Details

analyze1.2s (15.8%)

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)

sample3.2s (41.6%)

Symmetry

(sort y z)

Results

1.8s	10534×	body	128	invalid
1.4s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify91.0ms (1.2%)

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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(.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)

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))))
✓	2.4b	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
✓	5.5b	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))

series129.0ms (1.7%)

Counts

4 → 144

Calls

4 calls:

66.0ms	(/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2))
38.0ms	(.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (.f64 z 2)) (sqrt.f64 t))
19.0ms	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
6.0ms	(.f64 3 (/.f64 x (.f64 y 27)))

rewrite45.0ms (0.6%)

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:

10.0ms	(.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))))

simplify171.0ms (2.2%)

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

prune186.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	2	212

Error

Counts

212 → 2

Alt Table

Status	Error	Program
	1.2b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
▶	0.1b	(.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)))

Status

Error

Program

1.2b

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

▶

0.1b

(*.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)))

Compiler

Compiled 5840 to 4183 computations (28.4% saved)

localize17.0ms (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))
✓	2.4b	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
✓	5.5b	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))

series242.0ms (3.1%)

Counts

4 → 120

Calls

4 calls:

174.0ms	(.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)))
45.0ms	(.f64 (sqrt.f64 t) (/.f64 (.f64 1/9 (/.f64 x y)) (*.f64 z 2)))
17.0ms	(/.f64 (.f64 1/9 (/.f64 x y)) (.f64 z 2))
6.0ms	(*.f64 1/9 (/.f64 x y))

rewrite351.0ms (4.5%)

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:

313.0ms	(.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)))
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))

simplify191.0ms (2.5%)

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

prune221.0ms (2.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	249	1	250
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	250	2	252

Error

Counts

252 → 2

Alt Table

Status	Error	Program
▶	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))
✓	0.1b	(.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)))

Status

Error

Program

▶

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))

✓

0.1b

(*.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)))

Compiler

Compiled 8646 to 6089 computations (29.6% saved)

localize12.0ms (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))
✓	0.2b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	2.4b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.7b	(/.f64 x (*.f64 y z))

series303.0ms (3.9%)

Counts

4 → 48

Calls

4 calls:

197.0ms	(/.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))
43.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
42.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
20.0ms	(/.f64 x (*.f64 y z))

rewrite38.0ms (0.5%)

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:

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

simplify266.0ms (3.4%)

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

prune176.0ms (2.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	186	2	188

Error

Counts

188 → 2

Alt Table

Status	Error	Program
✓	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))
✓	0.1b	(.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)))

Status

Error

Program

✓

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))

✓

0.1b

(*.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)))

Compiler

Compiled 5703 to 3414 computations (40.1% saved)

regimes756.0ms (9.8%)

Accuracy

Total 0.3b remaining (97.3%)

Threshold costs 0.3b (97.3%)

Counts

49 → 1

Compiler

Compiled 15179 to 12499 computations (17.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	38
1	28	38
2	26	38

end83.0ms (1.1%)

Remove: (sort y z)
Compiler: Compiled 164 to 140 computations (14.6% saved)

Details

analyze1.2s (15.8%)

sample3.2s (41.6%)

simplify91.0ms (1.2%)

prune3.0ms (0%)

localize12.0ms (0.2%)

series129.0ms (1.7%)

rewrite45.0ms (0.6%)

simplify171.0ms (2.2%)

prune186.0ms (2.4%)

localize17.0ms (0.2%)

series242.0ms (3.1%)

rewrite351.0ms (4.5%)

simplify191.0ms (2.5%)

prune221.0ms (2.8%)

localize12.0ms (0.2%)

series303.0ms (3.9%)

rewrite38.0ms (0.5%)

simplify266.0ms (3.4%)

prune176.0ms (2.3%)

regimes756.0ms (9.8%)

simplify3.0ms (0%)

end83.0ms (1.1%)

Profiling