Details

analyze2.0ms (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)

sample1.6s (35.2%)

Results

961.0ms	6779×	body	128	valid
269.0ms	564×	body	1024	valid
190.0ms	544×	body	512	valid
90.0ms	357×	body	256	valid
8.0ms	12×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify61.0ms (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

8.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.8b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 5)
✓	1.1b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series40.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
14.0ms	(pow.f64 (+.f64 x eps) 5)

rewrite23.0ms (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:

10.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
3.0ms	(pow.f64 (+.f64 x eps) 5)

simplify138.0ms (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

prune289.0ms (6.5%)

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
	11.1b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
▶	9.0b	(+.f64 (pow.f64 eps 5) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))

Compiler

Compiled 4456 to 2852 computations (36% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series80.0ms (1.8%)

Counts

4 → 60

Calls

4 calls:

36.0ms	(*.f64 (pow.f64 eps 4) x)
30.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
12.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
2.0ms	(.f64 10 (.f64 eps eps))

rewrite38.0ms (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:

12.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
7.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
4.0ms	(.f64 10 (.f64 eps eps))
4.0ms	(*.f64 (pow.f64 eps 4) x)

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

760×	`distribute-rgt-in_binary64`
721×	`distribute-lft-in_binary64`
427×	`associate-l_binary64`
394×	`fma-def_binary64`
354×	`associate-r_binary64`

Counts

178 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3075
1	407	2568
2	1773	2537
3	5132	2537

prune424.0ms (9.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	156	3	159

Error

0.0b

Counts

159 → 3

Alt Table

Status	Error	Program
▶	11.1b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	9.0b	(+.f64 (pow.f64 eps 5) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))

Compiler

Compiled 5012 to 2557 computations (49% saved)

localize37.0ms (0.8%)

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 5 (pow.f64 x 4))
	0.2b	(.f64 10 (.f64 eps eps))
	0.2b	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 5 (pow.f64 x 4))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unpow-prod-down_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 27

Calls

1 calls:

6.0ms

(*.f64 5 (pow.f64 x 4))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

532×	`associate-/l*_binary64`
527×	`unswap-sqr_binary64`
465×	`associate-/l/_binary64`
448×	`associate-/r/_binary64`
442×	`fma-def_binary64`

Counts

27 → 34

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	54	293
1	96	281
2	205	263
3	560	263
4	939	257
5	1984	252
6	4935	252
7	4862	252

prune273.0ms (6.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	146	6	152

Error

0.0b

Counts

152 → 6

Alt Table

Status	Error	Program
	11.2b	(fma.f64 eps (.f64 (.f64 5 (.f64 x x)) (pow.f64 x (/.f64 4 2))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
▶	11.1b	(fma.f64 eps (.f64 (sqrt.f64 5) (.f64 (sqrt.f64 5) (pow.f64 x 4))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(fma.f64 eps (.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (.f64 5 (pow.f64 x 4)))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
✓	11.1b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	9.0b	(+.f64 (pow.f64 eps 5) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))

Compiler

Compiled 5430 to 2898 computations (46.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 5) (.f64 (sqrt.f64 5) (pow.f64 x 4)))
4.0ms	(*.f64 (sqrt.f64 5) (pow.f64 x 4))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`prod-exp_binary64`
9×	`sqrt-prod_binary64`

Counts

2 → 57

Calls

2 calls:

43.0ms	(.f64 (sqrt.f64 5) (.f64 (sqrt.f64 5) (pow.f64 x 4)))
6.0ms	(*.f64 (sqrt.f64 5) (pow.f64 x 4))

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-/l*_binary64`
279×	`log-div_binary64`
265×	`*-commutative_binary64`
246×	`sqr-pow_binary64`
223×	`distribute-rgt-in_binary64`

Counts

69 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	76	788
1	155	749
2	467	739
3	664	731
4	1241	722
5	2618	722
6	4632	722
7	4876	722

prune222.0ms (5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	11.2b	(fma.f64 eps (.f64 (.f64 5 (.f64 x x)) (pow.f64 x (/.f64 4 2))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
✓	11.1b	(fma.f64 eps (.f64 (sqrt.f64 5) (.f64 (sqrt.f64 5) (pow.f64 x 4))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(fma.f64 eps (.f64 (sqrt.f64 (.f64 5 (pow.f64 x 4))) (sqrt.f64 (.f64 5 (pow.f64 x 4)))) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
✓	11.1b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))))
	11.2b	(+.f64 (.f64 5 (.f64 eps (pow.f64 x 4))) (+.f64 (.f64 10 (.f64 (pow.f64 eps 3) (pow.f64 x 2))) (+.f64 (.f64 5 (.f64 (pow.f64 eps 4) x)) (.f64 10 (.f64 (pow.f64 eps 2) (pow.f64 x 3))))))
✓	9.0b	(+.f64 (pow.f64 eps 5) (fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x)))))

Compiler

Compiled 5076 to 3091 computations (39.1% saved)

regimes756.0ms (16.9%)

Accuracy

Total 0.4b remaining (72.3%)

Threshold costs 0.4b (72.3%)

Counts

124 → 3

Compiler

Compiled 7653 to 5500 computations (28.1% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	137
1	61	135
2	73	135
3	81	135
4	84	135
5	84	135

end182.0ms (4.1%)

Compiler: Compiled 383 to 260 computations (32.1% saved)

Details

analyze2.0ms (0%)

sample1.6s (35.2%)

simplify61.0ms (1.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series40.0ms (0.9%)

rewrite23.0ms (0.5%)

simplify138.0ms (3.1%)

prune289.0ms (6.5%)

localize14.0ms (0.3%)

series80.0ms (1.8%)

rewrite38.0ms (0.8%)

simplify76.0ms (1.7%)

prune424.0ms (9.5%)

localize37.0ms (0.8%)

series3.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify59.0ms (1.3%)

prune273.0ms (6.1%)

localize18.0ms (0.4%)

series14.0ms (0.3%)

rewrite52.0ms (1.2%)

simplify76.0ms (1.7%)

prune222.0ms (5%)

regimes756.0ms (16.9%)

bsearch4.0ms (0.1%)

simplify7.0ms (0.2%)

end182.0ms (4.1%)

Profiling