Details

analyze1.5s (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%	93.7%	6.3%	6
0%	90.5%	9.5%	7
0.8%	84.3%	14.9%	8
1.2%	81.2%	17.7%	9
1.8%	77.3%	21%	10
2.1%	75.2%	22.6%	11
2.4%	73.1%	24.5%	12
2.6%	72%	25.4%	13
2.8%	70.9%	26.3%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample3.9s (55.6%)

Results

1.3s	1799×	body	1024	valid
918.0ms	387×	body	8192	exit
684.0ms	4674×	body	128	valid
422.0ms	959×	body	512	valid
185.0ms	186×	body	2048	valid
183.0ms	638×	body	256	valid
56.0ms	103×	body	1024	invalid
51.0ms	117×	body	512	invalid
49.0ms	347×	body	128	invalid
25.0ms	89×	body	256	invalid

Compiler

Compiled 27 to 17 computations (37% saved)

simplify50.0ms (0.7%)

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%)

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

9.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.2b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	5.5b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series45.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

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

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`unpow-prod-down_binary64`

Counts

2 → 70

Calls

2 calls:

12.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
4.0ms	(/.f64 x (+.f64 x y))

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

276×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`
183×	`fma-def_binary64`
179×	`sub-neg_binary64`
176×	`times-frac_binary64`

Counts

118 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	3123
1	859	2987
2	3234	2833
3	4908	2833
4	4986	2833

prune93.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Error

0.0b

Counts

120 → 4

Alt Table

Status	Error	Program
✓	9.2b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
▶	9.2b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)) x)
	15.2b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
	9.7b	(/.f64 1 x)

Compiler

Compiled 3234 to 1571 computations (51.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)
✓	0.0b	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3))
	0.0b	(/.f64 x (+.f64 x y))
	5.5b	(pow.f64 (/.f64 x (+.f64 x y)) x)

series144.0ms (2%)

Counts

2 → 48

Calls

2 calls:

96.0ms	(pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)
47.0ms	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`unpow-prod-down_binary64`
64×	`*-un-lft-identity_binary64`
50×	`cbrt-prod_binary64`
48×	`times-frac_binary64`
44×	`cube-prod_binary64`

Counts

2 → 127

Calls

2 calls:

9.0ms	(pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)
8.0ms	(cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3))

simplify112.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-r_binary64`
367×	`fma-def_binary64`
255×	`associate-l_binary64`
241×	`times-frac_binary64`
234×	`associate-/l*_binary64`

Counts

175 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	523	6192
1	1477	6078
2	4980	6078

prune284.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	295	5	300

Error

Counts

300 → 5

Alt Table

Status	Error	Program
✓	9.2b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	9.2b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)) x)
	29.7b	(/.f64 (cbrt.f64 (-.f64 (+.f64 1 (fma.f64 (.f64 y y) 9/2 (.f64 (/.f64 (.f64 y y) x) 3/2))) (fma.f64 y 3 (fma.f64 (pow.f64 y 3) 9/2 (fma.f64 (/.f64 (pow.f64 y 3) x) 9/2 (/.f64 (pow.f64 y 3) (.f64 x x))))))) x)
	15.2b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
▶	9.7b	(/.f64 1 x)

Compiler

Compiled 9859 to 5034 computations (48.9% saved)

localize2.0ms (0%)

prune5.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

Counts

5 → 5

Alt Table

Status	Error	Program
✓	9.2b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
✓	9.2b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)) x)
	29.7b	(/.f64 (cbrt.f64 (-.f64 (+.f64 1 (fma.f64 (.f64 y y) 9/2 (.f64 (/.f64 (.f64 y y) x) 3/2))) (fma.f64 y 3 (fma.f64 (pow.f64 y 3) 9/2 (fma.f64 (/.f64 (pow.f64 y 3) x) 9/2 (/.f64 (pow.f64 y 3) (.f64 x x))))))) x)
▶	15.2b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
✓	9.7b	(/.f64 1 x)

Compiler

Compiled 148 to 97 computations (34.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 x (exp.f64 y)) y)
✓	0.0b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
✓	0.1b	(/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y))
✓	0.3b	(fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y)))

series99.0ms (1.4%)

Counts

4 → 80

Calls

4 calls:

38.0ms	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
27.0ms	(/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y))
25.0ms	(fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y)))
10.0ms	(/.f64 (*.f64 x (exp.f64 y)) y)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 112

Calls

4 calls:

7.0ms	(/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y))
4.0ms	(/.f64 (*.f64 x (exp.f64 y)) y)
2.0ms	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
0.0ms	(fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y)))

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/r*_binary64`
655×	`associate-/r/_binary64`
603×	`associate-l_binary64`
534×	`associate-*r/_binary64`
313×	`fma-def_binary64`

Counts

192 → 236

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	239	4189
1	549	3828
2	1810	3625
3	5043	3625

prune171.0ms (2.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	236	5	241

Error

Counts

241 → 5

Alt Table

Status	Error	Program
✓	9.2b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
	24.4b	(-.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 (.f64 y y) x) (+.f64 1/2 (/.f64 1/2 x)))) (+.f64 (/.f64 y x) (*.f64 (/.f64 (pow.f64 y 3) x) (+.f64 1/6 (/.f64 1/2 x)))))
✓	9.2b	(/.f64 (cbrt.f64 (pow.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) 3)) x)
✓	15.2b	(/.f64 (fma.f64 1/2 (/.f64 y (/.f64 (*.f64 x (exp.f64 y)) y)) (exp.f64 (neg.f64 y))) x)
✓	9.7b	(/.f64 1 x)

Compiler

Compiled 5370 to 1769 computations (67.1% saved)

regimes222.0ms (3.1%)

Accuracy

Total 0.4b remaining (93.8%)

Threshold costs 0.4b (93.8%)

Counts

39 → 3

Compiler

Compiled 1844 to 1251 computations (32.2% saved)

bsearch61.0ms (0.9%)

Steps

Iters	Range		Point
8	4.755261826446497e-5	0.06634301651847264	0.06506087734989285
5	-4426325923203828.5	-447.87440887633204	-1126.4152090125688

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0%)

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	21	41
1	30	41
2	32	41
3	33	41
4	32	41

end89.0ms (1.2%)

Compiler: Compiled 138 to 93 computations (32.6% saved)

Details

analyze1.5s (20.5%)

sample3.9s (55.6%)

simplify50.0ms (0.7%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series45.0ms (0.6%)

rewrite20.0ms (0.3%)

simplify106.0ms (1.5%)

prune93.0ms (1.3%)

localize9.0ms (0.1%)

series144.0ms (2%)

rewrite29.0ms (0.4%)

simplify112.0ms (1.6%)

prune284.0ms (4%)

localize2.0ms (0%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

series99.0ms (1.4%)

rewrite21.0ms (0.3%)

simplify108.0ms (1.5%)

prune171.0ms (2.4%)

regimes222.0ms (3.1%)

bsearch61.0ms (0.9%)

simplify3.0ms (0%)

end89.0ms (1.2%)

Profiling