Details

analyze1.2s (18.1%)

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 (17.8%)

Results

1.0s	8256×	body	128	valid
103.0ms	736×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (1.7%)

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

12.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.1b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

Compiler

Compiled 59 to 33 computations (44.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	11.8b	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))

series76.0ms (1.1%)

Counts

2 → 69

Calls

2 calls:

71.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
5.0ms	(-.f64 x (*.f64 y z))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 54

Calls

2 calls:

6.0ms	(/.f64 (-.f64 x (.f64 y z)) (-.f64 t (.f64 a z)))
2.0ms	(-.f64 x (*.f64 y z))

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

807×	`fma-def_binary64`
729×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
190×	`div-sub_binary64`
182×	`fma-neg_binary64`

Counts

123 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	205	3797
1	628	3572
2	2362	3442
3	4895	3442
4	5108	3442

prune101.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	8	127

Error

3.6b

Counts

127 → 8

Alt Table

Status	Error	Program
	36.3b	(/.f64 (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (-.f64 t (.f64 a z)))) (sqrt.f64 (-.f64 t (*.f64 a z))))
	32.3b	(/.f64 x (-.f64 t (*.f64 a z)))
	43.6b	(/.f64 y a)
	12.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (-.f64 x (.f64 y z)) (cbrt.f64 (-.f64 t (.f64 a z)))))
	13.0b	(.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (-.f64 t (.f64 z a))))
	13.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 x (.f64 y z)))) (.f64 (cbrt.f64 (-.f64 t (.f64 a z))) (cbrt.f64 (-.f64 t (.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 x (.f64 y z))) (cbrt.f64 (-.f64 t (*.f64 a z)))))
	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
▶	12.1b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))

Compiler

Compiled 3682 to 1102 computations (70.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
✓	3.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	12.7b	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))

series166.0ms (2.4%)

Counts

3 → 156

Calls

3 calls:

84.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
44.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))
38.0ms	(/.f64 x (-.f64 t (*.f64 z a)))

rewrite66.0ms (1%)

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:

13.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
6.0ms	(/.f64 (.f64 y z) (-.f64 t (.f64 z a)))
3.0ms	(/.f64 x (-.f64 t (*.f64 z a)))

simplify403.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

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

Counts

392 → 384

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	442	20992
1	1109	16821
2	4155	16485
3	4955	16485
4	5053	16485

prune268.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	379	5	384
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	386	6	392

Error

0.0b

Counts

392 → 6

Alt Table

Status	Error	Program
	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
▶	8.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.3b	(/.f64 (-.f64 y (/.f64 x z)) a)
	8.9b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (/.f64 y (/.f64 (-.f64 t (.f64 z a)) z)))
	12.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) x)) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
	10.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (.f64 z a))))))

Compiler

Compiled 20361 to 3254 computations (84% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
✓	2.9b	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
	3.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	8.3b	(/.f64 z (-.f64 t (*.f64 z a)))

series148.0ms (2.2%)

Counts

3 → 144

Calls

3 calls:

82.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
41.0ms	(.f64 y (/.f64 z (-.f64 t (.f64 z a))))
25.0ms	(/.f64 z (-.f64 t (*.f64 z a)))

rewrite27.0ms (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 → 113

Calls

3 calls:

7.0ms	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.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)))

simplify195.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-neg_binary64`
264×	`distribute-rgt-neg-in_binary64`
243×	`sub-neg_binary64`
208×	`associate-/l*_binary64`
206×	`times-frac_binary64`

Counts

257 → 256

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	317	8163
1	888	7655
2	3396	6961
3	4760	6960
4	4939	6960

prune208.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	307	6	313

Error

0.0b

Counts

313 → 6

Alt Table

Status	Error	Program
	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
✓	8.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.3b	(/.f64 (-.f64 y (/.f64 x z)) a)
	33.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 (/.f64 t z) a))))
	12.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) x)) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
▶	10.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (.f64 z a))))))

Compiler

Compiled 9313 to 2121 computations (77.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a)))))
	3.7b	(/.f64 x (-.f64 t (*.f64 z a)))
✓	3.7b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (*.f64 z a)))))
✓	8.8b	(cbrt.f64 (-.f64 t (*.f64 z a)))

series830.0ms (12.1%)

Counts

3 → 132

Calls

3 calls:

727.0ms

(/.f64 y (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a)))))

59.0ms

(cbrt.f64 (-.f64 t (*.f64 z a)))

43.0ms

(*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (*.f64 z a)))))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
31×	`times-frac_binary64`
29×	`add-exp-log_binary64`
28×	`cbrt-div_binary64`
24×	`associate-r_binary64`

Counts

3 → 117

Calls

3 calls:

19.0ms

(*.f64 (/.f64 y (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (*.f64 z a)))))

7.0ms

(/.f64 y (*.f64 (cbrt.f64 (-.f64 t (*.f64 z a))) (cbrt.f64 (-.f64 t (*.f64 z a)))))

2.0ms

(cbrt.f64 (-.f64 t (*.f64 z a)))

simplify166.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

763×	`times-frac_binary64`
508×	`associate-/r*_binary64`
477×	`associate-/l*_binary64`
283×	`fma-def_binary64`
208×	`*-commutative_binary64`

Counts

249 → 336

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	580	10388
1	1820	9199
2	5139	9199

prune443.0ms (6.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	545	0	545
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	545	6	551

Error

0.0b

Counts

551 → 6

Alt Table

Status	Error	Program
	12.2b	(.f64 (-.f64 x (.f64 y z)) (/.f64 1 (-.f64 t (*.f64 a z))))
✓	8.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 y (/.f64 z (-.f64 t (*.f64 z a)))))
	34.3b	(/.f64 (-.f64 y (/.f64 x z)) a)
	33.6b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (sqrt.f64 y) (/.f64 (sqrt.f64 y) (-.f64 (/.f64 t z) a))))
	12.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 t (.f64 z a)) x)) (/.f64 (.f64 y z) (-.f64 t (*.f64 z a))))
✓	10.4b	(-.f64 (/.f64 x (-.f64 t (.f64 z a))) (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 t (.f64 z a))) (cbrt.f64 (-.f64 t (.f64 z a))))) (/.f64 z (cbrt.f64 (-.f64 t (.f64 z a))))))

Compiler

Compiled 28212 to 8514 computations (69.8% saved)

regimes826.0ms (12.1%)

Accuracy

Total 1.7b remaining (98.2%)

Threshold costs 0b (0%)

Counts

121 → 3

Compiler

Compiled 17828 to 9456 computations (47% saved)

bsearch45.0ms (0.7%)

Steps

Iters	Range		Point
5	2.9074796888936914e-65	1.9274288652002883e-56	1.4041294918823914e-60
10	-5.318884613713878e+42	-2.9360723036365897e+32	-2.9630879677667778e+32

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`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	31	70
1	56	70
2	72	70
3	81	70
4	84	70
5	83	70

end97.0ms (1.4%)

Compiler: Compiled 241 to 130 computations (46.1% saved)

Details

analyze1.2s (18.1%)

sample1.2s (17.8%)

simplify118.0ms (1.7%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series76.0ms (1.1%)

rewrite11.0ms (0.2%)

simplify108.0ms (1.6%)

prune101.0ms (1.5%)

localize9.0ms (0.1%)

series166.0ms (2.4%)

rewrite66.0ms (1%)

simplify403.0ms (5.9%)

prune268.0ms (3.9%)

localize9.0ms (0.1%)

series148.0ms (2.2%)

rewrite27.0ms (0.4%)

simplify195.0ms (2.8%)

prune208.0ms (3%)

localize12.0ms (0.2%)

series830.0ms (12.1%)

rewrite45.0ms (0.7%)

simplify166.0ms (2.4%)

prune443.0ms (6.5%)

regimes826.0ms (12.1%)

bsearch45.0ms (0.7%)

simplify4.0ms (0.1%)

end97.0ms (1.4%)

Profiling