Details

analyze1.2s (20.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.6s (41.6%)

Results

967.0ms	6401×	body	128	valid
703.0ms	927×	body	1024	valid
287.0ms	603×	body	512	valid
186.0ms	1462×	body	128	invalid
117.0ms	180×	body	1024	invalid
93.0ms	321×	body	256	valid
87.0ms	213×	body	512	invalid
41.0ms	140×	body	256	invalid
5.0ms	4×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify49.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	56	16
4	119	16
5	280	16
6	672	16
7	2284	16
8	4398	16
9	4953	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

4.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.4b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	3.9b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series209.0ms (3.4%)

Counts

4 → 108

Calls

4 calls:

101.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
46.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
32.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
30.0ms	(/.f64 y (+.f64 y z))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
82×	`add-sqr-sqrt_binary64`
82×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

17.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
8.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
5.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify149.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary64`
358×	`times-frac_binary64`
355×	`associate-/l*_binary64`
264×	`associate-/r*_binary64`
248×	`associate-r_binary64`

Counts

303 → 430

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	612	9531
1	1653	9295
2	5034	9295

prune336.0ms (5.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	426	4	430
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	427	4	431

Error

Counts

431 → 4

Alt Table

Status	Error	Program
	5.6b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))) (cbrt.f64 (+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	7.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	3.6b	(+.f64 x (/.f64 1 y))
	4.4b	(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

Compiler

Compiled 12631 to 4733 computations (62.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

37.0ms

(+.f64 x (/.f64 1 y))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
321×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
282×	`associate-+l+_binary64`

Counts

42 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	322
1	88	302
2	189	299
3	419	299
4	1068	299
5	2246	299
6	3475	299
7	4871	299
8	4894	299
9	4906	299

prune19.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

Counts

32 → 4

Alt Table

Status	Error	Program
	4.8b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))
	7.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.6b	(+.f64 x (/.f64 1 y))
▶	4.4b	(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

Compiler

Compiled 398 to 270 computations (32.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))
	0.0b	(/.f64 y (+.f64 y z))
	3.9b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series102.0ms (1.7%)

Counts

1 → 36

Calls

1 calls:

102.0ms

(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

250×	`associate-/r/_binary64`
242×	`fma-neg_binary64`
174×	`cancel-sign-sub-inv_binary64`
158×	`sub-neg_binary64`
147×	`+-commutative_binary64`

Counts

52 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	1963
1	672	1826
2	2590	1660
3	4868	1660
4	4969	1660

prune163.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	224	0	224
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	224	4	228

Error

Counts

228 → 4

Alt Table

Status	Error	Program
▶	4.8b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))
	7.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.6b	(+.f64 x (/.f64 1 y))
✓	4.4b	(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

Compiler

Compiled 6849 to 3274 computations (52.2% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (/.f64 1 y))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y))))
✓	0.6b	(cbrt.f64 (+.f64 x (/.f64 1 y)))

series84.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

54.0ms

(cbrt.f64 (+.f64 x (/.f64 1 y)))

25.0ms

(*.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y))))

5.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
48×	`*-un-lft-identity_binary64`
47×	`cbrt-prod_binary64`
34×	`flip-+_binary64`
34×	`flip3-+_binary64`

Counts

3 → 145

Calls

3 calls:

20.0ms

(*.f64 (*.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))

13.0ms

(*.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y))))

4.0ms

(cbrt.f64 (+.f64 x (/.f64 1 y)))

simplify156.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
391×	`fma-neg_binary64`
321×	`times-frac_binary64`
259×	`associate-/r*_binary64`
200×	`associate-l_binary64`

Counts

217 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	5855
1	578	5353
2	1703	4851
3	4601	4782
4	4942	4782

prune328.0ms (5.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	414	4	418

Error

Counts

418 → 4

Alt Table

Status	Error	Program
✓	4.8b	(.f64 (.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) (cbrt.f64 (+.f64 x (/.f64 1 y)))) (cbrt.f64 (+.f64 x (/.f64 1 y))))
	7.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	3.6b	(+.f64 x (/.f64 1 y))
✓	4.4b	(+.f64 x (*.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (/.f64 1 y)))

Compiler

Compiled 12813 to 9057 computations (29.3% saved)

regimes311.0ms (5%)

Accuracy

Total 0.6b remaining (97.8%)

Threshold costs 0.6b (97.8%)

Counts

39 → 3

Compiler

Compiled 3732 to 2217 computations (40.6% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
10	1.0753709990712695e-53	1.0690785313847973e-37	1.0446930670683376e-37
1	-2.620375052359758e+85	-1.3481874700499111e+84	-5.97184375554952e+84

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	32
1	28	32
2	30	32
3	31	32
4	30	32

end62.0ms (1%)

Compiler: Compiled 105 to 74 computations (29.5% saved)

Details

analyze1.2s (20.1%)

sample2.6s (41.6%)

simplify49.0ms (0.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series209.0ms (3.4%)

rewrite49.0ms (0.8%)

simplify149.0ms (2.4%)

prune336.0ms (5.4%)

localize3.0ms (0.1%)

series4.0ms (0.1%)

rewrite38.0ms (0.6%)

simplify94.0ms (1.5%)

prune19.0ms (0.3%)

localize8.0ms (0.1%)

series102.0ms (1.7%)

rewrite4.0ms (0.1%)

simplify83.0ms (1.3%)

prune163.0ms (2.6%)

localize7.0ms (0.1%)

series84.0ms (1.4%)

rewrite55.0ms (0.9%)

simplify156.0ms (2.5%)

prune328.0ms (5.3%)

regimes311.0ms (5%)

bsearch42.0ms (0.7%)

simplify3.0ms (0%)

end62.0ms (1%)

Profiling