Details

analyze581.0ms (14.6%)

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
25%	74.9%	0.2%	7
25%	74.9%	0.2%	8
34.3%	65.5%	0.2%	9
39%	60.8%	0.2%	10
48.3%	51.5%	0.2%	11
53.7%	46.1%	0.2%	12
63.1%	36.7%	0.2%	13
64%	35.6%	0.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (26.9%)

Symmetry

(sort z t)

Results

888.0ms	8256×	body	128	valid
35.0ms	349×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify14.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

prune1.0ms (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

3.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 y (*.f64 z t))
✓	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))

series44.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

39.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
5.0ms	(-.f64 y (*.f64 z t))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

3.0ms	(/.f64 x (-.f64 y (*.f64 z t)))
2.0ms	(-.f64 y (*.f64 z t))

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

761×	`associate-/l*_binary64`
527×	`associate-/r*_binary64`
388×	`fma-def_binary64`
188×	`fma-neg_binary64`
173×	`associate-*l/_binary64`

Counts

135 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2389
1	332	2275
2	1159	2114
3	4821	2114
4	4954	2114

prune65.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	7	111

Error

3.1b

Counts

111 → 7

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
✓	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))
▶	3.5b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
	32.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
	4.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	4.1b	(.f64 (.f64 (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t)))) (cbrt.f64 (/.f64 x (-.f64 y (.f64 z t))))) (cbrt.f64 (/.f64 x (-.f64 y (*.f64 z t)))))
	30.9b	(/.f64 x y)

Compiler

Compiled 1921 to 569 computations (70.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 y (*.f64 z t))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
✓	3.2b	(/.f64 (-.f64 y (*.f64 z t)) x)

series50.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
15.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 110

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (-.f64 y (*.f64 z t)) x))
3.0ms	(/.f64 (-.f64 y (*.f64 z t)) x)

simplify128.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-/l*_binary64`
526×	`associate-/r*_binary64`
409×	`fma-def_binary64`
329×	`associate-/r/_binary64`
251×	`associate-/l/_binary64`

Counts

206 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	4158
1	402	3845
2	1455	3696
3	4932	3696
4	5008	3696

prune134.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	227	6	233

Error

3.1b

Counts

233 → 6

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
	4.2b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
✓	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	32.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
▶	4.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	31.0b	(/.f64 1 (/.f64 y x))

Compiler

Compiled 4272 to 1351 computations (68.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	1.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
✓	2.5b	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))

series207.0ms (5.2%)

Counts

4 → 120

Calls

4 calls:

94.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
48.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
28.0ms	(cbrt.f64 x)

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
41×	`cbrt-prod_binary64`
41×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
38×	`times-frac_binary64`

Counts

4 → 147

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
3.0ms	(/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z)))
1.0ms	(cbrt.f64 x)

simplify163.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

569×	`unswap-sqr_binary64`
473×	`cancel-sign-sub-inv_binary64`
434×	`associate-l_binary64`
297×	`associate-r_binary64`
213×	`times-frac_binary64`

Counts

267 → 243

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	5525
1	647	5072
2	3329	5004
3	3914	4941
4	5228	4941

prune138.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	278	7	285

Error

3.1b

Counts

285 → 7

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
▶	4.2b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
✓	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	46.0b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (/.f64 1 y) (pow.f64 x 1/3)))
	32.3b	(.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (-.f64 y (.f64 t z))))
✓	4.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	31.0b	(/.f64 1 (/.f64 y x))

Compiler

Compiled 6261 to 1460 computations (76.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
✓	0.7b	(-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x))
✓	5.6b	(/.f64 (*.f64 t z) x)

series66.0ms (1.7%)

Counts

3 → 69

Calls

3 calls:

35.0ms	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
17.0ms	(-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x))
15.0ms	(/.f64 (*.f64 t z) x)

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`times-frac_binary64`
126×	`add-sqr-sqrt_binary64`
111×	`*-un-lft-identity_binary64`
101×	`add-cube-cbrt_binary64`
91×	`prod-diff_binary64`

Counts

3 → 206

Calls

3 calls:

10.0ms	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
9.0ms	(-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x))
3.0ms	(/.f64 (*.f64 t z) x)

simplify167.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

525×	`associate-/l/_binary64`
355×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
239×	`distribute-rgt-neg-in_binary64`
196×	`distribute-lft-neg-in_binary64`

Counts

275 → 287

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	7166
1	663	6159
2	2381	5055
3	4714	5055
4	4926	5055

prune184.0ms (4.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	284	3	287
Fresh	3	1	4
Picked	0	1	1
Done	0	2	2
Total	287	7	294

Error

0.1b

Counts

294 → 7

Alt Table

Status	Error	Program
	34.4b	(/.f64 (/.f64 x (sqrt.f64 (-.f64 y (.f64 z t)))) (sqrt.f64 (-.f64 y (.f64 z t))))
✓	4.2b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 (*.f64 t z) x)))
✓	3.2b	(/.f64 x (-.f64 y (*.f64 z t)))
	3.4b	(/.f64 1 (-.f64 (/.f64 y x) (/.f64 t (/.f64 x z))))
	3.3b	(/.f64 1 (-.f64 (/.f64 y x) (*.f64 t (/.f64 z x))))
✓	4.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (-.f64 y (*.f64 t z))))
	32.4b	(/.f64 1 (-.f64 (/.f64 y x) (*.f64 (/.f64 t (sqrt.f64 x)) (/.f64 z (sqrt.f64 x)))))

Compiler

Compiled 8242 to 1976 computations (76% saved)

regimes545.0ms (13.6%)

Accuracy

Total 0.6b remaining (82.8%)

Threshold costs 0.6b (82.8%)

Counts

55 → 3

Compiler

Compiled 7083 to 4417 computations (37.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	60
1	35	60
2	51	60
3	62	60
4	68	60
5	69	60
6	68	60

end216.0ms (5.4%)

Compiler: Compiled 292 to 152 computations (47.9% saved)

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10

Details

analyze581.0ms (14.6%)

sample1.1s (26.9%)

simplify14.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series44.0ms (1.1%)

rewrite7.0ms (0.2%)

simplify86.0ms (2.2%)

prune65.0ms (1.6%)

localize8.0ms (0.2%)

series50.0ms (1.2%)

rewrite17.0ms (0.4%)

simplify128.0ms (3.2%)

prune134.0ms (3.3%)

localize8.0ms (0.2%)

series207.0ms (5.2%)

rewrite31.0ms (0.8%)

simplify163.0ms (4.1%)

prune138.0ms (3.5%)

localize7.0ms (0.2%)

series66.0ms (1.7%)

rewrite42.0ms (1%)

simplify167.0ms (4.2%)

prune184.0ms (4.6%)

regimes545.0ms (13.6%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end216.0ms (5.4%)

Profiling

Iter	Nodes	Cost
0	8	10
1	14	10
2	24	10
3	41	10
4	55	10
5	85	10
6	119	10
7	148	10
8	184	10
9	202	10
10	219	10
11	225	10
12	202	10