Details

analyze1.2s (17.3%)

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)

sample3.1s (43.8%)

Symmetry

(sort y z)

Results

1.7s	10735×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify90.0ms (1.3%)

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 (0.1%)

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

1.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.8b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
	2.6b	(.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)

localize12.0ms (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))))
✓	4.6b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	6.5b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series82.0ms (1.1%)

Counts

4 → 144

Calls

4 calls:

39.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
19.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
16.0ms	(.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)))

rewrite38.0ms (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:

9.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
6.0ms	(.f64 3 (/.f64 x (.f64 y 27)))
6.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
5.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

simplify168.0ms (2.4%)

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

prune187.0ms (2.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	211	2	213

Error

0.0b

Counts

213 → 2

Alt Table

Status	Error	Program
▶	0.9b	(.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)))
	1.1b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Status

Error

Program

▶

0.9b

(*.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)))

1.1b

(*.f64 1/3 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 5840 to 4183 computations (28.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.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))
✓	4.6b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
✓	6.5b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series126.0ms (1.8%)

Counts

4 → 120

Calls

4 calls:

60.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))
38.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
21.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
7.0ms	(*.f64 1/9 (/.f64 x y))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-exp-log_binary64`
60×	`add-cbrt-cube_binary64`
39×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`

Counts

4 → 143

Calls

4 calls:

8.0ms	(.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))
3.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))) (cbrt.f64 3))

simplify165.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/r/_binary64`
549×	`*-commutative_binary64`
213×	`times-frac_binary64`
183×	`associate--l+_binary64`
173×	`log-prod_binary64`

Counts

263 → 212

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	237	5748
1	525	4830
2	1979	4830
3	3303	4826
4	4789	4826
5	4942	4826

prune207.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	211	3	214

Error

0.0b

Counts

214 → 3

Alt Table

Status	Error	Program
▶	0.2b	(.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)))
✓	0.9b	(.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)))
	1.1b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 7199 to 5015 computations (30.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3))
✓	0.3b	(.f64 1/18 (/.f64 x (.f64 y z)))
✓	4.6b	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
✓	5.9b	(/.f64 x (*.f64 y z))

series193.0ms (2.7%)

Counts

4 → 84

Calls

4 calls:

80.0ms	(.f64 1/18 (/.f64 x (.f64 y z)))
60.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3))
37.0ms	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
16.0ms	(/.f64 x (*.f64 y z))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64`
33×	`add-cbrt-cube_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 122

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))
5.0ms	(.f64 1/18 (/.f64 x (.f64 y z)))
3.0ms	(/.f64 x (*.f64 y z))
3.0ms	(/.f64 (acos.f64 (.f64 (sqrt.f64 t) (.f64 1/18 (/.f64 x (*.f64 y z))))) (cbrt.f64 3))

simplify190.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-*r/_binary64`
637×	`times-frac_binary64`
583×	`associate-*l/_binary64`
442×	`associate-/r*_binary64`
364×	`associate-/l*_binary64`

Counts

206 → 173

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	189	4425
1	371	4123
2	1106	4123
3	4808	4123
4	5013	4123

prune293.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	173	3	176

Error

0.0b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	0.2b	(.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)))
✓	0.9b	(.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)))
▶	1.1b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 5521 to 3571 computations (35.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	4.6b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.9b	(/.f64 x (*.f64 y z))

series94.0ms (1.3%)

Counts

3 → 0

Calls

3 calls:

39.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
33.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
21.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64`
28×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
13×	`cbrt-unprod_binary64`

Counts

3 → 78

Calls

3 calls:

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

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

934×	`times-frac_binary64`
716×	`associate-*l/_binary64`
600×	`associate-*r/_binary64`
471×	`associate-/l*_binary64`
423×	`associate-/r*_binary64`

Counts

78 → 106

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1602
1	302	1346
2	1019	1345
3	5301	1345

prune54.0ms (0.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	132	3	135

Error

0.0b

Counts

135 → 3

Alt Table

Status	Error	Program
✓	0.2b	(.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)))
✓	0.9b	(.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)))
✓	1.1b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 2753 to 1223 computations (55.6% saved)

regimes609.0ms (8.6%)

Accuracy

Total 0.2b remaining (98.5%)

Threshold costs 0.2b (98.5%)

Counts

34 → 1

Compiler

Compiled 14125 to 11485 computations (18.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	25	35
2	24	35

end95.0ms (1.3%)

Remove: (sort y z)
Compiler: Compiled 175 to 147 computations (16% saved)

Details

analyze1.2s (17.3%)

sample3.1s (43.8%)

simplify90.0ms (1.3%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

series82.0ms (1.1%)

rewrite38.0ms (0.5%)

simplify168.0ms (2.4%)

prune187.0ms (2.6%)

localize15.0ms (0.2%)

series126.0ms (1.8%)

rewrite34.0ms (0.5%)

simplify165.0ms (2.3%)

prune207.0ms (2.9%)

localize16.0ms (0.2%)

series193.0ms (2.7%)

rewrite24.0ms (0.3%)

simplify190.0ms (2.7%)

prune293.0ms (4.1%)

localize10.0ms (0.1%)

series94.0ms (1.3%)

rewrite21.0ms (0.3%)

simplify47.0ms (0.7%)

prune54.0ms (0.8%)

regimes609.0ms (8.6%)

simplify2.0ms (0%)

end95.0ms (1.3%)

Profiling