Details

analyze1.5s (14.3%)

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)

sample5.3s (49.6%)

Results

1.3s	1719×	body	1024	valid
1.3s	2085×	body	1024	invalid
762.0ms	4541×	body	128	valid
584.0ms	1256×	body	512	valid
468.0ms	2706×	body	128	invalid
419.0ms	1019×	body	512	invalid
221.0ms	682×	body	256	valid
155.0ms	543×	body	256	invalid
63.0ms	58×	body	2048	valid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess44.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

672×	`fma-def_binary64`
472×	`associate-l_binary64`
454×	`associate-r_binary64`
251×	`unsub-neg_binary64`
219×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	154
1	113	154
2	244	154
3	610	154
4	1668	154
5	4483	154
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
464×	`fma-neg_binary64`
394×	`times-frac_binary64`
314×	`associate-l_binary64`
236×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	55	22
3	121	22
4	306	22
5	771	22
6	2013	22
7	3835	22

Stop Event

1×	node limit

Counts

1 → 2

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

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 (/.f64 K 2))
✓	0.0b	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
✓	0.0b	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
✓	8.3b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series48.0ms (0.4%)

Counts

4 → 92

Calls

24 calls:

4.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)	l	inf
3.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)	l	-inf
3.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)	K	0
3.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)	K	inf
3.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)	J	-inf

rewrite136.0ms (1.3%)

Algorithm

4×	egg-rewrite
3×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

458×	`log1p-expm1-u_binary64`
458×	`expm1-log1p-u_binary64`
239×	`unpow-prod-down_binary64`
217×	`log-prod_binary64`
151×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	295	36
2	4411	36
0	6	6
1	130	6
2	2131	6
0	6	6
0	11	14
1	236	14
2	3608	14
0	11	14
0	14	18
1	295	18
2	4408	18
0	14	18
0	5	6
1	107	6
2	1252	6

Stop Event

1×	node limit
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

4 → 58

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

632×	`associate-l_binary64`
447×	`associate-r_binary64`
444×	`cancel-sign-sub-inv_binary64`
368×	`associate--l+_binary64`
309×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2399
1	565	1992
2	1722	1933

Stop Event

1×	node limit

Counts

150 → 119

prune133.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	4	120

Error

Counts

120 → 4

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
	0.7b	(fma.f64 (.f64 2 l) (.f64 (cos.f64 (*.f64 1/2 K)) J) U)
	31.5b	(.f64 (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U)) (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (*.f64 K 1/2))) U)))
	8.1b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)

Compiler

Compiled 2869 to 1660 computations (42.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series112.0ms (1.1%)

Counts

4 → 108

Calls

30 calls:

9.0ms	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))	K	inf
7.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))	J	-inf
7.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))	J	0
6.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))	J	inf
6.0ms	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))	J	inf

rewrite63.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

304×	`expm1-udef_binary64`
304×	`log1p-udef_binary64`
172×	`add-sqr-sqrt_binary64`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	68
1	355	66
2	4239	66

Stop Event

1×	node limit

Counts

4 → 83

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
569×	`associate-l_binary64`
511×	`cancel-sign-sub-inv_binary64`
470×	`associate-r_binary64`
439×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	2763
1	313	2448
2	1117	2310

Stop Event

1×	node limit

Counts

191 → 120

prune144.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Error

Counts

124 → 4

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
▶	0.6b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	31.5b	(.f64 (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U)) (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (*.f64 K 1/2))) U)))
	8.1b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)

Compiler

Compiled 3274 to 2330 computations (28.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series56.0ms (0.5%)

Counts

3 → 84

Calls

21 calls:

5.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)	J	-inf
5.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)	U	0
5.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)	K	inf
5.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)	K	-inf
4.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)	K	0

rewrite52.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

312×	`prod-diff_binary64`
274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	324	43
2	3580	43

Stop Event

1×	node limit

Counts

3 → 61

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
602×	`associate-l_binary64`
513×	`associate-r_binary64`
352×	`cancel-sign-sub-inv_binary64`
299×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1930
1	297	1580
2	1031	1481

Stop Event

1×	node limit

Counts

145 → 95

prune139.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
✓	0.6b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	31.5b	(.f64 (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U)) (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (*.f64 K 1/2))) U)))
▶	8.1b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)

Compiler

Compiled 2605 to 1866 computations (28.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))
✓	0.1b	(.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
✓	0.1b	(.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
✓	39.1b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))

series170.0ms (1.6%)

Counts

4 → 96

Calls

24 calls:

14.0ms	(.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	l	-inf
13.0ms	(.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	K	-inf
13.0ms	(.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	K	inf
13.0ms	(.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	l	inf
11.0ms	(.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	l	-inf

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`log-prod_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
181×	`log-pow_binary64`
128×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	62
1	251	62
2	2977	62

Stop Event

1×	node limit

Counts

4 → 98

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

441×	`times-frac_binary64`
359×	`cancel-sign-sub-inv_binary64`
354×	`fma-def_binary64`
249×	`sub-neg_binary64`
222×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	3106
1	783	2956
2	3242	2951

Stop Event

1×	node limit

Counts

194 → 146

prune253.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	174	4	178

Error

Counts

178 → 4

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
✓	0.6b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	31.5b	(.f64 (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U)) (sqrt.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (*.f64 K 1/2))) U)))
✓	8.1b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)

Compiler

Compiled 6398 to 4293 computations (32.9% saved)

regimes2.0s (19.2%)

Accuracy

Total 0.0b remaining (13.6%)

Threshold costs 0.0b (13.6%)

Counts

186 → 1

Compiler

Compiled 43669 to 33446 computations (23.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	21	18

Stop Event

1×

saturated

end102.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 141 to 104 computations (26.2% saved)

Details

analyze1.5s (14.3%)

sample5.3s (49.6%)

preprocess44.0ms (0.4%)

simplify26.0ms (0.2%)

prune3.0ms (0%)

localize12.0ms (0.1%)

series48.0ms (0.4%)

rewrite136.0ms (1.3%)

simplify49.0ms (0.5%)

prune133.0ms (1.3%)

localize14.0ms (0.1%)

series112.0ms (1.1%)

rewrite63.0ms (0.6%)

simplify49.0ms (0.5%)

prune144.0ms (1.3%)

localize11.0ms (0.1%)

series56.0ms (0.5%)

rewrite52.0ms (0.5%)

simplify40.0ms (0.4%)

prune139.0ms (1.3%)

localize12.0ms (0.1%)

series170.0ms (1.6%)

rewrite56.0ms (0.5%)

simplify87.0ms (0.8%)

prune253.0ms (2.4%)

regimes2.0s (19.2%)

simplify3.0ms (0%)

end102.0ms (1%)

Profiling