Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25.7%	74.3%	0
25.7%	0%	74.3%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample2.2s (47.3%)

Results

1.3s	6814×	body	128	valid
444.0ms	543×	body	1024	valid
237.0ms	542×	body	512	valid
84.0ms	333×	body	256	valid
15.0ms	24×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

743×	`neg-mul-1_binary64`
672×	`distribute-rgt-neg-in_binary64`
436×	`unswap-sqr_binary64`
376×	`fma-def_binary64`
296×	`*-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	37	13
3	78	13
4	204	13
5	682	13
6	1848	13
7	3102	13
8	4873	13
9	5393	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

7.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.7b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 5)
✓	2.2b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series34.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
13.0ms	(pow.f64 (+.f64 x eps) 5)

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`unpow-prod-down_binary64`
63×	`*-un-lft-identity_binary64`
56×	`prod-diff_binary64`
50×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`

Counts

2 → 116

Calls

2 calls:

8.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
7.0ms	(pow.f64 (+.f64 x eps) 5)

simplify140.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
583×	`fma-neg_binary64`
341×	`unswap-sqr_binary64`
284×	`distribute-rgt-in_binary64`
253×	`cancel-sign-sub-inv_binary64`

Counts

164 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	5572
1	387	4254
2	1113	3001
3	2509	2956
4	4694	2956
5	4654	2956

prune194.0ms (4.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	162	3	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	3	166

Error

0.0b

Counts

166 → 3

Alt Table

Status	Error	Program
	10.0b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))
▶	7.8b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (.f64 5 (.f64 (pow.f64 eps 4) x))))
	9.9b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))

Compiler

Compiled 4400 to 2816 computations (36% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 eps 4) x)
✓	0.0b	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
✓	0.0b	(*.f64 (pow.f64 eps 3) (pow.f64 x 2))
✓	0.1b	(.f64 5 (.f64 (pow.f64 eps 4) x))

series64.0ms (1.4%)

Counts

4 → 0

Calls

4 calls:

20.0ms	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
17.0ms	(.f64 5 (.f64 (pow.f64 eps 4) x))
14.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 x 2))
13.0ms	(*.f64 (pow.f64 eps 4) x)

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
39×	`add-sqr-sqrt_binary64`
38×	`prod-exp_binary64`
25×	`associate-l_binary64`
19×	`unswap-sqr_binary64`

Counts

4 → 131

Calls

4 calls:

8.0ms	(.f64 5 (.f64 (pow.f64 eps 4) x))
6.0ms	(*.f64 (pow.f64 eps 3) (pow.f64 x 2))
5.0ms	(.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2)))
4.0ms	(*.f64 (pow.f64 eps 4) x)

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary64`
481×	`log-prod_binary64`
331×	`unswap-sqr_binary64`
292×	`exp-prod_binary64`
280×	`associate-/l*_binary64`

Counts

131 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	1861
1	335	1727
2	1255	1605
3	2383	1529
4	4367	1529
5	5059	1529

prune301.0ms (6.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Error

0.0b

Counts

155 → 3

Alt Table

Status	Error	Program
	10.0b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	7.8b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (.f64 5 (.f64 (pow.f64 eps 4) x))))
▶	9.9b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))

Compiler

Compiled 4249 to 3147 computations (25.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
✓	0.1b	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
✓	0.1b	(*.f64 5 (pow.f64 x 4))
✓	0.2b	(.f64 10 (.f64 eps eps))

series87.0ms (1.9%)

Counts

4 → 60

Calls

4 calls:

62.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
20.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
3.0ms	(*.f64 5 (pow.f64 x 4))
3.0ms	(.f64 10 (.f64 eps eps))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64`
52×	`add-cbrt-cube_binary64`
50×	`pow1_binary64`
36×	`prod-exp_binary64`
34×	`cbrt-unprod_binary64`

Counts

4 → 118

Calls

4 calls:

11.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
9.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
4.0ms	(.f64 10 (.f64 eps eps))
4.0ms	(*.f64 5 (pow.f64 x 4))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

760×	`distribute-rgt-in_binary64`
721×	`distribute-lft-in_binary64`
396×	`associate-l_binary64`
378×	`fma-def_binary64`
337×	`associate-r_binary64`

Counts

178 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	3089
1	413	2567
2	1708	2530
3	5009	2530

prune164.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Error

0.0b

Counts

151 → 5

Alt Table

Status	Error	Program
	10.0b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	7.8b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (.f64 5 (.f64 (pow.f64 eps 4) x))))
	10.0b	(fma.f64 eps (.f64 (.f64 5 (.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (pow.f64 x 4)))) (cbrt.f64 (pow.f64 x 4))) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
▶	10.0b	(fma.f64 eps (.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (.f64 5 (pow.f64 x 4)))) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
✓	9.9b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))

Compiler

Compiled 4231 to 2055 computations (51.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 5 (pow.f64 x 4))
✓	0.1b	(.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (*.f64 5 (pow.f64 x 4))))
	0.2b	(.f64 10 (.f64 eps eps))
✓	15.6b	(sqrt.f64 (*.f64 5 (pow.f64 x 4)))

series42.0ms (0.9%)

Counts

2 → 24

Calls

2 calls:

34.0ms	(sqrt.f64 (*.f64 5 (pow.f64 x 4)))
8.0ms	(.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (*.f64 5 (pow.f64 x 4))))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`pow1_binary64`
9×	`sqrt-pow1_binary64`
9×	`pow1/2_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 52

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (*.f64 5 (pow.f64 x 4))))
2.0ms	(sqrt.f64 (*.f64 5 (pow.f64 x 4)))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

555×	`fma-def_binary64`
459×	`*-commutative_binary64`
432×	`associate-l_binary64`
372×	`associate-/l*_binary64`
336×	`sqr-pow_binary64`

Counts

76 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	766
1	92	702
2	288	690
3	1083	677
4	1917	608
5	2732	608
6	4419	608
7	4869	608

prune243.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	176	5	181

Error

Counts

181 → 5

Alt Table

Status	Error	Program
	10.0b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))
✓	7.8b	(+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (pow.f64 eps 5) (.f64 5 (.f64 (pow.f64 eps 4) x))))
✓	10.0b	(fma.f64 eps (.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (.f64 5 (pow.f64 x 4)))) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	10.6b	(fma.f64 eps (sqrt.f64 (.f64 25 (pow.f64 x 8))) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
✓	9.9b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))

Compiler

Compiled 5846 to 3582 computations (38.7% saved)

regimes487.0ms (10.7%)

Accuracy

Total 1.1b remaining (85.4%)

Threshold costs 0b (0%)

Counts

98 → 3

Compiler

Compiled 5335 to 3903 computations (26.8% saved)

bsearch41.0ms (0.9%)

Steps

Iters	Range		Point
8	2.640808483504454e-52	1.4259179759861545e-49	1.1002273010802258e-50
5	-6.1873510108031905e-61	-1.5969877354767404e-61	-6.091962211134749e-61

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	101
1	48	101
2	48	101

end133.0ms (2.9%)

Compiler: Compiled 259 to 173 computations (33.2% saved)

Details

analyze1.0ms (0%)

sample2.2s (47.3%)

simplify62.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series34.0ms (0.7%)

rewrite24.0ms (0.5%)

simplify140.0ms (3.1%)

prune194.0ms (4.3%)

localize12.0ms (0.3%)

series64.0ms (1.4%)

rewrite29.0ms (0.6%)

simplify91.0ms (2%)

prune301.0ms (6.6%)

localize13.0ms (0.3%)

series87.0ms (1.9%)

rewrite37.0ms (0.8%)

simplify74.0ms (1.6%)

prune164.0ms (3.6%)

localize13.0ms (0.3%)

series42.0ms (0.9%)

rewrite11.0ms (0.2%)

simplify87.0ms (1.9%)

prune243.0ms (5.3%)

regimes487.0ms (10.7%)

bsearch41.0ms (0.9%)

simplify3.0ms (0.1%)

end133.0ms (2.9%)

Profiling