 to 4830 computations (24.7% saved)

regimes999.0ms (12.5%)

Accuracy

Total 0.0b remaining (11.3%)

Threshold costs 0.0b (11.3%)

Counts

90 → 1

Compiler

Compiled 23524 to 17318 computations (26.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	36	52
2	36	52

end1.0ms (0%)

Compiler: Compiled 38 to 30 computations (21.1% saved)

sample4.4s (55.1%)

Algorithm

1×

intervals

Results

1.0s	1658×	body	1024	valid
901.0ms	1958×	body	1024	invalid
466.0ms	4459×	body	128	valid
340.0ms	1156×	body	512	valid
314.0ms	3452×	body	128	invalid
273.0ms	1040×	body	512	invalid
140.0ms	681×	body	256	valid
87.0ms	502×	body	256	invalid
38.0ms	46×	body	2048	valid

Compiler

Compiled 230 to 179 computations (22.2% saved)

Details

analyze654.0ms (8.2%)

sample191.0ms (2.4%)

simplify67.0ms (0.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series13.0ms (0.2%)

rewrite18.0ms (0.2%)

simplify129.0ms (1.6%)

prune97.0ms (1.2%)

localize9.0ms (0.1%)

series94.0ms (1.2%)

rewrite6.0ms (0.1%)

simplify86.0ms (1.1%)

prune65.0ms (0.8%)

localize17.0ms (0.2%)

series108.0ms (1.3%)

rewrite24.0ms (0.3%)

simplify103.0ms (1.3%)

prune279.0ms (3.5%)

localize18.0ms (0.2%)

series131.0ms (1.6%)

rewrite18.0ms (0.2%)

simplify139.0ms (1.7%)

prune299.0ms (3.7%)

regimes999.0ms (12.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.4s (55.1%)

Profiling