Details

analyze918.0ms (13.9%)

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
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample86.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort y t)

Results

9.0ms	256×	body	128	valid
0.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

8.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series136.0ms (2%)

Counts

2 → 84

Calls

2 calls:

124.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
12.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
8.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

simplify163.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune255.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
▶	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	8.1b	(/.f64 x (*.f64 (-.f64 t z) (-.f64 y z)))
	26.2b	(/.f64 x (cbrt.f64 (.f64 (.f64 (.f64 (-.f64 y z) (-.f64 t z)) (.f64 (-.f64 y z) (-.f64 t z))) (*.f64 (-.f64 y z) (-.f64 t z)))))
	24.4b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	8.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	8.5b	(/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (.f64 (-.f64 y z) (-.f64 t z)) (cbrt.f64 x)))
	32.9b	(/.f64 (sqrt.f64 x) (/.f64 (-.f64 t z) (/.f64 (sqrt.f64 x) (-.f64 y z))))
	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))

Compiler

Compiled 5800 to 2151 computations (62.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

series133.0ms (2%)

Counts

2 → 72

Calls

2 calls:

116.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
17.0ms	(/.f64 x (-.f64 y z))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
176×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out--_binary64`

Counts

2 → 189

Calls

2 calls:

9.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
4.0ms	(/.f64 x (-.f64 y z))

simplify138.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

540×	`times-frac_binary64`
486×	`associate-/r*_binary64`
474×	`associate-/l*_binary64`
312×	`associate-/l/_binary64`
154×	`fma-def_binary64`

Counts

261 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	526	8754
1	1583	8488
2	5002	8488

prune222.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	266	4	270
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	272	7	279

Error

Counts

279 → 7

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y z))) (-.f64 t z)))
	23.5b	(/.f64 (/.f64 (/.f64 x (-.f64 y z)) (sqrt.f64 (-.f64 t z))) (sqrt.f64 (-.f64 t z)))
	8.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
	3.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	7.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))
	3.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))

Compiler

Compiled 7724 to 2369 computations (69.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))
✓	0.5b	(cbrt.f64 x)
✓	0.5b	(cbrt.f64 (-.f64 y z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

series153.0ms (2.3%)

Counts

4 → 72

Calls

4 calls:

49.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
40.0ms	(*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))
32.0ms	(cbrt.f64 x)
31.0ms	(cbrt.f64 (-.f64 y z))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`cbrt-prod_binary64`
48×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 130

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(cbrt.f64 (-.f64 y z))
1.0ms	(cbrt.f64 x)

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-def_binary64`
510×	`cancel-sign-sub-inv_binary64`
329×	`unswap-sqr_binary64`
274×	`associate-r_binary64`
261×	`fma-neg_binary64`

Counts

202 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	3700
1	710	3504
2	2315	3341
3	4818	3304
4	4958	3304

prune294.0ms (4.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	365	7	372

Error

Counts

372 → 7

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y z))) (-.f64 t z)))
	23.5b	(/.f64 (/.f64 (/.f64 x (-.f64 y z)) (sqrt.f64 (-.f64 t z))) (sqrt.f64 (-.f64 t z)))
	8.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
▶	3.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	7.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))
	3.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))

Compiler

Compiled 14176 to 4175 computations (70.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 t z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.6b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

series173.0ms (2.6%)

Counts

3 → 120

Calls

3 calls:

117.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
40.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))
17.0ms	(/.f64 x (-.f64 t z))

rewrite170.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1260×	`times-frac_binary64`
844×	`*-un-lft-identity_binary64`
844×	`add-sqr-sqrt_binary64`
468×	`add-cube-cbrt_binary64`
188×	`distribute-lft-out--_binary64`

Counts

3 → 660

Calls

3 calls:

21.0ms	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
9.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))
4.0ms	(/.f64 x (-.f64 t z))

simplify397.0ms (6%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-/r/_binary64`
672×	`times-frac_binary64`
271×	`associate-/l/_binary64`
167×	`fma-def_binary64`
153×	`distribute-rgt-in_binary64`

Counts

780 → 773

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	715	24963
1	2044	24462
2	5306	24462

prune520.0ms (7.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	773	7	780

Error

Counts

780 → 7

Alt Table

Status	Error	Program
✓	1.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (-.f64 y z))) (-.f64 t z)))
	23.5b	(/.f64 (/.f64 (/.f64 x (-.f64 y z)) (sqrt.f64 (-.f64 t z))) (sqrt.f64 (-.f64 t z)))
	8.1b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 t z))))
✓	3.1b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	1.6b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	7.2b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))
	3.3b	(.f64 (/.f64 x (.f64 (cbrt.f64 (-.f64 t z)) (cbrt.f64 (-.f64 t z)))) (/.f64 (/.f64 1 (-.f64 y z)) (cbrt.f64 (-.f64 t z))))

Compiler

Compiled 21902 to 6096 computations (72.2% saved)

regimes1.5s (22.6%)

Accuracy

Total 1.1b remaining (97.8%)

Threshold costs 0b (0%)

Counts

191 → 1

Compiler

Compiled 25197 to 14818 computations (41.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	15	43
1	19	43
2	25	43
3	27	43
4	28	43
5	28	43

end7.0ms (0.1%)

Compiler: Compiled 93 to 42 computations (54.8% saved)

sample1.0s (15.7%)

Algorithm

1×

intervals

Results

391.0ms	8000×	body	128	valid
19.0ms	423×	body	128	invalid

Compiler

Compiled 185 to 104 computations (43.8% saved)

Details

analyze918.0ms (13.9%)

sample86.0ms (1.3%)

simplify77.0ms (1.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series136.0ms (2%)

rewrite25.0ms (0.4%)

simplify163.0ms (2.5%)

prune255.0ms (3.8%)

localize7.0ms (0.1%)

series133.0ms (2%)

rewrite36.0ms (0.5%)

simplify138.0ms (2.1%)

prune222.0ms (3.4%)

localize15.0ms (0.2%)

series153.0ms (2.3%)

rewrite30.0ms (0.5%)

simplify120.0ms (1.8%)

prune294.0ms (4.4%)

localize9.0ms (0.1%)

series173.0ms (2.6%)

rewrite170.0ms (2.6%)

simplify397.0ms (6%)

prune520.0ms (7.8%)

regimes1.5s (22.6%)

simplify3.0ms (0.1%)

end7.0ms (0.1%)

sample1.0s (15.7%)

Profiling