Details

analyze646.0ms (9.6%)

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
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 (15.7%)

Symmetry

(sort z t)

Results

942.0ms	8256×	body	128	valid
45.0ms	414×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify120.0ms (1.8%)

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

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	7.6b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series134.0ms (2%)

Counts

2 → 84

Calls

2 calls:

125.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
9.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite24.0ms (0.4%)

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

simplify96.0ms (1.4%)

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

prune294.0ms (4.4%)

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
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	23.5b	(-.f64 1 (/.f64 x (exp.f64 (log.f64 (*.f64 (-.f64 y t) (-.f64 y z))))))
▶	0.8b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))
	6.1b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
	1.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	11.6b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 y t))) (+.f64 y z)))

Compiler

Compiled 6457 to 2659 computations (58.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))

series305.0ms (4.6%)

Counts

4 → 108

Calls

4 calls:

148.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))
82.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
38.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
42×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 163

Calls

4 calls:

20.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t)))
5.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify132.0ms (2%)

Algorithm

1×	egg-herbie

Rules

891×	`times-frac_binary64`
778×	`associate-/l*_binary64`
202×	`fma-def_binary64`
160×	`*-commutative_binary64`
98×	`+-commutative_binary64`

Counts

271 → 308

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	515	8279
1	1687	7240
2	4997	7240

prune302.0ms (4.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	342	6	348

Error

Counts

348 → 6

Alt Table

Status	Error	Program
	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 y t)))))
	23.5b	(-.f64 1 (/.f64 x (exp.f64 (log.f64 (*.f64 (-.f64 y t) (-.f64 y z))))))
✓	0.8b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))
	6.1b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
▶	1.1b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	11.6b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 y t))) (+.f64 y z)))

Compiler

Compiled 10939 to 3826 computations (65% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	2.3b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))

series152.0ms (2.3%)

Counts

2 → 72

Calls

2 calls:

126.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
26.0ms	(/.f64 x (-.f64 y z))

rewrite39.0ms (0.6%)

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:

13.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t))
4.0ms	(/.f64 x (-.f64 y z))

simplify145.0ms (2.2%)

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

prune248.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	258	2	260
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	261	5	266

Error

Counts

266 → 5

Alt Table

Status	Error	Program
	11.6b	(-.f64 1 (.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 y t))) (+.f64 y z)))
	1.1b	(-.f64 1 (/.f64 (/.f64 1 (/.f64 (-.f64 y z) x)) (-.f64 y t)))
▶	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y t) (/.f64 x (-.f64 y z)))))
✓	0.8b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))
	6.1b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))

Compiler

Compiled 8441 to 3004 computations (64.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 y z))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 y t) (/.f64 x (-.f64 y z))))
✓	2.3b	(/.f64 (-.f64 y t) (/.f64 x (-.f64 y z)))

series166.0ms (2.5%)

Counts

2 → 96

Calls

2 calls:

127.0ms	(/.f64 1 (/.f64 (-.f64 y t) (/.f64 x (-.f64 y z))))
38.0ms	(/.f64 (-.f64 y t) (/.f64 x (-.f64 y z)))

rewrite151.0ms (2.3%)

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:

21.0ms	(/.f64 1 (/.f64 (-.f64 y t) (/.f64 x (-.f64 y z))))
10.0ms	(/.f64 (-.f64 y t) (/.f64 x (-.f64 y z)))

simplify385.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

805×	`times-frac_binary64`
687×	`associate-/r/_binary64`
226×	`associate-/l/_binary64`
179×	`fma-def_binary64`
127×	`sub-neg_binary64`

Counts

717 → 709

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	702	24339
1	2086	23874
2	5300	23874

prune857.0ms (12.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	760	2	762
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	762	5	767

Error

Counts

767 → 5

Alt Table

Status	Error	Program
✓	1.1b	(-.f64 1 (/.f64 1 (/.f64 (-.f64 y t) (/.f64 x (-.f64 y z)))))
✓	0.8b	(-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 y t))))
	8.9b	(-.f64 1 (cbrt.f64 (/.f64 1 (pow.f64 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x) 3))))
	6.1b	(-.f64 1 (/.f64 x (-.f64 (fma.f64 y y (.f64 t z)) (.f64 y (+.f64 z t)))))
	0.9b	(-.f64 1 (/.f64 1 (*.f64 (/.f64 (-.f64 y t) x) (-.f64 y z))))

Compiler

Compiled 23428 to 7750 computations (66.9% saved)

regimes1.3s (19%)

Accuracy

Total 0.6b remaining (98.3%)

Threshold costs 0.6b (98.3%)

Counts

98 → 1

Compiler

Compiled 13673 to 9193 computations (32.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	26	16
2	38	16
3	45	16
4	50	16
5	51	16
6	49	16

end85.0ms (1.3%)

Remove: (sort z t)
Compiler: Compiled 156 to 104 computations (33.3% saved)

Details

analyze646.0ms (9.6%)

sample1.1s (15.7%)

simplify120.0ms (1.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series134.0ms (2%)

rewrite24.0ms (0.4%)

simplify96.0ms (1.4%)

prune294.0ms (4.4%)

localize11.0ms (0.2%)

series305.0ms (4.6%)

rewrite45.0ms (0.7%)

simplify132.0ms (2%)

prune302.0ms (4.5%)

localize7.0ms (0.1%)

series152.0ms (2.3%)

rewrite39.0ms (0.6%)

simplify145.0ms (2.2%)

prune248.0ms (3.7%)

localize13.0ms (0.2%)

series166.0ms (2.5%)

rewrite151.0ms (2.3%)

simplify385.0ms (5.8%)

prune857.0ms (12.8%)

regimes1.3s (19%)

simplify3.0ms (0%)

end85.0ms (1.3%)

Profiling