Details

analyze1.2s (20.5%)

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)

sample2.4s (40.8%)

Results

911.0ms	6319×	body	128	valid
634.0ms	980×	body	1024	valid
276.0ms	610×	body	512	valid
193.0ms	1470×	body	128	invalid
127.0ms	207×	body	1024	invalid
106.0ms	267×	body	512	invalid
98.0ms	345×	body	256	valid
43.0ms	158×	body	256	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

522×	`unswap-sqr_binary64`
363×	`fma-def_binary64`
253×	`associate-l_binary64`
215×	`associate-r_binary64`
204×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	57	16
4	138	16
5	332	16
6	893	16
7	3314	16

Stop Event

1×	node limit

Counts

1 → 2

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

5.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.5b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (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 y (+.f64 y z))
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	4.7b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series146.0ms (2.4%)

Counts

4 → 108

Calls

4 calls:

79.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
35.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
25.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
7.0ms	(/.f64 y (+.f64 y z))

rewrite77.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

374×	`fma-def_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
187×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	46
1	214	46
2	3333	46

Stop Event

1×	node limit

Counts

4 → 142

Calls

4 calls:

74.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
74.0ms	(/.f64 y (+.f64 y z))
74.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
74.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

347×	`fma-def_binary64`
340×	`associate-+r+_binary64`
334×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
244×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	362	5179
1	1193	5024
2	4951	5024

Stop Event

1×	node limit

Counts

250 → 265

prune228.0ms (3.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	260	5	265
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	261	5	266

Error

0.0b

Counts

266 → 5

Alt Table

Status	Error	Program
	5.9b	(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 y) 2)) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
	5.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)
	44.7b	(+.f64 x (/.f64 (exp.f64 (.f64 y (+.f64 (log.f64 (/.f64 -1 z)) (log.f64 (.f64 -1 y))))) y))
	10.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	2.0b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 8493 to 3891 computations (54.2% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

3.0ms

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

rewrite35.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
112×	`log1p-udef_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1692	7

Stop Event

1×	node limit

Counts

1 → 35

Calls

1 calls:

34.0ms

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	138
1	9	138

Stop Event

1×

saturated

Counts

59 → 38

prune29.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	37	6	43

Error

Counts

43 → 6

Alt Table

Status	Error	Program
	5.9b	(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 y) 2)) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
	5.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)
	44.7b	(+.f64 x (/.f64 (exp.f64 (.f64 y (+.f64 (log.f64 (/.f64 -1 z)) (log.f64 (.f64 -1 y))))) y))
	10.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.0b	(+.f64 x (/.f64 1 y))
▶	3.1b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

Compiler

Compiled 591 to 383 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x (/.f64 1 y))
✓	0.5b	(cbrt.f64 (+.f64 x (/.f64 1 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

series69.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

54.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)
15.0ms	(cbrt.f64 (+.f64 x (/.f64 1 y)))

rewrite49.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

777×	`log1p-expm1-u_binary64`
777×	`expm1-log1p-u_binary64`
483×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	188	16
2	2168	16

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

48.0ms	(cbrt.f64 (+.f64 x (/.f64 1 y)))
48.0ms	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

simplify40.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-neg_binary64`
404×	`unswap-sqr_binary64`
397×	`associate-r_binary64`
376×	`associate-l_binary64`
294×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1011
1	284	943
2	882	909
3	3919	908

Stop Event

1×	node limit

Counts

88 → 94

prune77.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	132	6	138

Error

Counts

138 → 6

Alt Table

Status	Error	Program
	5.9b	(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 y) 2)) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
▶	5.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)
	44.7b	(+.f64 x (/.f64 (exp.f64 (.f64 y (+.f64 (log.f64 (/.f64 -1 z)) (log.f64 (.f64 -1 y))))) y))
	10.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.0b	(+.f64 x (/.f64 1 y))
✓	3.1b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

Compiler

Compiled 2332 to 1709 computations (26.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y))
✓	0.0b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)
	4.7b	(pow.f64 (/.f64 y (+.f64 y z)) y)
✓	4.7b	(pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))

series385.0ms (6.4%)

Counts

3 → 84

Calls

3 calls:

305.0ms

(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)

53.0ms

(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y))

27.0ms

(pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
147×	`add-cbrt-cube_binary64`
147×	`log1p-expm1-u_binary64`
147×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	334	36
2	4609	36

Stop Event

1×	node limit

Counts

3 → 135

Calls

3 calls:

56.0ms

(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y))

56.0ms

(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)

56.0ms

(pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

916×	`fma-def_binary64`
323×	`times-frac_binary64`
290×	`*-commutative_binary64`
223×	`associate-/l*_binary64`
197×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	697	10785
1	2532	9780

Stop Event

1×	node limit

Counts

219 → 206

prune399.0ms (6.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	259	6	265

Error

Counts

265 → 6

Alt Table

Status	Error	Program
	5.9b	(fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 y) 2)) (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) (cbrt.f64 y)) x)
✓	5.5b	(fma.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) (+.f64 y y))) 1) (/.f64 (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y z)) y)) y) x)
	44.7b	(+.f64 x (/.f64 (exp.f64 (.f64 y (+.f64 (log.f64 (/.f64 -1 z)) (log.f64 (.f64 -1 y))))) y))
	10.1b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	2.0b	(+.f64 x (/.f64 1 y))
✓	3.1b	(pow.f64 (cbrt.f64 (+.f64 x (/.f64 1 y))) 3)

Compiler

Compiled 17301 to 9203 computations (46.8% saved)

regimes333.0ms (5.6%)

Accuracy

Total 2.3b remaining (99.7%)

Threshold costs 0b (0%)

Counts

56 → 3

Compiler

Compiled 4714 to 3023 computations (35.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
2×	`*-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	31	84
1	43	84
2	45	84
3	46	84

Stop Event

1×

saturated

end96.0ms (1.6%)

Compiler: Compiled 212 to 115 computations (45.8% saved)

Details

analyze1.2s (20.5%)

sample2.4s (40.8%)

simplify26.0ms (0.4%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series146.0ms (2.4%)

rewrite77.0ms (1.3%)

simplify97.0ms (1.6%)

prune228.0ms (3.8%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite35.0ms (0.6%)

simplify8.0ms (0.1%)

prune29.0ms (0.5%)

localize9.0ms (0.1%)

series69.0ms (1.2%)

rewrite49.0ms (0.8%)

simplify40.0ms (0.7%)

prune77.0ms (1.3%)

localize14.0ms (0.2%)

series385.0ms (6.4%)

rewrite58.0ms (1%)

simplify113.0ms (1.9%)

prune399.0ms (6.7%)

regimes333.0ms (5.6%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end96.0ms (1.6%)

Profiling