Details

analyze763.0ms (14%)

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
3.1%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample2.9s (53.9%)

Results

1.1s	1777×	body	1024	valid
655.0ms	4628×	body	128	valid
483.0ms	1089×	body	512	valid
167.0ms	614×	body	256	valid
149.0ms	148×	body	2048	valid
127.0ms	209×	body	1024	invalid
94.0ms	242×	body	512	invalid
60.0ms	423×	body	128	invalid
36.0ms	145×	body	256	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify47.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

740×	`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	9	17
1	16	13
2	25	13
3	53	13
4	116	13
5	276	13
6	665	13
7	2268	13
8	4318	13
9	4902	13

prune3.0ms (0.1%)

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

12.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.3b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)

Compiler

Compiled 44 to 22 computations (50% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series95.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

50.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
36.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
9.0ms	(/.f64 x (+.f64 x y))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 178

Calls

3 calls:

8.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
4.0ms	(/.f64 x (+.f64 x y))

simplify172.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

358×	`associate-/l*_binary64`
339×	`times-frac_binary64`
332×	`fma-def_binary64`
265×	`fma-neg_binary64`
253×	`associate-/r*_binary64`

Counts

250 → 273

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	564	7650
1	1419	7378
2	4947	7378
3	5165	7378

prune187.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	268	5	273
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	268	6	274

Error

Counts

274 → 6

Alt Table

Status	Error	Program
✓	12.3b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
	13.7b	(/.f64 (exp.f64 (neg.f64 y)) x)
▶	7.4b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x) (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)) x)
	23.1b	(-.f64 (/.f64 1 x) (/.f64 y x))
	10.4b	(/.f64 1 x)
	34.7b	(*.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))

Compiler

Compiled 7770 to 3035 computations (60.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (+.f64 x y))
✓	0.6b	(cbrt.f64 x)
✓	1.2b	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
✓	2.9b	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)

series152.0ms (2.8%)

Counts

4 → 84

Calls

4 calls:

53.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)
43.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
35.0ms	(cbrt.f64 x)
21.0ms	(cbrt.f64 (+.f64 x y))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`unpow-prod-down_binary64`
52×	`cbrt-prod_binary64`
50×	`*-un-lft-identity_binary64`
43×	`times-frac_binary64`
36×	`add-sqr-sqrt_binary64`

Counts

4 → 127

Calls

4 calls:

15.0ms	(pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x)
8.0ms	(pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)
2.0ms	(cbrt.f64 (+.f64 x y))
1.0ms	(cbrt.f64 x)

simplify180.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
356×	`times-frac_binary64`
274×	`associate-/l*_binary64`
263×	`associate-/r*_binary64`
207×	`sqr-pow_binary64`

Counts

211 → 261

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	676	7708
1	1905	7189
2	4958	7171
3	5290	7171

prune337.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	385	6	391

Error

Counts

391 → 6

Alt Table

Status	Error	Program
✓	12.3b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
	13.7b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.4b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x) (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)) x)
	23.1b	(-.f64 (/.f64 1 x) (/.f64 y x))
▶	10.4b	(/.f64 1 x)
	34.7b	(*.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))

Compiler

Compiled 18769 to 7113 computations (62.1% saved)

localize2.0ms (0%)

prune5.0ms (0.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	2	2
Total	6	6

Error

Counts

6 → 6

Alt Table

Status	Error	Program
✓	12.3b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
▶	13.7b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.4b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x) (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)) x)
	23.1b	(-.f64 (/.f64 1 x) (/.f64 y x))
✓	10.4b	(/.f64 1 x)
	34.7b	(*.f64 (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)) (sqrt.f64 (/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)))

Compiler

Compiled 125 to 61 computations (51.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (exp.f64 (neg.f64 y)) x)

series8.0ms (0.1%)

Counts

1 → 8

Calls

1 calls:

8.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

4.0ms

(/.f64 (exp.f64 (neg.f64 y)) x)

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-neg_binary64`
511×	`fma-def_binary64`
397×	`div-sub_binary64`
389×	`associate-/l*_binary64`
297×	`unswap-sqr_binary64`

Counts

39 → 46

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	565
1	149	524
2	369	516
3	905	516
4	2769	509
5	4190	509
6	5158	509

prune34.0ms (0.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	2	0	2
Picked	0	1	1
Done	0	3	3
Total	47	5	52

Error

Counts

52 → 5

Alt Table

Status	Error	Program
✓	12.3b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	13.7b	(/.f64 (exp.f64 (neg.f64 y)) x)
✓	7.4b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) x) (pow.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x y))) x)) x)
✓	10.4b	(/.f64 1 x)
	32.5b	(*.f64 (sqrt.f64 (/.f64 (exp.f64 (neg.f64 y)) x)) (sqrt.f64 (/.f64 (exp.f64 (neg.f64 y)) x)))

Compiler

Compiled 606 to 216 computations (64.4% saved)

regimes235.0ms (4.3%)

Accuracy

Total 0.4b remaining (97.6%)

Threshold costs 0.4b (97.6%)

Counts

38 → 3

Compiler

Compiled 2249 to 1119 computations (50.2% saved)

bsearch34.0ms (0.6%)

Steps

Iters	Range		Point
8	0.00038635523052552224	0.6863684800849544	0.6126071699760075
1	-1.041108704442834e+25	-1.177805376251782e+20	-3.468771897358665e+22

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-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	19	38
1	23	38
2	25	38
3	26	38
4	25	38

end80.0ms (1.5%)

Compiler: Compiled 123 to 71 computations (42.3% saved)

Details

analyze763.0ms (14%)

sample2.9s (53.9%)

simplify47.0ms (0.9%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series95.0ms (1.7%)

rewrite39.0ms (0.7%)

simplify172.0ms (3.2%)

prune187.0ms (3.4%)

localize16.0ms (0.3%)

series152.0ms (2.8%)

rewrite37.0ms (0.7%)

simplify180.0ms (3.3%)

prune337.0ms (6.2%)

localize2.0ms (0%)

prune5.0ms (0.1%)

localize4.0ms (0.1%)

series8.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify69.0ms (1.3%)

prune34.0ms (0.6%)

regimes235.0ms (4.3%)

bsearch34.0ms (0.6%)

simplify3.0ms (0.1%)

end80.0ms (1.5%)

Profiling