Details

analyze1.1s (9.8%)

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
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
25%	74.9%	0.2%	7
37.4%	62.4%	0.2%	8
37.4%	62.4%	0.2%	9
37.4%	62.4%	0.2%	10
37.4%	62.4%	0.2%	11
51.5%	48.3%	0.2%	12
56.9%	42.9%	0.2%	13
56.9%	42.9%	0.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (11.9%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify158.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

prune3.0ms (0%)

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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.5b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	5.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	5.0b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series93.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

43.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
35.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
15.0ms	(/.f64 2 (-.f64 y t))

rewrite90.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

34.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
16.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
7.0ms	(/.f64 2 (-.f64 y t))

simplify231.0ms (2%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune496.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	343	8	351
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
	4.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	26.3b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	6.5b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.3b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	28.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	5.0b	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
▶	3.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))

Compiler

Compiled 7659 to 3605 computations (52.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
✓	0.6b	(cbrt.f64 (-.f64 y t))
✓	3.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

series417.0ms (3.6%)

Counts

4 → 120

Calls

4 calls:

181.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
104.0ms	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
71.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
59.0ms	(cbrt.f64 (-.f64 y t))

rewrite285.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

312×	`times-frac_binary64`
213×	`add-sqr-sqrt_binary64`
211×	`*-un-lft-identity_binary64`
174×	`associate-r_binary64`
159×	`add-cube-cbrt_binary64`

Counts

4 → 318

Calls

4 calls:

91.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
20.0ms	(*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))
16.0ms	(/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))
4.0ms	(cbrt.f64 (-.f64 y t))

simplify459.0ms (4%)

Algorithm

1×	egg-herbie

Rules

515×	`associate-*l/_binary64`
488×	`associate-/l*_binary64`
332×	`times-frac_binary64`
296×	`associate-/r*_binary64`
265×	`associate-/l/_binary64`

Counts

438 → 471

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	687	15965
1	2028	13843
2	5438	13843

prune670.0ms (5.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	570	10	580

Error

Counts

580 → 10

Alt Table

Status	Error	Program
▶	4.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	26.3b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	6.5b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.6b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	5.3b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	28.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
	5.0b	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
✓	3.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))

Compiler

Compiled 22363 to 10906 computations (51.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 2) (-.f64 y t))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	4.0b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))

series233.0ms (2%)

Counts

4 → 96

Calls

4 calls:

112.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
62.0ms	(cbrt.f64 z)
43.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
15.0ms	(/.f64 (sqrt.f64 2) (-.f64 y t))

rewrite153.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

426×	`times-frac_binary64`
301×	`add-sqr-sqrt_binary64`
293×	`*-un-lft-identity_binary64`
226×	`associate-r_binary64`
207×	`add-cube-cbrt_binary64`

Counts

4 → 372

Calls

4 calls:

44.0ms	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
6.0ms	(/.f64 (sqrt.f64 2) (-.f64 y t))
6.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify450.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

603×	`associate-*r/_binary64`
546×	`associate-*l/_binary64`
524×	`associate-/l*_binary64`
322×	`times-frac_binary64`
285×	`associate-/r*_binary64`

Counts

468 → 482

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	500	13706
1	1509	11071
2	5407	11071

prune750.0ms (6.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	516	0	516
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	516	10	526

Error

Counts

526 → 10

Alt Table

Status	Error	Program
✓	4.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	26.3b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
	6.5b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
	5.6b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	5.3b	(.f64 (.f64 x (sqrt.f64 2)) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) z))
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	28.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
▶	5.0b	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
✓	3.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))

Compiler

Compiled 16614 to 8234 computations (50.4% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z))
✓	5.0b	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))

series104.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

63.0ms	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
28.0ms	(/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z))
13.0ms	(/.f64 -2 (-.f64 y t))

rewrite174.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

753×	`times-frac_binary64`
476×	`add-sqr-sqrt_binary64`
467×	`*-un-lft-identity_binary64`
333×	`add-cube-cbrt_binary64`
214×	`associate-r_binary64`

Counts

3 → 535

Calls

3 calls:

60.0ms	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
26.0ms	(/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z))
8.0ms	(/.f64 -2 (-.f64 y t))

simplify424.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

638×	`associate-/r*_binary64`
491×	`associate-/l*_binary64`
470×	`associate-/l/_binary64`
437×	`times-frac_binary64`
192×	`*-commutative_binary64`

Counts

643 → 688

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	685	15042
1	1831	14478
2	5263	14478

prune694.0ms (6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	687	1	688
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	689	9	698

Error

Counts

698 → 9

Alt Table

Status	Error	Program
✓	4.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	26.3b	(.f64 (sqrt.f64 (.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))))
✓	5.0b	(*.f64 x (/.f64 (/.f64 -2 (-.f64 y t)) (neg.f64 z)))
	5.1b	(.f64 x (.f64 -2 (/.f64 (/.f64 -1 z) (-.f64 y t))))
	5.6b	(/.f64 (/.f64 (*.f64 2 x) (-.f64 y t)) z)
	5.4b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	28.7b	(.f64 (.f64 x (/.f64 2 (-.f64 (.f64 y y) (.f64 t t)))) (/.f64 (+.f64 y t) z))
✓	3.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))
	5.7b	(.f64 x (.f64 (*.f64 (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (cbrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))))

Compiler

Compiled 15859 to 6832 computations (56.9% saved)

regimes2.9s (25.3%)

Accuracy

Total 1.5b remaining (97.6%)

Threshold costs 0b (0%)

Counts

259 → 1

Compiler

Compiled 41188 to 26722 computations (35.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	20	49
2	25	49
3	27	49
4	28	49
5	28	49

end153.0ms (1.3%)

Compiler: Compiled 255 to 162 computations (36.5% saved)

Details

analyze1.1s (9.8%)

sample1.4s (11.9%)

simplify158.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series93.0ms (0.8%)

rewrite90.0ms (0.8%)

simplify231.0ms (2%)

prune496.0ms (4.3%)

localize23.0ms (0.2%)

series417.0ms (3.6%)

rewrite285.0ms (2.5%)

simplify459.0ms (4%)

prune670.0ms (5.8%)

localize12.0ms (0.1%)

series233.0ms (2%)

rewrite153.0ms (1.3%)

simplify450.0ms (3.9%)

prune750.0ms (6.5%)

localize11.0ms (0.1%)

series104.0ms (0.9%)

rewrite174.0ms (1.5%)

simplify424.0ms (3.7%)

prune694.0ms (6%)

regimes2.9s (25.3%)

simplify3.0ms (0%)

end153.0ms (1.3%)

Profiling