Details

analyze1.1s (14.1%)

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)

sample3.4s (42%)

Symmetry

(sort y z)

Results

1.7s	8256×	body	128	valid
1.6s	10618×	body	128	invalid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify88.0ms (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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))

Compiler

Compiled 82 to 65 computations (20.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.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))))
✓	3.8b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	5.3b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series125.0ms (1.5%)

Counts

4 → 144

Calls

4 calls:

82.0ms	(.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))
18.0ms	(.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)))

rewrite43.0ms (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))
8.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
7.0ms	(.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))))

simplify166.0ms (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

prune178.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	209	3	212

Error

Counts

212 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
▶	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)))
	1.0b	(.f64 (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))))) (sqrt.f64 3)) (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2))))) (sqrt.f64 3)))

Compiler

Compiled 5907 to 4234 computations (28.3% 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))
✓	3.8b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
✓	5.3b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series142.0ms (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))
49.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
26.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
7.0ms	(*.f64 1/9 (/.f64 x y))

rewrite34.0ms (0.4%)

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:

9.0ms	(.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))

simplify179.0ms (2.2%)

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

prune179.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	212	3	215

Error

Counts

215 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	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)))
▶	1.0b	(.f64 (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))))) (sqrt.f64 3)) (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2))))) (sqrt.f64 3)))

Compiler

Compiled 7214 to 5022 computations (30.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(.f64 (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))))) (sqrt.f64 3)) (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2))))) (sqrt.f64 3)))
✓	1.0b	(/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2))))) (sqrt.f64 3))
	3.8b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
	5.3b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series183.0ms (2.3%)

Counts

2 → 96

Calls

2 calls:

124.0ms

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

59.0ms

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

rewrite103.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

310×	`add-sqr-sqrt_binary64`
282×	`sqrt-prod_binary64`
276×	`times-frac_binary64`
146×	`*-un-lft-identity_binary64`
146×	`add-cube-cbrt_binary64`

Counts

2 → 267

Calls

2 calls:

29.0ms

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

6.0ms

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

simplify397.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

570×	`times-frac_binary64`
316×	`associate-/r*_binary64`
315×	`*-commutative_binary64`
269×	`log-prod_binary64`
252×	`associate-/r/_binary64`

Counts

363 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	17919
1	542	14002
2	1676	12844
3	3073	12382
4	4522	12382
5	4997	12382

prune512.0ms (6.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	554	0	554
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	554	3	557

Error

Counts

557 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
✓	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)))
✓	1.0b	(.f64 (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))))) (sqrt.f64 3)) (/.f64 (sqrt.f64 (acos.f64 (.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2))))) (sqrt.f64 3)))

Compiler

Compiled 26717 to 17228 computations (35.5% saved)

regimes1.1s (13%)

Accuracy

Total 0.0b remaining (3.9%)

Threshold costs 0.0b (3.9%)

Counts

70 → 1

Compiler

Compiled 23339 to 18945 computations (18.8% 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	21	38
1	27	38
2	26	38

end105.0ms (1.3%)

Remove: (sort y z)
Compiler: Compiled 202 to 168 computations (16.8% saved)

Details

analyze1.1s (14.1%)

sample3.4s (42%)

simplify88.0ms (1.1%)

prune3.0ms (0%)

localize14.0ms (0.2%)

series125.0ms (1.5%)

rewrite43.0ms (0.5%)

simplify166.0ms (2.1%)

prune178.0ms (2.2%)

localize15.0ms (0.2%)

series142.0ms (1.8%)

rewrite34.0ms (0.4%)

simplify179.0ms (2.2%)

prune179.0ms (2.2%)

localize15.0ms (0.2%)

series183.0ms (2.3%)

rewrite103.0ms (1.3%)

simplify397.0ms (4.9%)

prune512.0ms (6.3%)

regimes1.1s (13%)

simplify2.0ms (0%)

end105.0ms (1.3%)

Profiling