Details

analyze1.5s (14.8%)

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 (53.1%)

Results

1.3s	1795×	body	1024	valid
1.3s	2045×	body	1024	invalid
755.0ms	4520×	body	128	valid
528.0ms	1180×	body	512	valid
427.0ms	2666×	body	128	invalid
420.0ms	1039×	body	512	invalid
213.0ms	706×	body	256	valid
143.0ms	527×	body	256	invalid
86.0ms	55×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify28.0ms (0.3%)

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

15.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.9b	(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)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
✓	0.2b	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
✓	7.0b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series48.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

34.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
11.0ms	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite105.0ms (1.1%)

Algorithm

6×	egg-rewrite
1×	batch-egg-rewrite

Rules

151×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`
140×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	295	30
2	4408	30
0	6	6
1	130	6
2	2131	6
0	6	6
0	14	18
1	295	18
2	4408	18
0	14	18
0	11	14
1	236	14
2	3608	14
0	11	14

Stop Event

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

Counts

3 → 29

Calls

3 calls:

105.0ms	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
105.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
105.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify42.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

594×	`associate-l_binary64`
445×	`associate-r_binary64`
378×	`cancel-sign-sub-inv_binary64`
357×	`associate--l+_binary64`
303×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2305
1	535	1898
2	1646	1845

Stop Event

1×	node limit

Counts

109 → 80

prune86.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	5	81

Error

0.2b

Counts

81 → 5

Alt Table

Status	Error	Program
	30.3b	(.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)))
	0.4b	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
	27.0b	(-.f64 (fma.f64 (exp.f64 l) J U) (/.f64 J (exp.f64 l)))
▶	0.4b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
	0.7b	(+.f64 (.f64 2 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) U)

Compiler

Compiled 2091 to 1249 computations (40.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series111.0ms (1.1%)

Counts

4 → 108

Calls

4 calls:

48.0ms	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
41.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
18.0ms	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))
3.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite66.0ms (0.7%)

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

Calls

4 calls:

64.0ms	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))
64.0ms	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
64.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
64.0ms	(*.f64 1/3 (pow.f64 l 3))

simplify46.0ms (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

prune143.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	119	6	125

Error

0.2b

Counts

125 → 6

Alt Table

Status	Error	Program
	24.5b	(/.f64 1 (/.f64 (-.f64 U (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) (-.f64 (.f64 U U) (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (*.f64 1/2 K)) J)) 2))))
▶	0.4b	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
	0.7b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))) 3)))
	24.6b	(+.f64 U (pow.f64 (sqrt.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) 2))
	27.0b	(-.f64 (fma.f64 (exp.f64 l) J U) (/.f64 J (exp.f64 l)))
✓	0.4b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))

Compiler

Compiled 3352 to 2392 computations (28.6% 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 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
✓	0.1b	(.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2)))
	0.1b	(*.f64 1/3 (pow.f64 l 3))

series72.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

51.0ms	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
18.0ms	(.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2)))
3.0ms	(fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

300×	`prod-diff_binary64`
265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	311	53
2	3561	53

Stop Event

1×	node limit

Counts

3 → 63

Calls

3 calls:

51.0ms	(fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))
51.0ms	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
51.0ms	(.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2)))

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
766×	`associate-l_binary64`
566×	`associate-r_binary64`
438×	`cancel-sign-sub-inv_binary64`
396×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	2354
1	319	1884
2	1195	1758

Stop Event

1×	node limit

Counts

147 → 101

prune139.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	114	6	120

Error

0.2b

Counts

120 → 6

Alt Table

Status	Error	Program
	24.5b	(/.f64 1 (/.f64 (-.f64 U (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) (-.f64 (.f64 U U) (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (*.f64 1/2 K)) J)) 2))))
✓	0.4b	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
▶	0.7b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))) 3)))
	24.6b	(+.f64 U (pow.f64 (sqrt.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) 2))
	27.0b	(-.f64 (fma.f64 (exp.f64 l) J U) (/.f64 J (exp.f64 l)))
✓	0.4b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))

Compiler

Compiled 2870 to 2075 computations (27.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))) 3))
	0.1b	(*.f64 1/3 (pow.f64 l 3))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))) 3)
✓	13.6b	(cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))

series1.0s (10.2%)

Counts

3 → 84

Calls

3 calls:

543.0ms

(pow.f64 (cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))))) 3)

420.0ms

(cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))))

52.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (pow.f64 (cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))))) 3))

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
238×	`prod-diff_binary64`
152×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	342	52
2	3635	52

Stop Event

1×	node limit

Counts

3 → 76

Calls

3 calls:

52.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (pow.f64 (cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))))) 3))

52.0ms

(pow.f64 (cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3))))) 3)

52.0ms

(cbrt.f64 (*.f64 J (fma.f64 2 l (*.f64 1/3 (pow.f64 l 3)))))

simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
322×	`cancel-sign-sub-inv_binary64`
182×	`associate--l+_binary64`
168×	`times-frac_binary64`
137×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	3115
1	517	2758
2	1640	2471

Stop Event

1×	node limit

Counts

160 → 139

prune171.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	152	6	158

Error

0.2b

Counts

158 → 6

Alt Table

Status	Error	Program
	24.5b	(/.f64 1 (/.f64 (-.f64 U (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) (-.f64 (.f64 U U) (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (*.f64 1/2 K)) J)) 2))))
✓	0.4b	(fma.f64 J (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cos.f64 (/.f64 K 2))) U)
✓	0.7b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (pow.f64 (cbrt.f64 (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))) 3)))
	24.6b	(+.f64 U (pow.f64 (sqrt.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J))) 2))
	27.0b	(-.f64 (fma.f64 (exp.f64 l) J U) (/.f64 J (exp.f64 l)))
✓	0.4b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))

Compiler

Compiled 4541 to 3440 computations (24.2% saved)

regimes749.0ms (7.5%)

Accuracy

Total 0.3b remaining (52.5%)

Threshold costs 0.3b (52.5%)

Counts

81 → 1

Compiler

Compiled 17042 to 12961 computations (23.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	16	22

Stop Event

1×

saturated

end119.0ms (1.2%)

Compiler: Compiled 184 to 139 computations (24.5% saved)

Details

analyze1.5s (14.8%)

sample5.3s (53.1%)

simplify28.0ms (0.3%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series48.0ms (0.5%)

rewrite105.0ms (1.1%)

simplify42.0ms (0.4%)

prune86.0ms (0.9%)

localize12.0ms (0.1%)

series111.0ms (1.1%)

rewrite66.0ms (0.7%)

simplify46.0ms (0.5%)

prune143.0ms (1.4%)

localize11.0ms (0.1%)

series72.0ms (0.7%)

rewrite53.0ms (0.5%)

simplify41.0ms (0.4%)

prune139.0ms (1.4%)

localize14.0ms (0.1%)

series1.0s (10.2%)

rewrite53.0ms (0.5%)

simplify53.0ms (0.5%)

prune171.0ms (1.7%)

regimes749.0ms (7.5%)

simplify3.0ms (0%)

end119.0ms (1.2%)

Profiling