Details

analyze8.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.4s (25.2%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify55.0ms (1%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune4.0ms (0.1%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	47.6b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.7b	(/.f64 1 (*.f64 i i))

series11.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(/.f64 1 (*.f64 i i))
3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 134

Calls

3 calls:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
3.0ms	(/.f64 1 (*.f64 i i))

simplify131.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
408×	`associate-l_binary64`
361×	`fma-def_binary64`
294×	`associate-r_binary64`

Counts

170 → 196

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2573
1	382	2324
2	977	2089
3	3418	2089
4	4641	2081
5	4949	2081
6	4780	2081

prune223.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	194	4	198

Error

0.0b

Counts

198 → 4

Alt Table

Status	Error	Program
	19.1b	(/.f64 1/4 (+.f64 (fma.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (cbrt.f64 4) (neg.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 i i))) (.f64 (cbrt.f64 (/.f64 1 (.f64 i i))) (cbrt.f64 (/.f64 1 (.f64 i i))))))) (fma.f64 (neg.f64 (cbrt.f64 (/.f64 1 (.f64 i i)))) (.f64 (cbrt.f64 (/.f64 1 (.f64 i i))) (cbrt.f64 (/.f64 1 (.f64 i i)))) (.f64 (cbrt.f64 (/.f64 1 (.f64 i i))) (.f64 (cbrt.f64 (/.f64 1 (.f64 i i))) (cbrt.f64 (/.f64 1 (*.f64 i i))))))))
	30.7b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))
	25.6b	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
▶	0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 3894 to 2878 computations (26.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (/.f64 1 i))
✓	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))
✓	0.2b	(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))
✓	0.2b	(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))

series28.0ms (0.5%)

Counts

4 → 39

Calls

4 calls:

14.0ms	(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))
6.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))
6.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))
1.0ms	(-.f64 2 (/.f64 1 i))

rewrite78.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

212×	`add-sqr-sqrt_binary64`
177×	`times-frac_binary64`
163×	`*-un-lft-identity_binary64`
98×	`add-cube-cbrt_binary64`
54×	`associate-r_binary64`

Counts

4 → 277

Calls

4 calls:

29.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))
9.0ms	(/.f64 (*.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i)))
7.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i)))
6.0ms	(-.f64 2 (/.f64 1 i))

simplify179.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
815×	`times-frac_binary64`
267×	`associate-*r/_binary64`
261×	`associate-*l/_binary64`
231×	`associate-l_binary64`

Counts

316 → 419

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	8462
1	965	7103
2	3290	7073
3	5470	7073

prune517.0ms (9.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	417	2	419
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	419	4	423

Error

0.0b

Counts

423 → 4

Alt Table

Status	Error	Program
▶	23.4b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i))))))
	30.7b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))))
	25.6b	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
✓	0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 13636 to 11918 computations (12.6% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 1 i) (/.f64 1 i))
✓	0.4b	(/.f64 1 (pow.f64 i 3))
✓	0.5b	(/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3))))
✓	22.7b	(.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i)))))

series24.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

8.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3))))
7.0ms	(/.f64 1 (pow.f64 i 3))
6.0ms	(.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i)))))
3.0ms	(*.f64 (/.f64 1 i) (/.f64 1 i))

rewrite119.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

422×	`add-sqr-sqrt_binary64`
358×	`times-frac_binary64`
229×	`*-un-lft-identity_binary64`
130×	`add-cube-cbrt_binary64`
117×	`difference-of-squares_binary64`

Counts

4 → 410

Calls

4 calls:

34.0ms	(.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i)))))
15.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3))))
11.0ms	(*.f64 (/.f64 1 i) (/.f64 1 i))
7.0ms	(/.f64 1 (pow.f64 i 3))

simplify307.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

298×	`distribute-rgt-in_binary64`
281×	`distribute-lft-in_binary64`
223×	`*-commutative_binary64`
205×	`associate-r_binary64`
204×	`associate-l_binary64`

Counts

446 → 530

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	395	11136
1	1122	10321
2	3935	9781
3	4651	9781
4	4936	9781

prune809.0ms (14.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	530	0	530
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	530	4	534

Error

0.0b

Counts

534 → 4

Alt Table

Status	Error	Program
✓	23.4b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i))))))
	30.7b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))))
▶	25.6b	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
✓	0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 26823 to 23315 computations (13.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 i 4))
✓	0.3b	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
	0.7b	(/.f64 1 (*.f64 i i))
✓	25.5b	(/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4))

series9.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
3.0ms	(/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4))
2.0ms	(/.f64 1 (pow.f64 i 4))

rewrite134.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

675×	`times-frac_binary64`
567×	`add-sqr-sqrt_binary64`
516×	`*-un-lft-identity_binary64`
182×	`difference-of-squares_binary64`
177×	`add-cube-cbrt_binary64`

Counts

3 → 435

Calls

3 calls:

24.0ms	(/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4))
24.0ms	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
3.0ms	(/.f64 1 (pow.f64 i 4))

simplify501.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

447×	`times-frac_binary64`
420×	`fma-def_binary64`
328×	`distribute-rgt-in_binary64`
306×	`distribute-lft-in_binary64`
299×	`fma-neg_binary64`

Counts

459 → 443

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	405	16687
1	906	16267
2	2780	16053
3	4373	15405
4	4709	15405
5	4972	15405
6	4885	15405

prune509.0ms (9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	483	0	483
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	483	4	487

Error

0.0b

Counts

487 → 4

Alt Table

Status	Error	Program
✓	23.4b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (.f64 (/.f64 (cbrt.f64 1/4) (-.f64 8 (/.f64 1 (pow.f64 i 3)))) (+.f64 (.f64 2 2) (+.f64 (.f64 (/.f64 1 i) (/.f64 1 i)) (.f64 2 (/.f64 1 i))))))
	30.7b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 1/4 (*.f64 i i) (pow.f64 i 4))))
✓	25.6b	(/.f64 1/4 (/.f64 (-.f64 16 (/.f64 1 (pow.f64 i 4))) (+.f64 (/.f64 1 (*.f64 i i)) 4)))
✓	0.2b	(.f64 (/.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (+.f64 2 (/.f64 1 i))) (/.f64 (cbrt.f64 1/4) (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 15955 to 12509 computations (21.6% saved)

regimes397.0ms (7%)

Accuracy

Total 0.1b remaining (97.5%)

Threshold costs 0.1b (97.5%)

Counts

193 → 1

Compiler

Compiled 7160 to 6039 computations (15.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	18	26
2	24	26
3	26	26
4	27	26
5	25	26

end99.0ms (1.8%)

Compiler: Compiled 131 to 111 computations (15.3% saved)

Details

analyze8.0ms (0.1%)

sample1.4s (25.2%)

simplify55.0ms (1%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series11.0ms (0.2%)

rewrite23.0ms (0.4%)

simplify131.0ms (2.3%)

prune223.0ms (4%)

localize12.0ms (0.2%)

series28.0ms (0.5%)

rewrite78.0ms (1.4%)

simplify179.0ms (3.2%)

prune517.0ms (9.2%)

localize21.0ms (0.4%)

series24.0ms (0.4%)

rewrite119.0ms (2.1%)

simplify307.0ms (5.5%)

prune809.0ms (14.4%)

localize9.0ms (0.2%)

series9.0ms (0.2%)

rewrite134.0ms (2.4%)

simplify501.0ms (8.9%)

prune509.0ms (9%)

regimes397.0ms (7%)

simplify2.0ms (0%)

end99.0ms (1.8%)

Profiling