Details

analyze486.0ms (3.5%)

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%	68.6%	31.4%	5
0%	65.5%	34.5%	6
0%	59.2%	40.8%	7
0%	51.4%	48.6%	8
0%	41.3%	58.7%	9
0%	28.4%	71.6%	10
2.3%	22.3%	75.4%	11
2.3%	21%	76.7%	12
2.7%	18%	79.3%	13
2.7%	16.4%	80.8%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample2.2s (15.5%)

Symmetry

(sort x y)

Results

1.4s	8256×	body	128	valid
660.0ms	4360×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify214.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

2140×	`distribute-rgt-in_binary64`
556×	`associate--r+_binary64`
551×	`associate-+l+_binary64`
551×	`unsub-neg_binary64`
546×	`associate-+r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	25
1	29	23
2	72	23
3	160	23
4	426	23
5	1097	23
6	1994	23
7	1981	23
8	1956	23
9	1972	23
10	1987	23
11	2037	23
12	2044	23
13	2248	23
14	2651	23
15	2447	23
16	2459	23
17	2465	23
18	2465	23
19	2557	23
20	4649	23
21	4720	23
22	4802	23
23	4878	23
24	7643	23

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
✓	0.2b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))
✓	0.5b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series1.1s (8.2%)

Counts

3 → 144

Calls

3 calls:

584.0ms	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))
311.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
241.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
28×	`pow1_binary64`
25×	`distribute-lft-out_binary64`
25×	`log-pow_binary64`
21×	`prod-diff_binary64`

Counts

3 → 94

Calls

3 calls:

8.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
5.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))
0.0ms	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))

simplify147.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

977×	`fma-neg_binary64`
440×	`associate--l+_binary64`
354×	`associate--r+_binary64`
345×	`associate-+l+_binary64`
318×	`unsub-neg_binary64`

Counts

238 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	362	5343
1	1090	4931
2	4053	4802
3	4581	4780
4	5237	4780

prune205.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	228	6	234
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	229	6	235

Error

0.1b

Counts

235 → 6

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 a (log.f64 (/.f64 1 t))) t))
	50.8b	(log.f64 (.f64 (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t)) (pow.f64 t (-.f64 a 1/2))))
	0.3b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
	0.6b	(-.f64 (+.f64 (log.f64 z) (.f64 a (log.f64 t))) (+.f64 t (+.f64 (log.f64 (/.f64 1 y)) (.f64 1/2 (log.f64 t)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (cbrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)))) (cbrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))
	32.3b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)) (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))

Compiler

Compiled 6307 to 2521 computations (60% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t)
✓	0.2b	(*.f64 a (log.f64 (/.f64 1 t)))
✓	0.4b	(+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t))))
✓	0.5b	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t)))))

series1.6s (11.3%)

Counts

4 → 76

Calls

4 calls:

813.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t)))))
435.0ms	(+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t))))
264.0ms	(*.f64 a (log.f64 (/.f64 1 t)))
54.0ms	(+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t)

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

85×	`log-prod_binary64`
57×	`*-un-lft-identity_binary64`
54×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`

Counts

4 → 165

Calls

4 calls:

7.0ms	(+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t)
6.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t)))))
5.0ms	(+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t))))
5.0ms	(*.f64 a (log.f64 (/.f64 1 t)))

simplify155.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-neg_binary64`
440×	`distribute-rgt-in_binary64`
242×	`cancel-sign-sub-inv_binary64`
239×	`sub-neg_binary64`
221×	`unsub-neg_binary64`

Counts

241 → 317

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	309	4210
1	813	3818
2	2529	3623
3	4469	3569
4	4981	3567
5	5045	3567

prune380.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	312	5	317
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	316	7	323

Error

0.0b

Counts

323 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 a (.f64 (cbrt.f64 (neg.f64 (log.f64 t))) (cbrt.f64 (neg.f64 (log.f64 t))))) (cbrt.f64 (log.f64 (/.f64 1 t)))) t))
	31.9b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (sqrt.f64 a) (*.f64 (neg.f64 (log.f64 t)) (sqrt.f64 a))) t))
	19.1b	(-.f64 (log.f64 (.f64 (+.f64 x y) (.f64 z (pow.f64 t -1/2)))) (+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t))
	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (+.f64 (.f64 a (neg.f64 (log.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (.f64 a (neg.f64 (log.f64 (cbrt.f64 t))))) t))
▶	0.3b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
	0.6b	(-.f64 (+.f64 (log.f64 z) (.f64 a (log.f64 t))) (+.f64 t (+.f64 (log.f64 (/.f64 1 y)) (.f64 1/2 (log.f64 t)))))
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) t))

Compiler

Compiled 10204 to 5813 computations (43% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
✓	0.3b	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
✓	0.6b	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
✓	0.6b	(cbrt.f64 z)

series3.2s (23%)

Counts

4 → 144

Calls

4 calls:

1.3s	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
1.0s	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
827.0ms	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
29.0ms	(cbrt.f64 z)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`log-prod_binary64`
19×	`*-un-lft-identity_binary64`
18×	`associate-+r+_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

6.0ms	(+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z)))
5.0ms	(+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z))))
2.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))

simplify126.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

489×	`associate-+l+_binary64`
437×	`associate--l+_binary64`
346×	`fma-neg_binary64`
329×	`+-commutative_binary64`
317×	`associate-+r+_binary64`

Counts

230 → 296

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	5941
1	1212	5295
2	4457	4872
3	5028	4872

prune442.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	313	1	314
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	314	7	321

Error

0.0b

Counts

321 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 a (.f64 (cbrt.f64 (neg.f64 (log.f64 t))) (cbrt.f64 (neg.f64 (log.f64 t))))) (cbrt.f64 (log.f64 (/.f64 1 t)))) t))
	31.9b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (sqrt.f64 a) (*.f64 (neg.f64 (log.f64 t)) (sqrt.f64 a))) t))
	19.1b	(-.f64 (log.f64 (.f64 (+.f64 x y) (.f64 z (pow.f64 t -1/2)))) (+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t))
▶	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (+.f64 (.f64 a (neg.f64 (log.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (.f64 a (neg.f64 (log.f64 (cbrt.f64 t))))) t))
✓	0.3b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
	0.3b	(+.f64 (/.f64 x y) (-.f64 (fma.f64 (log.f64 t) a (log.f64 z)) (-.f64 (fma.f64 1/2 (log.f64 t) t) (log.f64 y))))
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) t))

Compiler

Compiled 9456 to 4398 computations (53.5% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t))))
	0.5b	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 1/2 (log.f64 (/.f64 1 t)))))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.5b	(cbrt.f64 t)

series66.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

36.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
30.0ms	(cbrt.f64 t)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune529.0ms (3.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	281	7	288

Error

0.0b

Counts

288 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 a (.f64 (cbrt.f64 (neg.f64 (log.f64 t))) (cbrt.f64 (neg.f64 (log.f64 t))))) (cbrt.f64 (log.f64 (/.f64 1 t)))) t))
	19.1b	(-.f64 (log.f64 (.f64 (+.f64 x y) (.f64 z (pow.f64 t -1/2)))) (+.f64 (*.f64 a (log.f64 (/.f64 1 t))) t))
✓	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (+.f64 (.f64 a (neg.f64 (log.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))))) (.f64 a (neg.f64 (log.f64 (cbrt.f64 t))))) t))
✓	0.3b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (+.f64 (log.f64 (+.f64 y x)) (*.f64 2 (log.f64 (cbrt.f64 z)))) (log.f64 (cbrt.f64 z))) t))
	0.3b	(+.f64 (/.f64 x y) (-.f64 (fma.f64 (log.f64 t) a (log.f64 z)) (-.f64 (fma.f64 1/2 (log.f64 t) t) (log.f64 y))))
	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (+.f64 (.f64 a (neg.f64 (log.f64 (pow.f64 t 2/3)))) (*.f64 a (neg.f64 (log.f64 (cbrt.f64 t))))) t))
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 1/2 (log.f64 (/.f64 1 t))))) (+.f64 (.f64 (.f64 (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) (cbrt.f64 (neg.f64 (.f64 (log.f64 t) a)))) t))

Compiler

Compiled 11290 to 4052 computations (64.1% saved)

regimes2.7s (19.4%)

Accuracy

Total 0.3b remaining (86.6%)

Threshold costs 0.3b (86.6%)

Counts

172 → 1

Compiler

Compiled 57777 to 40457 computations (30% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-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	21	32
1	31	32
2	36	32
3	38	32
4	39	32
5	37	32

end158.0ms (1.1%)

Remove: (sort x y)
Compiler: Compiled 334 to 233 computations (30.2% saved)

Details

analyze486.0ms (3.5%)

sample2.2s (15.5%)

simplify214.0ms (1.5%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series1.1s (8.2%)

rewrite19.0ms (0.1%)

simplify147.0ms (1.1%)

prune205.0ms (1.5%)

localize17.0ms (0.1%)

series1.6s (11.3%)

rewrite34.0ms (0.2%)

simplify155.0ms (1.1%)

prune380.0ms (2.7%)

localize18.0ms (0.1%)

series3.2s (23%)

rewrite18.0ms (0.1%)

simplify126.0ms (0.9%)

prune442.0ms (3.2%)

localize27.0ms (0.2%)

series66.0ms (0.5%)

rewrite7.0ms (0.1%)

simplify65.0ms (0.5%)

prune529.0ms (3.8%)

regimes2.7s (19.4%)

simplify3.0ms (0%)

end158.0ms (1.1%)

Profiling