Details

analyze690.0ms (9.6%)

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)

sample124.0ms (1.7%)

Algorithm

1×

intervals

Results

28.0ms	47×	body	1024	valid
25.0ms	51×	body	1024	invalid
15.0ms	157×	body	128	valid
11.0ms	32×	body	512	valid
10.0ms	116×	body	128	invalid
7.0ms	30×	body	512	invalid
3.0ms	17×	body	256	valid
3.0ms	17×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify73.0ms (1%)

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 → 1

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	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

17.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	17.1b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 54 to 39 computations (27.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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)
6.6b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite114.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cbrt-cube_binary64`

Counts

3 → 129

Calls

3 calls:

20.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
19.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
9.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3543 to 880 computations (75.2% saved)

series88.0ms (1.2%)

Error

0.0b

Counts

3 → 28

Calls

3 calls:

54.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
13.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
5.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

Compiler

Compiled 1342 to 931 computations (30.6% saved)

simplify147.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
542×	`fma-neg_binary64`
374×	`distribute-rgt-in_binary64`
360×	`cancel-sign-sub-inv_binary64`
318×	`distribute-lft-in_binary64`

Counts

157 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2838
1	479	2479
2	1701	2399
3	4591	2399
4	5000	2399
5	4886	2399

prune54.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	3	90

Error

0.0b

Counts

90 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 (.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)) U)
	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	17.1b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))

Compiler

Compiled 1607 to 753 computations (53.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(sinh.f64 l)
0.0b	(.f64 (.f64 2 J) (sinh.f64 l))
0.0b	(fma.f64 (.f64 (.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)) U)

rewrite110.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

24×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`

Counts

3 → 107

Calls

3 calls:

17.0ms	(.f64 (.f64 2 J) (sinh.f64 l))
10.0ms	(sinh.f64 l)
9.0ms	(fma.f64 (.f64 (.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1613 to 981 computations (39.2% saved)

series106.0ms (1.5%)

Error

0.0b

Counts

3 → 28

Calls

3 calls:

69.0ms	(fma.f64 (.f64 (.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)) U)
18.0ms	(.f64 (.f64 2 J) (sinh.f64 l))
8.0ms	(sinh.f64 l)

Compiler

Compiled 1366 to 955 computations (30.1% saved)

simplify136.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
337×	`*-commutative_binary64`
301×	`fma-neg_binary64`
290×	`cancel-sign-sub-inv_binary64`
216×	`fma-def_binary64`

Counts

135 → 73

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	148	1799
1	328	1587
2	1000	1568
3	2613	1478
4	4669	1469
5	4948	1469
6	5003	1469

prune44.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Error

0.0b

Counts

76 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	29.4b	(fma.f64 (.f64 (.f64 2 J) (*.f64 (sqrt.f64 (sinh.f64 l)) (sqrt.f64 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	40.7b	(log1p.f64 (expm1.f64 (fma.f64 J (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))) U)))

Compiler

Compiled 1042 to 676 computations (35.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sinh.f64 l)
0.0b	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
0.1b	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
0.1b	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))

rewrite174.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
20×	`add-exp-log_binary64`
20×	`pow-prod-down_binary64`
19×	`add-cube-cbrt_binary64`

Counts

4 → 156

Calls

4 calls:

19.0ms	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
17.0ms	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
15.0ms	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))
10.0ms	(sinh.f64 l)

Compiler

Compiled 2744 to 1756 computations (36% saved)

series180.0ms (2.5%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

75.0ms	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
41.0ms	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
21.0ms	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))
6.0ms	(sinh.f64 l)

Compiler

Compiled 1918 to 1353 computations (29.5% saved)

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

601×	`times-frac_binary64`
433×	`fma-def_binary64`
297×	`fma-neg_binary64`
264×	`distribute-rgt-neg-in_binary64`
235×	`distribute-lft-neg-in_binary64`

Counts

193 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	3184
1	456	2817
2	1561	2791
3	4484	2789
4	4752	2789

prune48.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
▶	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	8.0b	(+.f64 (.f64 J (.f64 2 (cbrt.f64 (pow.f64 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))) 3)))) U)
	40.7b	(log1p.f64 (expm1.f64 (fma.f64 J (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))) U)))

Compiler

Compiled 1322 to 836 computations (36.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
0.1b	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite105.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
15×	`pow-prod-down_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 105

Calls

3 calls:

16.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
13.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
9.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 1550 to 1070 computations (31% saved)

series115.0ms (1.6%)

Error

Counts

3 → 39

Calls

3 calls:

58.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
27.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
21.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

Compiler

Compiled 1152 to 829 computations (28% saved)

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

509×	`prod-exp_binary64`
425×	`*-commutative_binary64`
300×	`cancel-sign-sub-inv_binary64`
283×	`unswap-sqr_binary64`
265×	`fma-neg_binary64`

Counts

144 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	1869
1	284	1690
2	1004	1680
3	2744	1671
4	4979	1671
5	4978	1671

prune45.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) U)
	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	8.0b	(+.f64 (.f64 J (.f64 2 (cbrt.f64 (pow.f64 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))) 3)))) U)
	40.7b	(log1p.f64 (expm1.f64 (fma.f64 J (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))) U)))

Compiler

Compiled 930 to 640 computations (31.2% saved)

regimes601.0ms (8.4%)

Accuracy

Total 0.1b remaining (68.8%)

Threshold costs 0.1b (68.8%)

Compiler

Compiled 11717 to 8614 computations (26.5% saved)

simplify3.0ms (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

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample3.9s (55%)

Algorithm

1×

intervals

Results

926.0ms	1675×	body	1024	valid
780.0ms	1844×	body	1024	invalid
424.0ms	4396×	body	128	valid
333.0ms	1176×	body	512	valid
311.0ms	3330×	body	128	invalid
262.0ms	987×	body	512	invalid
121.0ms	688×	body	256	valid
77.0ms	461×	body	256	invalid
51.0ms	65×	body	2048	valid

Compiler

Compiled 110 to 85 computations (22.7% saved)

Details

analyze690.0ms (9.6%)

sample124.0ms (1.7%)

simplify73.0ms (1%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite114.0ms (1.6%)

series88.0ms (1.2%)

simplify147.0ms (2.1%)

prune54.0ms (0.8%)

localize9.0ms (0.1%)

rewrite110.0ms (1.5%)

series106.0ms (1.5%)

simplify136.0ms (1.9%)

prune44.0ms (0.6%)

localize10.0ms (0.1%)

rewrite174.0ms (2.4%)

series180.0ms (2.5%)

simplify124.0ms (1.7%)

prune48.0ms (0.7%)

localize10.0ms (0.1%)

rewrite105.0ms (1.5%)

series115.0ms (1.6%)

simplify106.0ms (1.5%)

prune45.0ms (0.6%)

regimes601.0ms (8.4%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.9s (55%)

Profiling