Details

analyze1.3s (15.4%)

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
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample2.7s (31.6%)

Infinites

0% of outputs are infinite.

Symmetry

(sort y z)

Results

1.4s	10620×	body	128	invalid
1.2s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

2067×	`associate-/l*_binary64`
1151×	`associate-/l/_binary64`
961×	`associate-/r/_binary64`
904×	`*-commutative_binary64`
879×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	121	20
3	446	20
4	1750	20
5	3005	20
6	3002	20
7	3002	20
8	3753	20
9	4074	20
10	4215	20
11	4225	20
12	4229	20
13	4230	20
14	5398	20

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

1.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	1.7b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (/.f64 x (.f64 y 27)))
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	3.5b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	5.7b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series84.0ms (1%)

Counts

4 → 144

Calls

4 calls:

41.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
18.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
17.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
7.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64`
92×	`add-cbrt-cube_binary64`
41×	`prod-exp_binary64`
39×	`cbrt-unprod_binary64`
31×	`add-sqr-sqrt_binary64`

Counts

4 → 141

Calls

4 calls:

11.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
7.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
5.0ms	(.f64 3 (/.f64 x (.f64 y 27)))
5.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

simplify182.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

782×	`associate-/r/_binary64`
291×	`times-frac_binary64`
262×	`sub-neg_binary64`
198×	`associate-l_binary64`
191×	`log-prod_binary64`

Counts

285 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	5969
1	547	4670
2	2441	4667
3	4043	4667
4	4793	4667
5	4977	4667

prune198.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	210	3	213

Error

0.0b

Counts

213 → 3

Alt Table

Status	Error	Program
	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
▶	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 3 (.f64 (.f64 (/.f64 z x) y) 54)) (sqrt.f64 t))))

Compiler

Compiled 5898 to 4233 computations (28.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
✓	0.3b	(*.f64 1/9 (/.f64 x y))
✓	3.5b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
✓	5.7b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series234.0ms (2.7%)

Counts

4 → 120

Calls

4 calls:

165.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
42.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
19.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
7.0ms	(*.f64 1/9 (/.f64 x y))

rewrite54.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`add-exp-log_binary64`
73×	`add-cbrt-cube_binary64`
60×	`add-sqr-sqrt_binary64`
45×	`times-frac_binary64`
43×	`prod-exp_binary64`

Counts

4 → 173

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3)))
10.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
5.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
5.0ms	(*.f64 1/9 (/.f64 x y))

simplify291.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

619×	`associate-/r/_binary64`
250×	`associate-*r/_binary64`
241×	`times-frac_binary64`
223×	`associate-/l*_binary64`
216×	`associate-l_binary64`

Counts

293 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	7427
1	710	5571
2	2746	5570
3	4207	5570
4	4852	5570
5	4942	5570

prune375.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	248	2	250
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	250	3	253

Error

Counts

253 → 3

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
	0.3b	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))

Compiler

Compiled 8720 to 6151 computations (29.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
✓	1.0b	(/.f64 1 (sqrt.f64 3))
	3.5b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
	5.7b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series201.0ms (2.3%)

Counts

2 → 48

Calls

2 calls:

201.0ms	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
49×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

2 → 132

Calls

2 calls:

15.0ms	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
3.0ms	(/.f64 1 (sqrt.f64 3))

simplify236.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-neg_binary64`
505×	`times-frac_binary64`
429×	`associate-/l*_binary64`
316×	`fma-def_binary64`
292×	`associate-*l/_binary64`

Counts

180 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	5079
1	320	4207
2	988	4044
3	2339	3996
4	2592	3996
5	3291	3996
6	4397	3996
7	4986	3996
8	4832	3996

prune297.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	259	3	262

Error

Counts

262 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
▶	0.3b	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))

Compiler

Compiled 7974 to 5561 computations (30.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
✓	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	3.5b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	4.5b	(/.f64 x (*.f64 y z))

series273.0ms (3.2%)

Counts

4 → 48

Calls

4 calls:

175.0ms	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
46.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
34.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
18.0ms	(/.f64 x (*.f64 y z))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
41×	`add-exp-log_binary64`

Counts

4 → 156

Calls

4 calls:

8.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
7.0ms	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
6.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
3.0ms	(/.f64 x (*.f64 y z))

simplify242.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-/r*_binary64`
639×	`associate-/l*_binary64`
424×	`*-commutative_binary64`
368×	`associate-/l/_binary64`
183×	`associate-/r/_binary64`

Counts

204 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	258	5876
1	543	5459
2	1608	5459
3	4010	5459
4	4732	5459
5	4955	5459
6	4994	5459
7	4926	5459

prune206.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2)))) (sqrt.f64 3)))
✓	0.3b	(/.f64 (/.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))) (.f64 (cbrt.f64 3) (cbrt.f64 3))) (cbrt.f64 3))
	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3)))

Compiler

Compiled 5726 to 3433 computations (40% saved)

regimes1.2s (14.1%)

Accuracy

Total 0.4b remaining (97.7%)

Threshold costs 0.4b (97.7%)

Counts

73 → 1

Compiler

Compiled 28030 to 22693 computations (19% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	19	32
2	19	32

end216.0ms (2.5%)

Compiler: Compiled 171 to 143 computations (16.4% saved)

Details

analyze1.3s (15.4%)

sample2.7s (31.6%)

simplify91.0ms (1.1%)

prune4.0ms (0%)

localize13.0ms (0.2%)

series84.0ms (1%)

rewrite41.0ms (0.5%)

simplify182.0ms (2.1%)

prune198.0ms (2.3%)

localize16.0ms (0.2%)

series234.0ms (2.7%)

rewrite54.0ms (0.6%)

simplify291.0ms (3.4%)

prune375.0ms (4.3%)

localize16.0ms (0.2%)

series201.0ms (2.3%)

rewrite39.0ms (0.4%)

simplify236.0ms (2.7%)

prune297.0ms (3.4%)

localize13.0ms (0.2%)

series273.0ms (3.2%)

rewrite37.0ms (0.4%)

simplify242.0ms (2.8%)

prune206.0ms (2.4%)

regimes1.2s (14.1%)

simplify2.0ms (0%)

end216.0ms (2.5%)

Profiling