Details

analyze638.0ms (6.5%)

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)

sample181.0ms (1.9%)

Algorithm

1×

intervals

Results

32.0ms	58×	body	1024	valid
24.0ms	57×	body	1024	invalid
13.0ms	146×	body	128	valid
11.0ms	34×	body	512	valid
10.0ms	111×	body	128	invalid
8.0ms	29×	body	512	invalid
3.0ms	16×	body	256	valid
2.0ms	13×	body	256	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify59.0ms (0.6%)

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

17.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.4b	(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 3 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)
✓	0.2b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	4.8b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series50.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

39.0ms	(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)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

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

simplify177.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
281×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

172 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3960
1	572	3266
2	2075	3044
3	4373	3044
4	4843	3044
5	4992	3044
6	4994	3044
7	4848	3044

prune133.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	3	170

Error

0.3b

Counts

170 → 3

Alt Table

Status	Error	Program
	17.4b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))
	0.9b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)
▶	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4545 to 1705 computations (62.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 l)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(.f64 J (.f64 2 (sinh.f64 l)))

series94.0ms (1%)

Counts

3 → 84

Calls

3 calls:

60.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
25.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite7.0ms (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 → 41

Calls

3 calls:

4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(sinh.f64 l)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify97.0ms (1%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
581×	`fma-neg_binary64`
432×	`*-commutative_binary64`
278×	`associate-+l+_binary64`
224×	`associate--l+_binary64`

Counts

125 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2596
1	465	2480
2	1467	2171
3	4147	2171
4	4936	2171
5	4957	2171

prune88.0ms (0.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Error

0.3b

Counts

91 → 7

Alt Table

Status	Error	Program
▶	0.6b	(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)
	17.4b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))
	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	11.0b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	0.9b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	37.2b	(fma.f64 (.f64 J (.f64 2 (exp.f64 (log.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2122 to 1286 computations (39.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
✓	0.5b	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
✓	0.5b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series306.0ms (3.1%)

Counts

4 → 72

Calls

4 calls:

192.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
39.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
38.0ms	(cbrt.f64 J)
37.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 110

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l))))
5.0ms	(.f64 (cbrt.f64 J) (.f64 2 (sinh.f64 l)))
4.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
1.0ms	(cbrt.f64 J)

simplify139.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-def_binary64`
377×	`unswap-sqr_binary64`
304×	`associate-r_binary64`
286×	`associate-l_binary64`
250×	`exp-prod_binary64`

Counts

182 → 166

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2350
1	367	2038
2	1519	1958
3	3400	1731
4	4552	1719
5	4959	1719
6	5000	1719
7	4898	1719

prune228.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	203	8	211

Error

0.3b

Counts

211 → 8

Alt Table

Status	Error	Program
✓	0.6b	(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)
	17.4b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))
▶	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	11.0b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	35.7b	(fma.f64 (.f64 (cbrt.f64 J) (.f64 (pow.f64 J 2/3) (*.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	0.9b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	37.2b	(fma.f64 (.f64 J (.f64 2 (exp.f64 (log.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 5186 to 2561 computations (50.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
✓	14.4b	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))

series2.1s (21.9%)

Counts

3 → 72

Calls

3 calls:

1.3s

(*.f64 (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))))

778.0ms

(cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l))))

55.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l))))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`associate-*r/_binary64`
29×	`pow1_binary64`
17×	`cbrt-div_binary64`
17×	`sinh-def_binary64`
16×	`pow1/3_binary64`

Counts

3 → 90

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l))))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))) (cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l)))))

3.0ms

(cbrt.f64 (*.f64 J (*.f64 2 (sinh.f64 l))))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
493×	`*-commutative_binary64`
301×	`fma-neg_binary64`
199×	`associate-l_binary64`
195×	`associate-r_binary64`

Counts

162 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	220	4102
1	519	3680
2	1473	3235
3	3725	2717
4	4895	2717
5	4952	2717

prune439.0ms (4.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	301	0	301
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	301	8	309

Error

0.3b

Counts

309 → 8

Alt Table

Status	Error	Program
✓	0.6b	(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)
	17.4b	(+.f64 U (.f64 J (.f64 (cos.f64 (*.f64 1/2 K)) (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))))
✓	0.7b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	11.0b	(fma.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (.f64 J (.f64 2 (sinh.f64 l)))) (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	35.7b	(fma.f64 (.f64 (cbrt.f64 J) (.f64 (pow.f64 J 2/3) (*.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	0.9b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	37.2b	(fma.f64 (.f64 J (.f64 2 (exp.f64 (log.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 10962 to 7055 computations (35.6% saved)

regimes635.0ms (6.5%)

Accuracy

Total 0.0b remaining (53.6%)

Threshold costs 0.0b (53.6%)

Counts

63 → 1

Compiler

Compiled 14603 to 10549 computations (27.8% 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

end2.0ms (0%)

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

sample4.1s (42.1%)

Algorithm

1×

intervals

Results

898.0ms	1625×	body	1024	valid
858.0ms	1991×	body	1024	invalid
420.0ms	4428×	body	128	valid
362.0ms	1193×	body	512	valid
315.0ms	3338×	body	128	invalid
278.0ms	940×	body	512	invalid
127.0ms	695×	body	256	valid
87.0ms	498×	body	256	invalid
55.0ms	59×	body	2048	valid

Compiler

Compiled 221 to 161 computations (27.1% saved)

Details

analyze638.0ms (6.5%)

sample181.0ms (1.9%)

simplify59.0ms (0.6%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series50.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify177.0ms (1.8%)

prune133.0ms (1.4%)

localize9.0ms (0.1%)

series94.0ms (1%)

rewrite7.0ms (0.1%)

simplify97.0ms (1%)

prune88.0ms (0.9%)

localize12.0ms (0.1%)

series306.0ms (3.1%)

rewrite30.0ms (0.3%)

simplify139.0ms (1.4%)

prune228.0ms (2.3%)

localize12.0ms (0.1%)

series2.1s (21.9%)

rewrite25.0ms (0.3%)

simplify131.0ms (1.3%)

prune439.0ms (4.5%)

regimes635.0ms (6.5%)

simplify2.0ms (0%)

end2.0ms (0%)

sample4.1s (42.1%)

Profiling