Details

analyze1.2s (14.2%)

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
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
13.2%	86.5%	0.2%	10
17%	82.8%	0.2%	11
18.2%	81.5%	0.2%	12
21.7%	78.1%	0.2%	13
32.9%	66.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (13.7%)

Results

1.0s	8256×	body	128	valid
80.0ms	720×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1539×	`fma-neg_binary64`
1346×	`fma-def_binary64`
1046×	`div-sub_binary64`
750×	`associate-/r/_binary64`
420×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	26	16
2	49	16
3	96	16
4	183	16
5	339	16
6	657	16
7	1726	16
8	2830	16
9	2687	16
10	2951	16
11	3172	16
12	3258	16
13	4297	16
14	5213	16

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

11.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	0.0b	(-.f64 t (*.f64 a z))
✓	11.1b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series75.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

65.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 t (*.f64 a z))
5.0ms	(-.f64 x (*.f64 y z))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 t (*.f64 a z))
2.0ms	(-.f64 x (*.f64 y z))

simplify113.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

886×	`fma-def_binary64`
731×	`cancel-sign-sub-inv_binary64`
207×	`sub-neg_binary64`
192×	`fma-neg_binary64`
173×	`times-frac_binary64`

Counts

152 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	4118
1	671	3825
2	2454	3679
3	4965	3679
4	4935	3679

prune124.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Error

3.4b

Counts

164 → 8

Alt Table

Status	Error	Program
	12.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	30.0b	(/.f64 x (-.f64 t (*.f64 a z)))
	35.8b	(.f64 (/.f64 (-.f64 x (.f64 y z)) (.f64 (-.f64 t (.f64 z a)) (fma.f64 z a t))) (+.f64 t (*.f64 a z)))
	41.2b	(/.f64 y a)
	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
▶	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	36.9b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (/.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	32.7b	(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 y z) (.f64 y z))) (.f64 (-.f64 t (.f64 z a)) (fma.f64 y z x)))

Compiler

Compiled 4221 to 1207 computations (71.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 a z))
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
✓	3.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	11.4b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series153.0ms (1.8%)

Counts

3 → 114

Calls

3 calls:

78.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
39.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
36.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`times-frac_binary64`
135×	`prod-diff_binary64`
120×	`add-sqr-sqrt_binary64`
117×	`*-un-lft-identity_binary64`
115×	`add-cube-cbrt_binary64`

Counts

3 → 236

Calls

3 calls:

16.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
4.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
3.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

simplify350.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

441×	`fma-neg_binary64`
243×	`unsub-neg_binary64`
216×	`associate-/l*_binary64`
216×	`times-frac_binary64`
203×	`associate-l_binary64`

Counts

350 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	21196
1	1104	16095
2	4152	15759
3	4952	15759
4	5052	15759

prune353.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	509	4	513
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	514	7	521

Error

Counts

521 → 7

Alt Table

Status	Error	Program
	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
▶	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
	7.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)
	11.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (fma.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (cbrt.f64 t) (neg.f64 (.f64 z a)))))

Compiler

Compiled 23511 to 3725 computations (84.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
✓	2.9b	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
	3.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	8.0b	(/.f64 (-.f64 t (*.f64 a z)) z)

series113.0ms (1.3%)

Counts

3 → 144

Calls

3 calls:

68.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
36.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
8.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)

rewrite310.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Rules

1556×	`times-frac_binary64`
949×	`add-sqr-sqrt_binary64`
934×	`*-un-lft-identity_binary64`
928×	`add-cube-cbrt_binary64`
660×	`prod-diff_binary64`

Counts

3 → 845

Calls

3 calls:

42.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (/.f64 (-.f64 t (.f64 a z)) z)))
5.0ms	(/.f64 y (/.f64 (-.f64 t (*.f64 a z)) z))
3.0ms	(/.f64 (-.f64 t (*.f64 a z)) z)

simplify1.4s (16.3%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
600×	`fma-udef_binary64`
521×	`unsub-neg_binary64`
200×	`sub-neg_binary64`
176×	`distribute-neg-frac_binary64`

Counts

989 → 1424

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1154	97355
1	2883	70114
2	4679	68596
3	5859	68596

prune842.0ms (9.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1493	1	1494
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	1495	6	1501

Error

Counts

1501 → 6

Alt Table

Status	Error	Program
▶	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))
	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	7.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)

Compiler

Compiled 102117 to 12680 computations (87.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))
✓	2.9b	(/.f64 y (.f64 (-.f64 t (.f64 a z)) (/.f64 1 z)))
	3.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	8.2b	(.f64 (-.f64 t (.f64 a z)) (/.f64 1 z))

series134.0ms (1.6%)

Counts

3 → 144

Calls

3 calls:

85.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))
40.0ms	(/.f64 y (.f64 (-.f64 t (.f64 a z)) (/.f64 1 z)))
9.0ms	(.f64 (-.f64 t (.f64 a z)) (/.f64 1 z))

rewrite91.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`prod-diff_binary64`
189×	`times-frac_binary64`
155×	`add-sqr-sqrt_binary64`
146×	`*-un-lft-identity_binary64`
143×	`add-cube-cbrt_binary64`

Counts

3 → 317

Calls

3 calls:

19.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))
8.0ms	(.f64 (-.f64 t (.f64 a z)) (/.f64 1 z))
6.0ms	(/.f64 y (.f64 (-.f64 t (.f64 a z)) (/.f64 1 z)))

simplify383.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-neg_binary64`
257×	`times-frac_binary64`
249×	`associate-l_binary64`
205×	`associate-r_binary64`
204×	`associate-/r*_binary64`

Counts

461 → 521

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	556	25829
1	1325	19986
2	4461	19410
3	4982	19410

prune513.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	591	0	591
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	591	6	597

Error

Counts

597 → 6

Alt Table

Status	Error	Program
✓	7.5b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 y (.f64 (-.f64 t (*.f64 a z)) (/.f64 1 z))))
	11.5b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
	12.0b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
✓	11.4b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	7.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.0b	(/.f64 (-.f64 y (/.f64 x z)) a)

Compiler

Compiled 29602 to 8471 computations (71.4% saved)

regimes894.0ms (10.4%)

Accuracy

Total 1.7b remaining (97.9%)

Threshold costs 0b (0%)

Counts

106 → 3

Compiler

Compiled 14927 to 8335 computations (44.2% saved)

bsearch23.0ms (0.3%)

Steps

Iters	Range		Point
4	2.0291238249150153e-170	2.1487811174216832e-162	6.890244941997684e-165
3	-1.907992320878839e-74	-2.1735319764344004e-75	-5.011713591805735e-75

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	45	52
2	66	52
3	78	52
4	85	52
5	86	52
6	85	52

end85.0ms (1%)

Compiler: Compiled 196 to 113 computations (42.3% saved)

Details

analyze1.2s (14.2%)

sample1.2s (13.7%)

simplify120.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series75.0ms (0.9%)

rewrite12.0ms (0.1%)

simplify113.0ms (1.3%)

prune124.0ms (1.4%)

localize8.0ms (0.1%)

series153.0ms (1.8%)

rewrite63.0ms (0.7%)

simplify350.0ms (4.1%)

prune353.0ms (4.1%)

localize8.0ms (0.1%)

series113.0ms (1.3%)

rewrite310.0ms (3.6%)

simplify1.4s (16.3%)

prune842.0ms (9.8%)

localize13.0ms (0.1%)

series134.0ms (1.6%)

rewrite91.0ms (1.1%)

simplify383.0ms (4.5%)

prune513.0ms (6%)

regimes894.0ms (10.4%)

bsearch23.0ms (0.3%)

simplify4.0ms (0%)

end85.0ms (1%)

Profiling