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)

sample2.4s (43.6%)

Results

1.5s	6806×	body	128	valid
483.0ms	530×	body	1024	valid
236.0ms	552×	body	512	valid
90.0ms	348×	body	256	valid
13.0ms	20×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify61.0ms (1.1%)

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

6.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.5b	(-.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)
✓	1.0b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series38.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
18.0ms	(pow.f64 (+.f64 x eps) 5)

rewrite21.0ms (0.4%)

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:

9.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
3.0ms	(pow.f64 (+.f64 x eps) 5)

simplify142.0ms (2.6%)

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

prune201.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	161	4	165
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	161	5	166

Error

0.0b

Counts

166 → 5

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
	11.9b	(+.f64 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
	14.2b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	14.4b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
▶	6.8b	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))

Compiler

Compiled 4535 to 2906 computations (35.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series68.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

21.0ms	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))
19.0ms	(fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5))
15.0ms	(.f64 (pow.f64 eps 3) (.f64 x x))
13.0ms	(*.f64 (pow.f64 eps 4) x)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
19×	`associate-l_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`prod-exp_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(.f64 (pow.f64 eps 3) (.f64 x x))
4.0ms	(*.f64 (pow.f64 eps 4) x)
0.0ms	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))
0.0ms	(fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5))

simplify103.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

557×	`distribute-rgt-in_binary64`
550×	`distribute-lft-in_binary64`
388×	`fma-def_binary64`
347×	`exp-prod_binary64`
343×	`associate-+l+_binary64`

Counts

154 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	2392
1	259	2203
2	814	2161
3	1793	2061
4	4793	2061
5	5050	2061

prune164.0ms (3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Error

0.0b

Counts

132 → 5

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
▶	11.9b	(+.f64 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
	14.2b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	14.4b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
✓	6.8b	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))

Compiler

Compiled 3371 to 2218 computations (34.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)
✓	11.4b	(fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
✓	12.9b	(fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))
✓	24.7b	(cbrt.f64 (pow.f64 x 5))

series291.0ms (5.3%)

Counts

4 → 72

Calls

4 calls:

132.0ms	(fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
60.0ms	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)
59.0ms	(fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))
38.0ms	(cbrt.f64 (pow.f64 x 5))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`cbrt-prod_binary64`
10×	`unpow-prod-down_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 61

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)
1.0ms	(cbrt.f64 (pow.f64 x 5))
0.0ms	(fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
0.0ms	(fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (*.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

521×	`times-frac_binary64`
346×	`cancel-sign-sub-inv_binary64`
282×	`unswap-sqr_binary64`
274×	`fma-neg_binary64`
179×	`associate-r_binary64`

Counts

133 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	3109
1	643	2896
2	2041	2552
3	4610	2552
4	4986	2552
5	4876	2552

prune1.0s (18.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	340	5	345

Error

0.0b

Counts

345 → 5

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	11.9b	(+.f64 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
▶	14.2b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	14.4b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
✓	6.8b	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))

Compiler

Compiled 23563 to 15959 computations (32.3% saved)

localize11.0ms (0.2%)

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))
✓	0.1b	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
✓	0.2b	(.f64 10 (.f64 eps eps))

series46.0ms (0.8%)

Counts

4 → 60

Calls

4 calls:

26.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
14.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
3.0ms	(*.f64 5 (pow.f64 x 4))
3.0ms	(.f64 10 (.f64 eps eps))

rewrite41.0ms (0.7%)

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)))
10.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
4.0ms	(.f64 10 (.f64 eps eps))
4.0ms	(*.f64 5 (pow.f64 x 4))

simplify154.0ms (2.8%)

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

prune223.0ms (4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
✓	6.5b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))
✓	11.9b	(+.f64 (fma.f64 (pow.f64 (.f64 (cbrt.f64 (+.f64 x eps)) (cbrt.f64 (+.f64 x eps))) 5) (pow.f64 (cbrt.f64 (+.f64 x eps)) 5) (neg.f64 (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5)))))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))) (.f64 (cbrt.f64 (pow.f64 x 5)) (.f64 (cbrt.f64 (pow.f64 x 5)) (cbrt.f64 (pow.f64 x 5))))))
✓	14.2b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	14.4b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
	15.9b	(fma.f64 eps (cbrt.f64 (.f64 125 (pow.f64 x 12))) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
✓	6.8b	(fma.f64 10 (.f64 (pow.f64 eps 3) (.f64 x x)) (fma.f64 5 (*.f64 (pow.f64 eps 4) x) (pow.f64 eps 5)))

Compiler

Compiled 4182 to 2016 computations (51.8% saved)

regimes190.0ms (3.4%)

Accuracy

Total 1.0b remaining (96.2%)

Threshold costs 1.0b (96.2%)

Counts

23 → 3

Compiler

Compiled 1393 to 1008 computations (27.6% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	85
1	32	85
2	36	85
3	38	85
4	39	85
5	39	85

end162.0ms (2.9%)

Compiler: Compiled 280 to 193 computations (31.1% saved)

Details

analyze2.0ms (0%)

sample2.4s (43.6%)

simplify61.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series38.0ms (0.7%)

rewrite21.0ms (0.4%)

simplify142.0ms (2.6%)

prune201.0ms (3.6%)

localize15.0ms (0.3%)

series68.0ms (1.2%)

rewrite14.0ms (0.3%)

simplify103.0ms (1.9%)

prune164.0ms (3%)

localize17.0ms (0.3%)

series291.0ms (5.3%)

rewrite8.0ms (0.1%)

simplify121.0ms (2.2%)

prune1.0s (18.3%)

localize11.0ms (0.2%)

series46.0ms (0.8%)

rewrite41.0ms (0.7%)

simplify154.0ms (2.8%)

prune223.0ms (4%)

regimes190.0ms (3.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end162.0ms (2.9%)

Profiling