Details

analyze1.2s (16.2%)

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)

sample230.0ms (3%)

Algorithm

1×

intervals

Results

58.0ms	70×	body	1024	invalid
47.0ms	47×	body	1024	valid
28.0ms	47×	body	512	valid
21.0ms	137×	body	128	valid
16.0ms	107×	body	128	invalid
12.0ms	26×	body	512	invalid
8.0ms	24×	body	256	valid
5.0ms	15×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify91.0ms (1.2%)

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

prune6.0ms (0.1%)

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

20.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.1b	(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)

localize21.0ms (0.3%)

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)
✓	6.5b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite12.0ms (0.2%)

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:

8.0ms	(-.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)

series191.0ms (2.5%)

Counts

2 → 56

Calls

2 calls:

185.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
5.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify216.0ms (2.9%)

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 → 178

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

prune69.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Error

0.1b

Counts

179 → 2

Alt Table

Status	Error	Program
	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2379 to 1035 computations (56.5% saved)

localize9.0ms (0.1%)

Local error

Found 2 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)

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

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

series140.0ms (1.9%)

Counts

2 → 60

Calls

2 calls:

133.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
7.0ms	(sinh.f64 l)

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-def_binary64`
504×	`associate-l_binary64`
423×	`associate-r_binary64`
398×	`sub-neg_binary64`
268×	`associate-+l+_binary64`

Counts

80 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	2060
1	368	1654
2	1186	1603
3	4459	1603
4	5000	1603
5	4952	1603

prune54.0ms (0.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	5	137
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	10.6b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	32.6b	(fma.f64 (.f64 J (.f64 2 (exp.f64 (log.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	30.7b	(.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)))
	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)))

Compiler

Compiled 1563 to 949 computations (39.3% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	0.2b	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite7.0ms (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:

6.0ms	(.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)

series143.0ms (1.9%)

Counts

2 → 64

Calls

2 calls:

113.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
29.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

simplify110.0ms (1.5%)

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 → 163

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

prune76.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
▶	10.6b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	17.2b	(fma.f64 (.f64 (.f64 J (sqrt.f64 (cos.f64 (.f64 1/2 K)))) (sqrt.f64 (cos.f64 (.f64 1/2 K)))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	42.0b	(.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 2050 to 1436 computations (30% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 l)
✓	0.1b	(.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	40.2b	(cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sinh-def_binary64`
22×	`pow1_binary64`
11×	`add-cbrt-cube_binary64`
10×	`associate-*l/_binary64`
10×	`frac-times_binary64`

Counts

3 → 67

Calls

3 calls:

5.0ms

(*.f64 (*.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))

4.0ms

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

0.0ms

(fma.f64 (*.f64 J (*.f64 2 (cbrt.f64 (*.f64 (*.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

series164.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

132.0ms

(fma.f64 (*.f64 J (*.f64 2 (cbrt.f64 (*.f64 (*.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

24.0ms

(*.f64 (*.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))

8.0ms

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

simplify110.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
671×	`fma-neg_binary64`
289×	`associate-+l+_binary64`
245×	`cancel-sign-sub-inv_binary64`
237×	`associate--l+_binary64`

Counts

139 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3324
1	482	2449
2	1518	2240
3	4578	2240
4	5134	2240

prune135.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	289	5	294

Error

Counts

294 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
✓	10.6b	(fma.f64 (.f64 J (.f64 2 (cbrt.f64 (.f64 (.f64 (sinh.f64 l) (sinh.f64 l)) (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	17.2b	(fma.f64 (.f64 (.f64 J (sqrt.f64 (cos.f64 (.f64 1/2 K)))) (sqrt.f64 (cos.f64 (.f64 1/2 K)))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 l 2)) U)
	42.0b	(.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 3818 to 2034 computations (46.7% saved)

regimes388.0ms (5.1%)

Accuracy

Total 0.1b remaining (70.1%)

Threshold costs 0.1b (70.1%)

Compiler

Compiled 8322 to 5888 computations (29.2% 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)

sample4.0s (53%)

Algorithm

1×

intervals

Results

904.0ms	1655×	body	1024	valid
831.0ms	2004×	body	1024	invalid
389.0ms	4378×	body	128	valid
360.0ms	1237×	body	512	valid
294.0ms	974×	body	512	invalid
290.0ms	3412×	body	128	invalid
120.0ms	672×	body	256	valid
81.0ms	482×	body	256	invalid
48.0ms	58×	body	2048	valid

Compiler

Compiled 151 to 114 computations (24.5% saved)

Details

analyze1.2s (16.2%)

sample230.0ms (3%)

simplify91.0ms (1.2%)

prune6.0ms (0.1%)

localize21.0ms (0.3%)

rewrite12.0ms (0.2%)

series191.0ms (2.5%)

simplify216.0ms (2.9%)

prune69.0ms (0.9%)

localize9.0ms (0.1%)

rewrite2.0ms (0%)

series140.0ms (1.9%)

simplify108.0ms (1.4%)

prune54.0ms (0.7%)

localize12.0ms (0.2%)

rewrite7.0ms (0.1%)

series143.0ms (1.9%)

simplify110.0ms (1.5%)

prune76.0ms (1%)

localize17.0ms (0.2%)

rewrite13.0ms (0.2%)

series164.0ms (2.2%)

simplify110.0ms (1.5%)

prune135.0ms (1.8%)

regimes388.0ms (5.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.0s (53%)

Profiling