Details

analyze1.9s (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
0%	93.6%	6.4%	9
0%	90.5%	9.5%	10
0%	90.5%	9.5%	11
0%	85%	15%	12
0%	82.3%	17.7%	13
0%	82.3%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.4s (36.4%)

Results

1.1s	6332×	body	128	valid
843.0ms	359×	body	8192	exit
679.0ms	953×	body	1024	valid
284.0ms	610×	body	512	valid
199.0ms	1334×	body	128	invalid
123.0ms	357×	body	256	valid
57.0ms	126×	body	512	invalid
55.0ms	93×	body	1024	invalid
23.0ms	79×	body	256	invalid
4.0ms	4×	body	2048	valid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify53.0ms (0.6%)

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

8.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.3b	(+.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	8.0b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series250.0ms (2.7%)

Counts

3 → 84

Calls

3 calls:

137.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
76.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
36.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
72×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

18.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
9.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
6.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)

simplify203.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

379×	`fma-def_binary64`
342×	`times-frac_binary64`
339×	`associate-/l*_binary64`
255×	`associate-/r*_binary64`
245×	`fma-neg_binary64`

Counts

244 → 362

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	586	8617
1	1575	8411
2	4997	8411
3	5189	8411

prune306.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	356	6	362
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	357	6	363

Error

Counts

363 → 6

Alt Table

Status	Error	Program
	22.6b	(+.f64 x (-.f64 (fma.f64 1/2 (+.f64 (.f64 (/.f64 z y) (/.f64 z y)) (/.f64 (.f64 z z) y)) (/.f64 1 y)) (/.f64 z y)))
	17.7b	(+.f64 x (/.f64 (-.f64 1 z) y))
	13.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
	8.3b	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
▶	3.3b	(+.f64 x (/.f64 1 y))
	8.7b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))

Compiler

Compiled 11425 to 4383 computations (61.6% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0%)

Counts

1 → 24

Calls

1 calls:

4.0ms

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

rewrite7.0ms (0.1%)

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:

6.0ms

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

simplify95.0ms (1%)

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

prune23.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	28	6	34

Error

Counts

34 → 6

Alt Table

Status	Error	Program
	22.6b	(+.f64 x (-.f64 (fma.f64 1/2 (+.f64 (.f64 (/.f64 z y) (/.f64 z y)) (/.f64 (.f64 z z) y)) (/.f64 1 y)) (/.f64 z y)))
	17.7b	(+.f64 x (/.f64 (-.f64 1 z) y))
	13.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	8.3b	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
✓	3.3b	(+.f64 x (/.f64 1 y))
	8.7b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))

Compiler

Compiled 472 to 304 computations (35.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
✓	0.0b	(/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y)))
	8.0b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series232.0ms (2.5%)

Counts

3 → 84

Calls

3 calls:

106.0ms	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
75.0ms	(/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))
51.0ms	(/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y)))

rewrite143.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

732×	`times-frac_binary64`
433×	`*-un-lft-identity_binary64`
334×	`add-sqr-sqrt_binary64`
334×	`add-cube-cbrt_binary64`
288×	`unpow-prod-down_binary64`

Counts

3 → 441

Calls

3 calls:

45.0ms	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
15.0ms	(/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y)))
9.0ms	(/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))

simplify302.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

393×	`fma-def_binary64`
313×	`associate-/r*_binary64`
275×	`associate-/r/_binary64`
270×	`times-frac_binary64`
258×	`associate-/l*_binary64`

Counts

525 → 633

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	731	17906
1	1879	16908
2	5019	16908

prune562.0ms (6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	723	1	724
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	724	6	730

Error

Counts

730 → 6

Alt Table

Status	Error	Program
	17.7b	(+.f64 x (/.f64 (-.f64 1 z) y))
	17.7b	(+.f64 x (/.f64 1 (-.f64 (+.f64 y (fma.f64 y z (.f64 1/2 (.f64 y (.f64 z z))))) (.f64 1/2 (*.f64 z z)))))
	13.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	8.3b	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
✓	3.3b	(+.f64 x (/.f64 1 y))
▶	8.7b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))

Compiler

Compiled 23543 to 8851 computations (62.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	8.0b	(pow.f64 (/.f64 y (+.f64 z y)) y)

series171.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

57.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y)))
40.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
38.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)
34.0ms	(cbrt.f64 y)

rewrite110.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

267×	`times-frac_binary64`
200×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
142×	`associate-r_binary64`
138×	`unpow-prod-down_binary64`

Counts

4 → 315

Calls

4 calls:

42.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y)))
7.0ms	(pow.f64 (/.f64 y (+.f64 z y)) y)
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify206.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

641×	`associate-/l*_binary64`
606×	`times-frac_binary64`
310×	`fma-def_binary64`
270×	`associate-/l/_binary64`
232×	`*-commutative_binary64`

Counts

387 → 506

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	692	12386
1	1973	9933
2	5241	9933

prune395.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	540	0	540
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	540	6	546

Error

Counts

546 → 6

Alt Table

Status	Error	Program
	17.7b	(+.f64 x (/.f64 (-.f64 1 z) y))
	17.7b	(+.f64 x (/.f64 1 (-.f64 (+.f64 y (fma.f64 y z (.f64 1/2 (.f64 y (.f64 z z))))) (.f64 1/2 (*.f64 z z)))))
	13.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	8.3b	(+.f64 x (/.f64 1 (/.f64 y (pow.f64 (/.f64 y (+.f64 y z)) y))))
✓	3.3b	(+.f64 x (/.f64 1 y))
✓	8.7b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) (cbrt.f64 y))))

Compiler

Compiled 18742 to 6072 computations (67.6% saved)

regimes747.0ms (8%)

Accuracy

Total 0.3b remaining (93%)

Threshold costs 0.3b (93%)

Counts

83 → 3

Compiler

Compiled 9972 to 5272 computations (47.1% saved)

bsearch60.0ms (0.6%)

Steps

Iters	Range		Point
9	1.965486903487692e-17	4.231810663880872e-12	4.168760836533945e-12
4	-1.524263141240576e+36	-4.0552067332036987e+34	-5.305071840263071e+34

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

end82.0ms (0.9%)

Compiler: Compiled 140 to 92 computations (34.3% saved)

Details

analyze1.9s (20.5%)

sample3.4s (36.4%)

simplify53.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series250.0ms (2.7%)

rewrite51.0ms (0.5%)

simplify203.0ms (2.2%)

prune306.0ms (3.3%)

localize3.0ms (0%)

series4.0ms (0%)

rewrite7.0ms (0.1%)

simplify95.0ms (1%)

prune23.0ms (0.2%)

localize10.0ms (0.1%)

series232.0ms (2.5%)

rewrite143.0ms (1.5%)

simplify302.0ms (3.2%)

prune562.0ms (6%)

localize12.0ms (0.1%)

series171.0ms (1.8%)

rewrite110.0ms (1.2%)

simplify206.0ms (2.2%)

prune395.0ms (4.2%)

regimes747.0ms (8%)

bsearch60.0ms (0.6%)

simplify3.0ms (0%)

end82.0ms (0.9%)

Profiling