Details

analyze735.0ms (16.3%)

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
12.5%	87.3%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
43.7%	56.1%	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 16 to 11 computations (31.3% saved)

sample1.1s (25%)

Symmetry

(sort z t)

Results

994.0ms	8256×	body	128	valid
63.0ms	414×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify118.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

prune2.0ms (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

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.4b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series140.0ms (3.1%)

Counts

2 → 84

Calls

2 calls:

131.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
9.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite24.0ms (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:

10.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify103.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
589×	`associate-/l*_binary64`
505×	`associate-/r*_binary64`
195×	`fma-def_binary64`
134×	`*-commutative_binary64`

Counts

173 → 187

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	5989
1	1376	5678
2	5010	5678

prune175.0ms (3.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	6.1b	(-.f64 1 (/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 y t) (-.f64 y z)) 3))))
	0.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	0.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 6363 to 2607 computations (59% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
✓	6.4b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series153.0ms (3.4%)

Counts

2 → 96

Calls

2 calls:

124.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
29.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
28×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 89

Calls

2 calls:

10.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)
8.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

786×	`times-frac_binary64`
597×	`associate-/l*_binary64`
482×	`associate-/r*_binary64`
193×	`fma-def_binary64`
158×	`associate-/r/_binary64`

Counts

185 → 198

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	401	6774
1	1379	6393
2	5094	6393

prune229.0ms (5.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	289	1	290
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	290	4	294

Error

Counts

294 → 4

Alt Table

Status	Error	Program
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
▶	0.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	1.6b	(-.f64 1 (/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))))
✓	0.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 8709 to 3623 computations (58.4% saved)

localize31.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	1.1b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

series203.0ms (4.5%)

Counts

2 → 72

Calls

2 calls:

186.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
16.0ms	(/.f64 x (-.f64 y z))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
176×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out--_binary64`

Counts

2 → 189

Calls

2 calls:

19.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
4.0ms	(/.f64 x (-.f64 y z))

simplify159.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

709×	`times-frac_binary64`
587×	`associate-/l*_binary64`
544×	`associate-/r*_binary64`
305×	`associate-/l/_binary64`
166×	`fma-def_binary64`

Counts

261 → 260

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	547	9298
1	1717	9038
2	5431	9038

prune182.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	260	4	264

Error

Counts

264 → 4

Alt Table

Status	Error	Program
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
✓	0.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
▶	1.6b	(-.f64 1 (/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))))
✓	0.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 8365 to 2961 computations (64.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y t) x)
✓	0.4b	(/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x)))
✓	3.3b	(*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))

series177.0ms (3.9%)

Counts

3 → 124

Calls

3 calls:

134.0ms	(/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x)))
33.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))
9.0ms	(/.f64 (-.f64 y t) x)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
34×	`times-frac_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 125

Calls

3 calls:

11.0ms	(/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x)))
9.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))
4.0ms	(/.f64 (-.f64 y t) x)

simplify114.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

675×	`times-frac_binary64`
581×	`associate-/l*_binary64`
467×	`associate-/r*_binary64`
181×	`fma-def_binary64`
142×	`associate-*l/_binary64`

Counts

249 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	455	7314
1	1474	6965
2	5147	6965

prune184.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	233	0	233
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	233	4	237

Error

Counts

237 → 4

Alt Table

Status	Error	Program
	1.8b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
✓	0.5b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
✓	1.6b	(-.f64 1 (/.f64 1 (*.f64 (-.f64 y z) (/.f64 (-.f64 y t) x))))
✓	0.1b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 7028 to 2994 computations (57.4% saved)

regimes354.0ms (7.8%)

Accuracy

Total 0.7b remaining (98.5%)

Threshold costs 0.7b (98.5%)

Counts

54 → 1

Compiler

Compiled 7511 to 4875 computations (35.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`cancel-sign-sub-inv_binary64`
14×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`
12×	`+-commutative_binary64`
12×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	33	18
2	61	18
3	96	16
4	120	16
5	125	16
6	121	16

end65.0ms (1.4%)

Remove: (sort z t)
Compiler: Compiled 126 to 86 computations (31.7% saved)

Details

analyze735.0ms (16.3%)

sample1.1s (25%)

simplify118.0ms (2.6%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series140.0ms (3.1%)

rewrite24.0ms (0.5%)

simplify103.0ms (2.3%)

prune175.0ms (3.9%)

localize9.0ms (0.2%)

series153.0ms (3.4%)

rewrite24.0ms (0.5%)

simplify109.0ms (2.4%)

prune229.0ms (5.1%)

localize31.0ms (0.7%)

series203.0ms (4.5%)

rewrite47.0ms (1%)

simplify159.0ms (3.5%)

prune182.0ms (4%)

localize9.0ms (0.2%)

series177.0ms (3.9%)

rewrite32.0ms (0.7%)

simplify114.0ms (2.5%)

prune184.0ms (4.1%)

regimes354.0ms (7.8%)

simplify5.0ms (0.1%)

end65.0ms (1.4%)

Profiling