Details

analyze716.0ms (12.5%)

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 (18.8%)

Symmetry

(sort z t)

Results

961.0ms	8256×	body	128	valid
52.0ms	459×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify121.0ms (2.1%)

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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	7.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series132.0ms (2.3%)

Counts

2 → 84

Calls

2 calls:

123.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite20.0ms (0.3%)

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:

8.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
6.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify109.0ms (1.9%)

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

prune198.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	181	6	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	6	188

Error

Counts

188 → 6

Alt Table

Status	Error	Program
	2.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	30.3b	(-.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 y t))))
▶	0.8b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	2.3b	(-.f64 1 (*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
	10.6b	(-.f64 1 (cbrt.f64 (.f64 (.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 y t))) (/.f64 x (.f64 (-.f64 y z) (-.f64 y t)))) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))))

Compiler

Compiled 6477 to 2655 computations (59% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.9b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
✓	6.7b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series152.0ms (2.7%)

Counts

2 → 96

Calls

2 calls:

124.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
28.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

rewrite30.0ms (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:

16.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
8.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

simplify101.0ms (1.8%)

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

prune276.0ms (4.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	288	2	290
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	291	5	296

Error

Counts

296 → 5

Alt Table

Status	Error	Program
	2.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	30.3b	(-.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
▶	0.8b	(-.f64 1 (/.f64 (/.f64 1 1) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	2.0b	(-.f64 1 (/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x)))

Compiler

Compiled 8774 to 3663 computations (58.3% 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))
✓	0.9b	(/.f64 (/.f64 1 1) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
	6.7b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series125.0ms (2.2%)

Counts

1 → 48

Calls

1 calls:

125.0ms

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

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

205×	`times-frac_binary64`
85×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
85×	`add-cube-cbrt_binary64`
61×	`add-exp-log_binary64`

Counts

1 → 152

Calls

1 calls:

10.0ms

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

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
568×	`associate-/l*_binary64`
475×	`associate-/r*_binary64`
271×	`associate-l_binary64`
153×	`fma-def_binary64`

Counts

200 → 227

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	350	7379
1	1214	6931
2	5218	6931

prune350.0ms (6.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	391	5	396

Error

Counts

396 → 5

Alt Table

Status	Error	Program
	2.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	30.3b	(-.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
✓	0.8b	(-.f64 1 (/.f64 (/.f64 1 1) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
▶	2.0b	(-.f64 1 (/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x)))

Compiler

Compiled 12060 to 5610 computations (53.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y t) x)
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	2.8b	(/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x))

series140.0ms (2.4%)

Counts

3 → 100

Calls

3 calls:

119.0ms	(/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x))
11.0ms	(/.f64 1 (-.f64 y z))
9.0ms	(/.f64 (-.f64 y t) x)

rewrite119.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

1059×	`times-frac_binary64`
669×	`*-un-lft-identity_binary64`
669×	`add-sqr-sqrt_binary64`
401×	`add-cube-cbrt_binary64`
134×	`distribute-lft-out--_binary64`

Counts

3 → 548

Calls

3 calls:

15.0ms	(/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x))
8.0ms	(/.f64 (-.f64 y t) x)
4.0ms	(/.f64 1 (-.f64 y z))

simplify355.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

689×	`times-frac_binary64`
437×	`associate-/l/_binary64`
426×	`associate-/r/_binary64`
179×	`fma-def_binary64`
141×	`distribute-rgt-in_binary64`

Counts

648 → 584

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	691	22427
1	2230	22005
2	5136	22005

prune458.0ms (8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	584	0	584
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	584	5	589

Error

Counts

589 → 5

Alt Table

Status	Error	Program
	2.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	30.3b	(-.f64 1 (*.f64 (/.f64 (sqrt.f64 x) (-.f64 y z)) (/.f64 (sqrt.f64 x) (-.f64 y t))))
	7.3b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
✓	0.8b	(-.f64 1 (/.f64 (/.f64 1 1) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
✓	2.0b	(-.f64 1 (/.f64 (/.f64 1 (-.f64 y z)) (/.f64 (-.f64 y t) x)))

Compiler

Compiled 18650 to 7346 computations (60.6% saved)

regimes842.0ms (14.7%)

Accuracy

Total 0.6b remaining (98.9%)

Threshold costs 0.6b (98.9%)

Counts

109 → 1

Compiler

Compiled 15260 to 10393 computations (31.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	22	28
2	34	28
3	45	28
4	52	28
5	55	28
6	56	28
7	55	28

end226.0ms (3.9%)

Compiler: Compiled 178 to 112 computations (37.1% saved)

Details

analyze716.0ms (12.5%)

sample1.1s (18.8%)

simplify121.0ms (2.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series132.0ms (2.3%)

rewrite20.0ms (0.3%)

simplify109.0ms (1.9%)

prune198.0ms (3.5%)

localize8.0ms (0.1%)

series152.0ms (2.7%)

rewrite30.0ms (0.5%)

simplify101.0ms (1.8%)

prune276.0ms (4.8%)

localize9.0ms (0.2%)

series125.0ms (2.2%)

rewrite28.0ms (0.5%)

simplify117.0ms (2%)

prune350.0ms (6.1%)

localize8.0ms (0.1%)

series140.0ms (2.4%)

rewrite119.0ms (2.1%)

simplify355.0ms (6.2%)

prune458.0ms (8%)

regimes842.0ms (14.7%)

simplify3.0ms (0.1%)

end226.0ms (3.9%)

Profiling