Details

analyze1.2s (15.5%)

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
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 (15%)

Results

1.0s	8256×	body	128	valid
93.0ms	727×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (1.5%)

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

8.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.6b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize7.0ms (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))
✓	8.4b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series73.0ms (0.9%)

Counts

3 → 78

Calls

3 calls:

59.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
9.0ms	(-.f64 x (*.f64 y z))
5.0ms	(-.f64 t (*.f64 a z))

rewrite12.0ms (0.2%)

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))

simplify124.0ms (1.6%)

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

prune133.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	9	164

Error

1.7b

Counts

164 → 9

Alt Table

Status	Error	Program
	36.6b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	35.7b	(.f64 (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))) (sqrt.f64 (/.f64 (-.f64 x (.f64 y z)) (-.f64 t (*.f64 a z)))))
	43.7b	(-.f64 (fma.f64 (/.f64 a t) (/.f64 (.f64 z x) t) (fma.f64 (/.f64 (.f64 a a) (pow.f64 t 3)) (.f64 z (.f64 z x)) (/.f64 x t))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y (.f64 z z)) t) (fma.f64 (/.f64 y t) z (/.f64 y (/.f64 (pow.f64 (/.f64 t z) 3) (*.f64 a a))))))
	8.8b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	42.3b	(/.f64 y a)
	38.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	26.4b	(/.f64 x (-.f64 t (*.f64 a z)))
▶	8.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
	36.6b	(neg.f64 (/.f64 (.f64 y z) (-.f64 t (.f64 z a))))

Compiler

Compiled 4321 to 1251 computations (71% saved)

localize9.0ms (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))))
✓	2.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	8.7b	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))

series133.0ms (1.7%)

Counts

3 → 114

Calls

3 calls:

70.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 y z) (-.f64 t (*.f64 a z))))
32.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 a z)))
31.0ms	(/.f64 x (-.f64 t (*.f64 a z)))

rewrite67.0ms (0.8%)

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:

19.0ms	(-.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)))

simplify378.0ms (4.7%)

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

prune426.0ms (5.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	510	3	513
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	515	7	522

Error

0.0b

Counts

522 → 7

Alt Table

Status	Error	Program
▶	6.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	36.6b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	7.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 z (cbrt.f64 (-.f64 t (.f64 a z))))))
	43.7b	(-.f64 (fma.f64 (/.f64 a t) (/.f64 (.f64 z x) t) (fma.f64 (/.f64 (.f64 a a) (pow.f64 t 3)) (.f64 z (.f64 z x)) (/.f64 x t))) (fma.f64 (/.f64 a t) (/.f64 (.f64 y (.f64 z z)) t) (fma.f64 (/.f64 y t) z (/.f64 y (/.f64 (pow.f64 (/.f64 t z) 3) (*.f64 a a))))))
	8.8b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	38.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	35.5b	(/.f64 (-.f64 y (/.f64 x z)) a)

Compiler

Compiled 23627 to 3770 computations (84% saved)

localize11.0ms (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 z (-.f64 t (*.f64 z a)))))
	2.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	2.2b	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
✓	8.5b	(/.f64 z (-.f64 t (*.f64 z a)))

series111.0ms (1.4%)

Counts

3 → 144

Calls

3 calls:

66.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
30.0ms	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
15.0ms	(/.f64 z (-.f64 t (*.f64 z a)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
15×	`fma-neg_binary64`

Counts

3 → 112

Calls

3 calls:

7.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
6.0ms	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
3.0ms	(/.f64 z (-.f64 t (*.f64 z a)))

simplify239.0ms (3%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-neg_binary64`
271×	`distribute-rgt-neg-in_binary64`
245×	`sub-neg_binary64`
210×	`associate-/l*_binary64`
210×	`times-frac_binary64`

Counts

256 → 254

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	8156
1	892	7648
2	3421	6954
3	4795	6953
4	4999	6953
5	4928	6953

prune228.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	321	3	324
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	324	7	331

Error

Counts

331 → 7

Alt Table

Status	Error	Program
	36.6b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	23.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 z y) t))
▶	1.8b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	8.8b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	38.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	35.5b	(/.f64 (-.f64 y (/.f64 x z)) a)
	6.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (.f64 z (/.f64 1 (-.f64 t (.f64 z a))))))

Compiler

Compiled 9828 to 2244 computations (77.2% saved)

localize11.0ms (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 y (-.f64 (/.f64 t z) a)))
	2.0b	(/.f64 x (-.f64 t (*.f64 a z)))
✓	2.7b	(/.f64 y (-.f64 (/.f64 t z) a))

series109.0ms (1.4%)

Counts

2 → 78

Calls

2 calls:

75.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
34.0ms	(/.f64 y (-.f64 (/.f64 t z) a))

rewrite153.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

620×	`add-sqr-sqrt_binary64`
591×	`times-frac_binary64`
463×	`*-un-lft-identity_binary64`
360×	`prod-diff_binary64`
348×	`add-cube-cbrt_binary64`

Counts

2 → 463

Calls

2 calls:

29.0ms	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
6.0ms	(/.f64 y (-.f64 (/.f64 t z) a))

simplify626.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
300×	`fma-udef_binary64`
271×	`fma-neg_binary64`
257×	`unsub-neg_binary64`
240×	`associate-+r-_binary64`

Counts

541 → 577

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	679	49084
1	1715	29863
2	4201	29743
3	5015	29743

prune425.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	684	0	684
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	684	7	691

Error

Counts

691 → 7

Alt Table

Status	Error	Program
	36.6b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	23.9b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (/.f64 (.f64 z y) t))
✓	1.8b	(-.f64 (/.f64 x (-.f64 t (*.f64 a z))) (/.f64 y (-.f64 (/.f64 t z) a)))
	8.8b	(/.f64 1 (/.f64 (-.f64 t (.f64 a z)) (-.f64 x (.f64 y z))))
	38.4b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 x (.f64 y z)) 3)) (-.f64 t (.f64 a z)))
	35.5b	(/.f64 (-.f64 y (/.f64 x z)) a)
	6.6b	(-.f64 (/.f64 x (-.f64 t (.f64 a z))) (.f64 y (.f64 z (/.f64 1 (-.f64 t (.f64 z a))))))

Compiler

Compiled 38568 to 5388 computations (86% saved)

regimes2.0s (24.8%)

Accuracy

Total 3.2b remaining (99.1%)

Threshold costs 0b (0%)

Counts

236 → 1

Compiler

Compiled 38308 to 20114 computations (47.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	22	22
2	38	22
3	48	22
4	55	22
5	57	22
6	57	22

end157.0ms (2%)

Compiler: Compiled 175 to 107 computations (38.9% saved)

Details

analyze1.2s (15.5%)

sample1.2s (15%)

simplify116.0ms (1.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series73.0ms (0.9%)

rewrite12.0ms (0.2%)

simplify124.0ms (1.6%)

prune133.0ms (1.7%)

localize9.0ms (0.1%)

series133.0ms (1.7%)

rewrite67.0ms (0.8%)

simplify378.0ms (4.7%)

prune426.0ms (5.3%)

localize11.0ms (0.1%)

series111.0ms (1.4%)

rewrite29.0ms (0.4%)

simplify239.0ms (3%)

prune228.0ms (2.8%)

localize11.0ms (0.1%)

series109.0ms (1.4%)

rewrite153.0ms (1.9%)

simplify626.0ms (7.8%)

prune425.0ms (5.3%)

regimes2.0s (24.8%)

simplify3.0ms (0%)

end157.0ms (2%)

Profiling