Details

analyze560.0ms (8.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
6.2%	79.6%	14.2%	8
7.8%	75.7%	16.5%	9
11.7%	68.6%	19.6%	10
20.3%	49.3%	30.4%	11
22.2%	44.4%	33.4%	12
25.2%	37.3%	37.5%	13
28%	27.3%	44.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.4s (21.4%)

Results

814.0ms	8256×	body	128	valid
471.0ms	4492×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1052×	`fma-def_binary64`
423×	`fabs-mul_binary64`
333×	`distribute-rgt-in_binary64`
319×	`div-sub_binary64`
307×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	19	12
2	45	12
3	105	12
4	219	12
5	360	12
6	617	12
7	1698	12
8	2037	12
9	2629	12
10	3437	12
11	3909	12
12	4557	12
13	5039	12

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

8.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
✓	7.5b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series80.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

53.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
28.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

rewrite60.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
177×	`pow1/3_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`
162×	`log-div_binary64`

Counts

2 → 86

Calls

2 calls:

58.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
58.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	176	21
2	2548	21
3	5023	21
0	0	0
1	0	0

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
478×	`associate-/r/_binary64`
476×	`distribute-rgt-in_binary64`
460×	`associate-/r*_binary64`
347×	`distribute-rgt-out_binary64`

Counts

146 → 110

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	62	1308
1	176	1196
2	423	1196
3	995	1182
4	2408	1174
5	3792	1171
6	4311	1171
7	5046	1171

prune80.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	103	8	111

Error

0.0b

Counts

111 → 8

Alt Table

Status	Error	Program
	9.0b	(/.f64 (/.f64 (/.f64 (*.f64 (cosh.f64 x) y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
	8.3b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
	10.3b	(.f64 (/.f64 y z) (+.f64 (fma.f64 x 1/2 (.f64 1/24 (pow.f64 x 3))) (/.f64 1 x)))
	8.1b	(.f64 (/.f64 y x) (.f64 (cosh.f64 x) (/.f64 1 z)))
	7.9b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
✓	8.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	8.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x))) 2) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
▶	7.0b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

Compiler

Compiled 1790 to 732 computations (59.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
✓	0.0b	(/.f64 y (exp.f64 x))
✓	0.0b	(*.f64 (exp.f64 x) y)
✓	6.6b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

series105.0ms (1.6%)

Counts

4 → 64

Calls

4 calls:

65.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))
21.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
13.0ms	(/.f64 y (exp.f64 x))
5.0ms	(*.f64 (exp.f64 x) y)

rewrite83.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary64`
265×	`log1p-udef_binary64`
235×	`fma-neg_binary64`
146×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`

Counts

4 → 136

Calls

4 calls:

80.0ms	(+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (*.f64 1/2 (/.f64 y (exp.f64 x))))
80.0ms	(/.f64 y (exp.f64 x))
80.0ms	(*.f64 (exp.f64 x) y)
80.0ms	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	52
1	286	48
2	4016	48
3	5022	48
0	0	0
1	0	0

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-neg_binary64`
498×	`times-frac_binary64`
379×	`*-commutative_binary64`
262×	`associate-/l*_binary64`
262×	`cancel-sign-sub-inv_binary64`

Counts

200 → 168

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	1217
1	204	1117
2	527	1109
3	1603	1098
4	3296	1098
5	4834	1098
6	4980	1098

prune122.0ms (1.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	167	9	176

Error

Counts

176 → 9

Alt Table

Status	Error	Program
	9.0b	(/.f64 (/.f64 (/.f64 (*.f64 (cosh.f64 x) y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x)) z)
	8.3b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
	8.1b	(.f64 (/.f64 y x) (.f64 (cosh.f64 x) (/.f64 1 z)))
▶	7.9b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	36.2b	(.f64 (/.f64 1/2 (sqrt.f64 (.f64 x z))) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) (sqrt.f64 (*.f64 x z))))
	8.7b	(*.f64 (/.f64 1/2 x) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) z))
✓	8.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	8.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x))) 2) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
✓	7.0b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

Compiler

Compiled 4010 to 1670 computations (58.4% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
✓	0.5b	(/.f64 1 (*.f64 z (/.f64 x y)))
✓	7.0b	(*.f64 z (/.f64 x y))

series82.0ms (1.3%)

Counts

3 → 108

Calls

3 calls:

53.0ms	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
16.0ms	(/.f64 1 (*.f64 z (/.f64 x y)))
12.0ms	(*.f64 z (/.f64 x y))

rewrite66.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

564×	`log-prod_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
177×	`pow3_binary64`
170×	`log-pow_binary64`

Counts

3 → 109

Calls

3 calls:

64.0ms	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
64.0ms	(/.f64 1 (*.f64 z (/.f64 x y)))
64.0ms	(*.f64 z (/.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	212	26
2	2716	26
3	5015	26
0	0	0
1	0	0

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
446×	`distribute-rgt-in_binary64`
409×	`associate-/r/_binary64`
394×	`associate-/r*_binary64`
330×	`*-commutative_binary64`

Counts

217 → 121

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	49	1341
1	141	1273
2	331	1273
3	711	1269
4	1850	1257
5	3494	1254
6	4079	1254
7	4881	1254
8	5034	1254

prune142.0ms (2.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	121	9	130

Error

Counts

130 → 9

Alt Table

Status	Error	Program
	8.1b	(.f64 (/.f64 y x) (.f64 (cosh.f64 x) (/.f64 1 z)))
▶	7.5b	(/.f64 (/.f64 (cosh.f64 x) z) (/.f64 x y))
✓	7.9b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	36.2b	(.f64 (/.f64 1/2 (sqrt.f64 (.f64 x z))) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) (sqrt.f64 (*.f64 x z))))
	8.7b	(*.f64 (/.f64 1/2 x) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) z))
✓	8.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	8.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x))) 2) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
	8.3b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
✓	7.0b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

Compiler

Compiled 1879 to 761 computations (59.5% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (cosh.f64 x) z)
✓	7.1b	(/.f64 (/.f64 (cosh.f64 x) z) (/.f64 x y))

series172.0ms (2.7%)

Counts

2 → 60

Calls

2 calls:

122.0ms	(/.f64 (/.f64 (cosh.f64 x) z) (/.f64 x y))
50.0ms	(/.f64 (cosh.f64 x) z)

rewrite102.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
209×	`log-div_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
156×	`log-pow_binary64`

Counts

2 → 90

Calls

2 calls:

98.0ms	(/.f64 (cosh.f64 x) z)
98.0ms	(/.f64 (/.f64 (cosh.f64 x) z) (/.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	182	18
2	2751	18
3	5115	18
0	0	0
1	0	0

simplify122.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

555×	`associate-l_binary64`
543×	`associate-r_binary64`
493×	`unswap-sqr_binary64`
471×	`associate-/l*_binary64`
401×	`distribute-rgt-out_binary64`

Counts

150 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	1233
1	188	1145
2	444	1145
3	1078	1141
4	3659	1139
5	5228	1139

prune152.0ms (2.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	112	9	121

Error

Counts

121 → 9

Alt Table

Status	Error	Program
	8.1b	(.f64 (/.f64 y x) (.f64 (cosh.f64 x) (/.f64 1 z)))
✓	7.5b	(/.f64 (/.f64 (cosh.f64 x) z) (/.f64 x y))
✓	7.9b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	36.2b	(.f64 (/.f64 1/2 (sqrt.f64 (.f64 x z))) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) (sqrt.f64 (*.f64 x z))))
	8.7b	(*.f64 (/.f64 1/2 x) (/.f64 (fma.f64 (exp.f64 x) y (/.f64 y (exp.f64 x))) z))
✓	8.0b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
	8.8b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cosh.f64 x) (/.f64 y x))) 2) (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
	8.3b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
✓	7.0b	(/.f64 (+.f64 (.f64 1/2 (.f64 (exp.f64 x) y)) (.f64 1/2 (/.f64 y (exp.f64 x)))) (.f64 z x))

Compiler

Compiled 1783 to 669 computations (62.5% saved)

regimes2.4s (37.7%)

Accuracy

Total 0.6b remaining (95.7%)

Threshold costs 0.6b (95.7%)

Counts

150 → 3

Compiler

Compiled 12327 to 8137 computations (34% saved)

bsearch26.0ms (0.4%)

Steps

Iters	Range		Point
1	8.216848882298793e+88	2.0049034536189358e+96	4.13020256225072e+92
2	-410798315936.56506	-358403502575.77783	-404248964266.4667

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66
1	30	66
2	30	66

end241.0ms (3.8%)

Compiler: Compiled 246 to 146 computations (40.7% saved)

Details

analyze560.0ms (8.8%)

sample1.4s (21.4%)

simplify85.0ms (1.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series80.0ms (1.3%)

rewrite60.0ms (0.9%)

simplify91.0ms (1.4%)

prune80.0ms (1.3%)

localize10.0ms (0.2%)

series105.0ms (1.6%)

rewrite83.0ms (1.3%)

simplify87.0ms (1.4%)

prune122.0ms (1.9%)

localize6.0ms (0.1%)

series82.0ms (1.3%)

rewrite66.0ms (1%)

simplify104.0ms (1.6%)

prune142.0ms (2.2%)

localize16.0ms (0.3%)

series172.0ms (2.7%)

rewrite102.0ms (1.6%)

simplify122.0ms (1.9%)

prune152.0ms (2.4%)

regimes2.4s (37.7%)

bsearch26.0ms (0.4%)

simplify6.0ms (0.1%)

end241.0ms (3.8%)

Profiling