Details

analyze581.0ms (10.8%)

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)

sample1.5s (27.2%)

Results

855.0ms	8256×	body	128	valid
515.0ms	4463×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify85.0ms (1.6%)

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

8.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.2b	(/.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))
✓	7.7b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series82.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

55.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
27.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

rewrite56.0ms (1%)

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 → 88

Calls

2 calls:

54.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
54.0ms	(/.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

simplify85.0ms (1.6%)

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

148 → 112

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

prune93.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Error

0.0b

Counts

113 → 6

Alt Table

Status	Error	Program
	8.1b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
▶	6.7b	(.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))
	8.0b	(+.f64 (.f64 1/720 (/.f64 (.f64 y (pow.f64 x 5)) z)) (+.f64 (.f64 1/2 (/.f64 (.f64 y x) z)) (+.f64 (/.f64 y (.f64 z x)) (.f64 1/24 (/.f64 (*.f64 y (pow.f64 x 3)) z)))))
	8.3b	(.f64 (cosh.f64 x) (.f64 (/.f64 y x) (/.f64 1 z)))
	7.7b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	35.7b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))

Compiler

Compiled 1781 to 721 computations (59.5% saved)

localize24.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 1/720 (pow.f64 x 5))
✓	0.2b	(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))
✓	6.2b	(.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))

series131.0ms (2.4%)

Counts

3 → 48

Calls

3 calls:

124.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))

4.0ms

(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))

3.0ms

(*.f64 1/720 (pow.f64 x 5))

rewrite76.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

217×	`add-sqr-sqrt_binary64`
209×	`log1p-expm1-u_binary64`
209×	`expm1-log1p-u_binary64`
209×	`prod-diff_binary64`
204×	`add-cbrt-cube_binary64`

Counts

3 → 69

Calls

3 calls:

74.0ms

(*.f64 1/720 (pow.f64 x 5))

74.0ms

(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))

74.0ms

(*.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (*.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	448	51
2	4909	51
3	5081	51
0	0	0
1	0	0

simplify161.0ms (3%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
653×	`associate-*l/_binary64`
524×	`associate-/l*_binary64`
447×	`*-commutative_binary64`
407×	`associate-/r*_binary64`

Counts

117 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	1163
1	158	1161
2	383	1107
3	939	1059
4	1894	1059
5	2967	1059
6	3685	1059
7	3885	1059
8	3949	1059
9	3992	1059
10	4121	1059
11	4271	1059
12	4928	1059
13	4944	1059

prune244.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Error

0.0b

Counts

96 → 7

Alt Table

Status	Error	Program
	8.1b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
✓	6.7b	(.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))
	32.6b	(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (.f64 1/720 (pow.f64 x 5)))) 2)) (.f64 (/.f64 z y) (-.f64 (/.f64 1 x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))))))
	8.0b	(+.f64 (/.f64 y (.f64 x z)) (.f64 (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))) (/.f64 y z)))
	8.3b	(.f64 (cosh.f64 x) (.f64 (/.f64 y x) (/.f64 1 z)))
▶	7.7b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	35.7b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))

Compiler

Compiled 2908 to 2023 computations (30.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
✓	0.3b	(/.f64 1 (*.f64 z (/.f64 x y)))
✓	7.0b	(*.f64 z (/.f64 x y))

series84.0ms (1.6%)

Counts

3 → 108

Calls

3 calls:

55.0ms	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
16.0ms	(/.f64 1 (*.f64 z (/.f64 x y)))
11.0ms	(*.f64 z (/.f64 x y))

rewrite59.0ms (1.1%)

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 → 111

Calls

3 calls:

57.0ms	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
57.0ms	(/.f64 1 (*.f64 z (/.f64 x y)))
57.0ms	(*.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

simplify102.0ms (1.9%)

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

219 → 123

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

prune87.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	122	8	130

Error

0.0b

Counts

130 → 8

Alt Table

Status	Error	Program
	8.3b	(.f64 (cosh.f64 x) (.f64 (/.f64 y x) (/.f64 1 z)))
▶	7.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
✓	7.7b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	7.7b	(.f64 (cosh.f64 x) (/.f64 1 (/.f64 (.f64 z x) y)))
	8.1b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
✓	6.7b	(.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))
	32.6b	(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (.f64 1/720 (pow.f64 x 5)))) 2)) (.f64 (/.f64 z y) (-.f64 (/.f64 1 x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))))))
	35.7b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))

Compiler

Compiled 1901 to 792 computations (58.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
✓	7.0b	(/.f64 y (*.f64 z x))

series69.0ms (1.3%)

Counts

2 → 36

Calls

2 calls:

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

rewrite55.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

506×	`log-prod_binary64`
239×	`pow2_binary64`
190×	`pow-unpow_binary64`
171×	`pow1/3_binary64`
164×	`expm1-udef_binary64`

Counts

2 → 93

Calls

2 calls:

54.0ms	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
54.0ms	(/.f64 y (*.f64 z x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	171	19
2	2369	19
3	5255	19
0	0	0
1	0	0

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
448×	`distribute-rgt-in_binary64`
411×	`associate-/r/_binary64`
397×	`associate-/r*_binary64`
328×	`*-commutative_binary64`

Counts

129 → 104

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	48	837
1	138	769
2	328	769
3	709	765
4	1854	753
5	3491	750
6	4077	750
7	4879	750
8	5032	750

prune74.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	104	8	112

Error

Counts

112 → 8

Alt Table

Status	Error	Program
	8.3b	(.f64 (cosh.f64 x) (.f64 (/.f64 y x) (/.f64 1 z)))
✓	7.5b	(.f64 (cosh.f64 x) (/.f64 y (.f64 z x)))
	8.1b	(.f64 y (/.f64 (fma.f64 1/2 (exp.f64 x) (/.f64 1/2 (exp.f64 x))) (.f64 z x)))
✓	6.7b	(.f64 (/.f64 y z) (+.f64 (/.f64 1 x) (+.f64 (.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5))))))
	32.6b	(/.f64 (-.f64 (pow.f64 x -2) (pow.f64 (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (.f64 1/720 (pow.f64 x 5)))) 2)) (.f64 (/.f64 z y) (-.f64 (/.f64 1 x) (fma.f64 x 1/2 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/720 (pow.f64 x 5)))))))
	9.0b	(.f64 (cosh.f64 x) (.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (/.f64 1 (.f64 z x)))))
✓	7.7b	(.f64 (cosh.f64 x) (/.f64 1 (.f64 z (/.f64 x y))))
	35.7b	(*.f64 (/.f64 (cosh.f64 x) (sqrt.f64 z)) (/.f64 (/.f64 y x) (sqrt.f64 z)))

Compiler

Compiled 1507 to 600 computations (60.2% saved)

regimes1.5s (28.2%)

Accuracy

Total 0.3b remaining (82.7%)

Threshold costs 0.3b (82.7%)

Counts

160 → 3

Compiler

Compiled 13858 to 9252 computations (33.2% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	70
1	25	70
2	25	70

end128.0ms (2.4%)

Compiler: Compiled 255 to 149 computations (41.6% saved)

Details

analyze581.0ms (10.8%)

sample1.5s (27.2%)

simplify85.0ms (1.6%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series82.0ms (1.5%)

rewrite56.0ms (1%)

simplify85.0ms (1.6%)

prune93.0ms (1.7%)

localize24.0ms (0.5%)

series131.0ms (2.4%)

rewrite76.0ms (1.4%)

simplify161.0ms (3%)

prune244.0ms (4.6%)

localize8.0ms (0.1%)

series84.0ms (1.6%)

rewrite59.0ms (1.1%)

simplify102.0ms (1.9%)

prune87.0ms (1.6%)

localize5.0ms (0.1%)

series69.0ms (1.3%)

rewrite55.0ms (1%)

simplify87.0ms (1.6%)

prune74.0ms (1.4%)

regimes1.5s (28.2%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end128.0ms (2.4%)

Profiling