Details

analyze492.0ms (2.6%)

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%	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)

sample2.3s (12.1%)

Symmetry

(sort x y)

Results

1.5s	8256×	body	128	valid
728.0ms	4515×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify214.0ms (1.1%)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.3b	(+.f64 (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t) (*.f64 (-.f64 a 1/2) (log.f64 t)))
▶	0.3b	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))

Compiler

Compiled 118 to 76 computations (35.6% 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))
✓	0.6b	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

series1.2s (6.5%)

Counts

3 → 144

Calls

3 calls:

647.0ms	(fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))
342.0ms	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t)
254.0ms	(+.f64 (log.f64 (+.f64 x y)) (log.f64 z))

rewrite22.0ms (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:

7.0ms	(-.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))

simplify156.0ms (0.8%)

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

prune226.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	228	6	234
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	6	236

Error

0.1b

Counts

236 → 6

Alt Table

Status	Error	Program
	41.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))
	1.4b	(.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))))
	38.8b	(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))))
▶	0.2b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t))
	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
	56.0b	(log.f64 (.f64 (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t)) (pow.f64 t (-.f64 a 1/2))))

Compiler

Compiled 6315 to 2511 computations (60.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t)
✓	0.1b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t))
✓	0.2b	(*.f64 (log.f64 t) (-.f64 a 1/2))
✓	0.3b	(+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2)))

series2.2s (11.3%)

Counts

4 → 156

Calls

4 calls:

880.0ms	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t))
690.0ms	(+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2)))
536.0ms	(-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t)
63.0ms	(*.f64 (log.f64 t) (-.f64 a 1/2))

rewrite42.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
54×	`prod-diff_binary64`
53×	`add-cube-cbrt_binary64`
40×	`associate-+r+_binary64`

Counts

4 → 173

Calls

4 calls:

10.0ms	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t))
6.0ms	(*.f64 (log.f64 t) (-.f64 a 1/2))
5.0ms	(+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2)))
5.0ms	(-.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 t) (-.f64 a 1/2))) t)

simplify192.0ms (1%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-neg_binary64`
286×	`+-commutative_binary64`
254×	`associate--l+_binary64`
245×	`associate--r+_binary64`
231×	`fma-def_binary64`

Counts

329 → 322

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	430	6957
1	1072	5939
2	3840	5917
3	4964	5917
4	4949	5917

prune429.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	316	6	322
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	319	9	328

Error

0.0b

Counts

328 → 9

Alt Table

Status	Error	Program
	16.4b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2))) t))
	34.4b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (+.f64 (log.f64 z) (.f64 (fma.f64 (sqrt.f64 a) (sqrt.f64 a) (neg.f64 (.f64 1/2 1))) (log.f64 t))) (.f64 (fma.f64 (neg.f64 1/2) 1 (.f64 1/2 1)) (log.f64 t))) t))
	22.5b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 t) (-.f64 a 1/2) (log.f64 z)) 3)) t))
	22.4b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (/.f64 (.f64 (log.f64 t) (-.f64 (pow.f64 a 3) 1/8)) (+.f64 (.f64 a a) (+.f64 (.f64 1/2 1/2) (.f64 a 1/2))))) t))
	41.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))
▶	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
	56.0b	(log.f64 (.f64 (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t)) (pow.f64 t (-.f64 a 1/2))))
	0.7b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (.f64 (.f64 (log.f64 t) (*.f64 (cbrt.f64 (-.f64 a 1/2)) (cbrt.f64 (-.f64 a 1/2)))) (cbrt.f64 (-.f64 a 1/2)))) t))
	30.1b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (.f64 (sqrt.f64 (log.f64 t)) (.f64 (sqrt.f64 (log.f64 t)) (-.f64 a 1/2)))) t))

Compiler

Compiled 9298 to 4412 computations (52.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (*.f64 1/2 (log.f64 t)))
✓	0.1b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
✓	0.3b	(*.f64 a (log.f64 t))
✓	0.3b	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 a (log.f64 t))))

series2.1s (11.1%)

Counts

4 → 104

Calls

4 calls:

1.0s	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 a (log.f64 t))))
861.0ms	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
215.0ms	(*.f64 a (log.f64 t))
8.0ms	(+.f64 t (*.f64 1/2 (log.f64 t)))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
23×	`add-log-exp_binary64`
23×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

4 → 129

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
6.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (*.f64 a (log.f64 t))))
3.0ms	(*.f64 a (log.f64 t))
3.0ms	(+.f64 t (*.f64 1/2 (log.f64 t)))

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-neg_binary64`
351×	`associate--l+_binary64`
307×	`associate-+l+_binary64`
294×	`associate--r+_binary64`
231×	`associate-+r+_binary64`

Counts

233 → 293

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	6668
1	1198	5760
2	4797	5756
3	5167	5756

prune290.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	295	7	302

Error

0.0b

Counts

302 → 7

Alt Table

Status	Error	Program
	16.4b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2))) t))
	22.5b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (cbrt.f64 (pow.f64 (fma.f64 (log.f64 t) (-.f64 a 1/2) (log.f64 z)) 3)) t))
	41.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))
✓	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
	56.0b	(log.f64 (.f64 (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t)) (pow.f64 t (-.f64 a 1/2))))
	0.6b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (cbrt.f64 a) (log.f64 t))))) (+.f64 t (.f64 1/2 (log.f64 t))))
▶	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 a (log.f64 (cbrt.f64 t)))))) (+.f64 t (.f64 1/2 (log.f64 t))))

Compiler

Compiled 9349 to 3394 computations (63.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series4.3s (22.7%)

Counts

4 → 120

Calls

4 calls:

2.0s	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 a (log.f64 (cbrt.f64 t))))))
1.2s	(.f64 a (.f64 2 (log.f64 (cbrt.f64 t))))
1.1s	(+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 a (log.f64 (cbrt.f64 t))))
33.0ms	(cbrt.f64 t)

rewrite41.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`log-prod_binary64`
54×	`distribute-lft-in_binary64`
54×	`distribute-rgt-in_binary64`
41×	`*-un-lft-identity_binary64`
33×	`cbrt-prod_binary64`

Counts

4 → 140

Calls

4 calls:

12.0ms	(+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 a (log.f64 (cbrt.f64 t))))))
11.0ms	(+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (*.f64 a (log.f64 (cbrt.f64 t))))
5.0ms	(.f64 a (.f64 2 (log.f64 (cbrt.f64 t))))
1.0ms	(cbrt.f64 t)

simplify165.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
245×	`sub-neg_binary64`
245×	`fma-def_binary64`
192×	`+-commutative_binary64`

Counts

260 → 272

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	5104
1	853	4506
2	2834	4025
3	4508	4005
4	4957	4005

prune374.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	290	7	297

Error

Counts

297 → 7

Alt Table

Status	Error	Program
	41.2b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))) (sqrt.f64 (fma.f64 (-.f64 a 1/2) (log.f64 t) (-.f64 (+.f64 (log.f64 (+.f64 x y)) (log.f64 z)) t))))
	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (fma.f64 a (.f64 2 (log.f64 (cbrt.f64 t))) (.f64 a (log.f64 (cbrt.f64 t)))))) (+.f64 t (*.f64 1/2 (log.f64 t))))
✓	0.2b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (.f64 a (log.f64 t)))) (+.f64 t (.f64 1/2 (log.f64 t))))
	56.0b	(log.f64 (.f64 (/.f64 (.f64 z (+.f64 y x)) (exp.f64 t)) (pow.f64 t (-.f64 a 1/2))))
	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 y x)) (+.f64 (log.f64 z) (+.f64 (.f64 a (.f64 2 (log.f64 (cbrt.f64 t)))) (.f64 a (log.f64 (pow.f64 t 1/3)))))) (+.f64 t (.f64 1/2 (log.f64 t))))
	16.4b	(+.f64 (log.f64 (+.f64 y x)) (-.f64 (+.f64 (log.f64 z) (/.f64 (*.f64 (log.f64 t) (fma.f64 a a -1/4)) (+.f64 a 1/2))) t))
	0.3b	(-.f64 (+.f64 (log.f64 (+.f64 x y)) (fma.f64 3 (.f64 a (.f64 -1/3 (neg.f64 (log.f64 t)))) (log.f64 z))) (+.f64 t (*.f64 1/2 (log.f64 t))))

Compiler

Compiled 9915 to 4163 computations (58% saved)

regimes3.9s (20.5%)

Accuracy

Total 0.2b remaining (87.7%)

Threshold costs 0.2b (87.7%)

Counts

247 → 1

Compiler

Compiled 83275 to 55238 computations (33.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	25	32
2	31	32
3	33	32
4	34	32
5	33	32

end148.0ms (0.8%)

Remove: (sort x y)
Compiler: Compiled 302 to 198 computations (34.4% saved)

Details

analyze492.0ms (2.6%)

sample2.3s (12.1%)

simplify214.0ms (1.1%)

prune4.0ms (0%)

localize13.0ms (0.1%)

series1.2s (6.5%)

rewrite22.0ms (0.1%)

simplify156.0ms (0.8%)

prune226.0ms (1.2%)

localize15.0ms (0.1%)

series2.2s (11.3%)

rewrite42.0ms (0.2%)

simplify192.0ms (1%)

prune429.0ms (2.2%)

localize17.0ms (0.1%)

series2.1s (11.1%)

rewrite34.0ms (0.2%)

simplify152.0ms (0.8%)

prune290.0ms (1.5%)

localize22.0ms (0.1%)

series4.3s (22.7%)

rewrite41.0ms (0.2%)

simplify165.0ms (0.9%)

prune374.0ms (1.9%)

regimes3.9s (20.5%)

simplify3.0ms (0%)

end148.0ms (0.8%)

Profiling