Details

analyze590.0ms (11.3%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (20.5%)

Symmetry

(sort y t)

Results

948.0ms	8256×	body	128	valid
47.0ms	374×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

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

8.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	8.5b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series136.0ms (2.6%)

Counts

2 → 84

Calls

2 calls:

126.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

11.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify123.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune168.0ms (3.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	185	8	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
	24.1b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
	25.7b	(cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z))) (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	8.8b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
▶	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	31.5b	(*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	9.1b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
✓	8.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 5795 to 2143 computations (63% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series148.0ms (2.8%)

Counts

3 → 96

Calls

3 calls:

122.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
17.0ms	(/.f64 x (-.f64 t z))
8.0ms	(/.f64 1 (-.f64 y z))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

14.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
10.0ms	(/.f64 x (-.f64 t z))
4.0ms	(/.f64 1 (-.f64 y z))

simplify161.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune258.0ms (4.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	274	4	278
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	278	9	287

Error

Counts

287 → 9

Alt Table

Status	Error	Program
	3.3b	(/.f64 (*.f64 (/.f64 1 (-.f64 y z)) x) (-.f64 t z))
	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	8.8b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
▶	1.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
✓	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.3b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	2.3b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))) (cbrt.f64 (.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z))))) (cbrt.f64 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))))
	24.1b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
✓	8.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 7520 to 2972 computations (60.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	1.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

series125.0ms (2.4%)

Counts

1 → 48

Calls

1 calls:

125.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 150

Calls

1 calls:

11.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

simplify175.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
530×	`times-frac_binary64`
481×	`associate-/r*_binary64`
452×	`associate-/l*_binary64`
309×	`associate-/l/_binary64`

Counts

198 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	495	7582
1	1498	7346
2	4934	7270
3	5647	7270

prune191.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	4	2	6
Picked	0	1	1
Done	0	2	2
Total	272	7	279

Error

Counts

279 → 7

Alt Table

Status	Error	Program
	3.3b	(/.f64 (*.f64 (/.f64 1 (-.f64 y z)) x) (-.f64 t z))
▶	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	8.4b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 t z)) (-.f64 y z)))
✓	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	8.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 x (cbrt.f64 (-.f64 t z))) (-.f64 y z)))

Compiler

Compiled 7622 to 2323 computations (69.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

series162.0ms (3.1%)

Counts

2 → 96

Calls

2 calls:

129.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
33.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

rewrite159.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

1245×	`times-frac_binary64`
825×	`*-un-lft-identity_binary64`
825×	`add-sqr-sqrt_binary64`
457×	`add-cube-cbrt_binary64`
184×	`distribute-lft-out--_binary64`

Counts

2 → 621

Calls

2 calls:

24.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
11.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

simplify397.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/r/_binary64`
654×	`times-frac_binary64`
231×	`associate-/l/_binary64`
167×	`fma-def_binary64`
144×	`distribute-rgt-in_binary64`

Counts

717 → 720

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	23791
1	1959	23320
2	5004	23320

prune456.0ms (8.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	777	0	777
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	777	7	784

Error

Counts

784 → 7

Alt Table

Status	Error	Program
	3.3b	(/.f64 (*.f64 (/.f64 1 (-.f64 y z)) x) (-.f64 t z))
✓	2.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	8.4b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 t z)) (-.f64 y z)))
✓	1.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
✓	8.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
	3.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 x (cbrt.f64 (-.f64 t z))) (-.f64 y z)))

Compiler

Compiled 21969 to 6114 computations (72.2% saved)

regimes486.0ms (9.3%)

Accuracy

Total 1.5b remaining (99%)

Threshold costs 0b (0%)

Counts

74 → 3

Compiler

Compiled 8418 to 4861 computations (42.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	26	81
2	32	81
3	34	81
4	35	81
5	35	81

end219.0ms (4.2%)

Compiler: Compiled 346 to 151 computations (56.4% saved)

Details

analyze590.0ms (11.3%)

sample1.1s (20.5%)

simplify76.0ms (1.5%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series136.0ms (2.6%)

rewrite25.0ms (0.5%)

simplify123.0ms (2.3%)

prune168.0ms (3.2%)

localize7.0ms (0.1%)

series148.0ms (2.8%)

rewrite38.0ms (0.7%)

simplify161.0ms (3.1%)

prune258.0ms (4.9%)

localize6.0ms (0.1%)

series125.0ms (2.4%)

rewrite33.0ms (0.6%)

simplify175.0ms (3.3%)

prune191.0ms (3.7%)

localize7.0ms (0.1%)

series162.0ms (3.1%)

rewrite159.0ms (3%)

simplify397.0ms (7.6%)

prune456.0ms (8.7%)

regimes486.0ms (9.3%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end219.0ms (4.2%)

Profiling