Details

analyze612.0ms (14.4%)

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 (36.1%)

Results

969.0ms	8256×	body	128	valid
490.0ms	4553×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify85.0ms (2%)

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

prune2.0ms (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

9.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.7b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cosh.f64 x) (/.f64 y x))
✓	9.1b	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

series93.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

61.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
32.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
5.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

simplify113.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

860×	`times-frac_binary64`
530×	`fma-def_binary64`
444×	`associate-l_binary64`
362×	`associate-r_binary64`
348×	`associate-/r/_binary64`

Counts

124 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2288
1	432	2019
2	1488	2017
3	4433	2011
4	4988	2011

prune85.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Error

0.0b

Counts

121 → 10

Alt Table

Status	Error	Program
	37.0b	(cbrt.f64 (pow.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)) 3))
	37.5b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 (cosh.f64 x) (/.f64 y x)) z) (/.f64 (.f64 (cosh.f64 x) (/.f64 y x)) z)) (/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)))
	29.1b	(.f64 (sqrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (sqrt.f64 (.f64 (/.f64 y (*.f64 z x)) (cosh.f64 x))))
	37.7b	(/.f64 (*.f64 (/.f64 y x) (/.f64 (cosh.f64 x) (sqrt.f64 z))) (sqrt.f64 z))
	9.8b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	10.3b	(/.f64 (cosh.f64 x) (/.f64 z (/.f64 y x)))
▶	5.1b	(/.f64 (.f64 (cosh.f64 x) y) (.f64 z x))
	36.0b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x))) z)
	9.8b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
	6.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))))

Compiler

Compiled 2103 to 699 computations (66.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cosh.f64 x) y)
✓	4.9b	(/.f64 (.f64 (cosh.f64 x) y) (.f64 z x))

series89.0ms (2.1%)

Counts

2 → 60

Calls

2 calls:

64.0ms	(/.f64 (.f64 (cosh.f64 x) y) (.f64 z x))
25.0ms	(*.f64 (cosh.f64 x) y)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`cbrt-unprod_binary64`
5×	`prod-exp_binary64`

Counts

2 → 45

Calls

2 calls:

5.0ms	(/.f64 (.f64 (cosh.f64 x) y) (.f64 z x))
3.0ms	(*.f64 (cosh.f64 x) y)

simplify80.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

762×	`associate-/r*_binary64`
579×	`associate-*l/_binary64`
459×	`associate-*r/_binary64`
387×	`associate-/l/_binary64`
276×	`fma-def_binary64`

Counts

105 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1888
1	360	1647
2	1391	1642
3	4701	1636
4	4976	1636

prune71.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	90	9	99

Error

0.0b

Counts

99 → 9

Alt Table

Status	Error	Program
	6.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x)))) (cbrt.f64 (.f64 (/.f64 y (.f64 z x)) (cosh.f64 x))))
▶	5.5b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 (*.f64 z x)))
	32.9b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 z x))
	37.7b	(/.f64 (*.f64 (/.f64 y x) (/.f64 (cosh.f64 x) (sqrt.f64 z))) (sqrt.f64 z))
	9.8b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.0b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x))) z)
	9.8b	(.f64 (.f64 (cosh.f64 x) (/.f64 y x)) (/.f64 1 z))
	9.2b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) z) x)
	5.5b	(/.f64 1 (/.f64 (.f64 z x) (.f64 (cosh.f64 x) y)))

Compiler

Compiled 1575 to 553 computations (64.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (cosh.f64 x) y)
✓	0.3b	(/.f64 1 (*.f64 z x))
✓	5.1b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 (*.f64 z x)))

series69.0ms (1.6%)

Counts

2 → 36

Calls

2 calls:

61.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 (*.f64 z x)))
8.0ms	(/.f64 1 (*.f64 z x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64`
30×	`prod-exp_binary64`
28×	`add-cbrt-cube_binary64`
12×	`cbrt-unprod_binary64`
12×	`div-exp_binary64`

Counts

2 → 74

Calls

2 calls:

9.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 1 (*.f64 z x)))
3.0ms	(/.f64 1 (*.f64 z x))

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-*l/_binary64`
492×	`associate-*r/_binary64`
434×	`associate-/l*_binary64`
342×	`fma-def_binary64`
311×	`log-div_binary64`

Counts

110 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1888
1	340	1594
2	1074	1288
3	3827	1288
4	4938	1288
5	5056	1288

prune89.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	147	7	154

Error

Counts

154 → 7

Alt Table

Status	Error	Program
▶	5.5b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 (/.f64 1 z) x))
	32.9b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 z x))
	37.7b	(/.f64 (*.f64 (/.f64 y x) (/.f64 (cosh.f64 x) (sqrt.f64 z))) (sqrt.f64 z))
	9.8b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.0b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x))) z)
	9.2b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) z) x)
	5.5b	(/.f64 1 (/.f64 (.f64 z x) (.f64 (cosh.f64 x) y)))

Compiler

Compiled 2478 to 1007 computations (59.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (cosh.f64 x) y)
✓	0.2b	(/.f64 (/.f64 1 z) x)
✓	5.1b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 (/.f64 1 z) x))

series69.0ms (1.6%)

Counts

2 → 60

Calls

2 calls:

60.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 (/.f64 1 z) x))
9.0ms	(/.f64 (/.f64 1 z) x)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
79×	`add-sqr-sqrt_binary64`
79×	`add-cube-cbrt_binary64`
46×	`add-exp-log_binary64`

Counts

2 → 149

Calls

2 calls:

11.0ms	(.f64 (.f64 (cosh.f64 x) y) (/.f64 (/.f64 1 z) x))
6.0ms	(/.f64 (/.f64 1 z) x)

simplify137.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
564×	`associate-/r/_binary64`
489×	`*-commutative_binary64`
353×	`associate-/l/_binary64`
351×	`associate-/r*_binary64`

Counts

209 → 224

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	195	3537
1	506	3143
2	1653	3143
3	3205	3143
4	4690	3143
5	5062	3143

prune133.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	266	7	273

Error

Counts

273 → 7

Alt Table

Status	Error	Program
✓	5.5b	(.f64 (.f64 (cosh.f64 x) y) (/.f64 (/.f64 1 z) x))
	32.9b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 y)) (sqrt.f64 y)) (*.f64 z x))
	37.7b	(/.f64 (*.f64 (/.f64 y x) (/.f64 (cosh.f64 x) (sqrt.f64 z))) (sqrt.f64 z))
	9.8b	(/.f64 (.f64 (.f64 (cosh.f64 x) y) (/.f64 1 x)) z)
	36.0b	(/.f64 (.f64 (.f64 (cosh.f64 x) (sqrt.f64 (/.f64 y x))) (sqrt.f64 (/.f64 y x))) z)
	9.2b	(/.f64 (/.f64 (*.f64 (cosh.f64 x) y) z) x)
	5.5b	(/.f64 1 (/.f64 (.f64 z x) (.f64 (cosh.f64 x) y)))

Compiler

Compiled 4965 to 2232 computations (55% saved)

regimes662.0ms (15.5%)

Accuracy

Total 0.3b remaining (78.4%)

Threshold costs 0.3b (78.4%)

Counts

83 → 3

Compiler

Compiled 7005 to 4358 computations (37.8% saved)

bsearch50.0ms (1.2%)

Steps

Iters	Range		Point
9	111972074225858.7	4.047453272049763e+22	149749414749544.78
2	-8.169496143921464e-15	-1.5005289135583298e-19	-5.365992924946917e-16

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	28	51
2	27	51

end89.0ms (2.1%)

Compiler: Compiled 171 to 99 computations (42.1% saved)

Details

analyze612.0ms (14.4%)

sample1.5s (36.1%)

simplify85.0ms (2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series93.0ms (2.2%)

rewrite15.0ms (0.3%)

simplify113.0ms (2.7%)

prune85.0ms (2%)

localize6.0ms (0.1%)

series89.0ms (2.1%)

rewrite10.0ms (0.2%)

simplify80.0ms (1.9%)

prune71.0ms (1.7%)

localize7.0ms (0.2%)

series69.0ms (1.6%)

rewrite17.0ms (0.4%)

simplify90.0ms (2.1%)

prune89.0ms (2.1%)

localize8.0ms (0.2%)

series69.0ms (1.6%)

rewrite31.0ms (0.7%)

simplify137.0ms (3.2%)

prune133.0ms (3.1%)

regimes662.0ms (15.5%)

bsearch50.0ms (1.2%)

simplify3.0ms (0.1%)

end89.0ms (2.1%)

Profiling