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 (31.7%)

Results

1.0s	6820×	body	128	valid
254.0ms	518×	body	1024	valid
201.0ms	544×	body	512	valid
99.0ms	354×	body	256	valid
12.0ms	20×	body	2048	valid

Compiler

Compiled 63 to 46 computations (27% saved)

simplify60.0ms (1.2%)

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

7.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.9b	(-.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)
✓	1.2b	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

series39.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(pow.f64 (+.f64 x eps) 5)
17.0ms	(-.f64 (pow.f64 (+.f64 x eps) 5) (pow.f64 x 5))

rewrite25.0ms (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)

simplify135.0ms (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

prune221.0ms (4.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	160	5	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	5	166

Error

0.0b

Counts

166 → 5

Alt Table

Status	Error	Program
	8.3b	(+.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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
	9.7b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	9.8b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
▶	8.3b	(+.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)))))
	53.1b	(/.f64 (-.f64 (pow.f64 (+.f64 eps x) 10) (pow.f64 x 10)) (+.f64 (pow.f64 x 5) (pow.f64 (+.f64 eps x) 5)))

Compiler

Compiled 4564 to 2898 computations (36.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series56.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

22.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
21.0ms	(fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
10.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
2.0ms	(.f64 10 (.f64 eps eps))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary64`
50×	`add-exp-log_binary64`
50×	`pow1_binary64`
33×	`cbrt-unprod_binary64`
33×	`prod-exp_binary64`

Counts

4 → 101

Calls

4 calls:

13.0ms	(.f64 (.f64 x x) (.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x)))
8.0ms	(.f64 (.f64 10 (*.f64 eps eps)) (+.f64 eps x))
4.0ms	(.f64 10 (.f64 eps eps))
0.0ms	(fma.f64 5 (.f64 (pow.f64 eps 4) x) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))

simplify79.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

794×	`distribute-rgt-in_binary64`
755×	`distribute-lft-in_binary64`
554×	`fma-def_binary64`
362×	`associate-l_binary64`
305×	`associate-r_binary64`

Counts

185 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	3802
1	362	3149
2	1585	3105
3	5117	3105

prune330.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
▶	8.3b	(+.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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
	9.7b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	9.8b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
✓	8.3b	(+.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)))))
	53.1b	(/.f64 (-.f64 (pow.f64 (+.f64 eps x) 10) (pow.f64 x 10)) (+.f64 (pow.f64 x 5) (pow.f64 (+.f64 eps x) 5)))

Compiler

Compiled 4636 to 2370 computations (48.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (cbrt.f64 x) 5)
✓	0.9b	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)
✓	11.7b	(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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
✓	13.1b	(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))

series445.0ms (8.6%)

Counts

4 → 72

Calls

4 calls:

170.0ms	(pow.f64 (cbrt.f64 x) 5)
121.0ms	(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))
112.0ms	(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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
42.0ms	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`

Counts

4 → 67

Calls

4 calls:

5.0ms	(pow.f64 (cbrt.f64 (+.f64 x eps)) 5)
2.0ms	(pow.f64 (cbrt.f64 x) 5)
0.0ms	(fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))

simplify164.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

521×	`times-frac_binary64`
318×	`associate-/l*_binary64`
286×	`unswap-sqr_binary64`
181×	`associate-r_binary64`
171×	`sqr-pow_binary64`

Counts

139 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3879
1	682	3374
2	2109	2802
3	4888	2802

prune455.0ms (8.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
✓	8.3b	(+.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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
▶	9.7b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	9.8b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
✓	8.3b	(+.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)))))
	53.1b	(/.f64 (-.f64 (pow.f64 (+.f64 eps x) 10) (pow.f64 x 10)) (+.f64 (pow.f64 x 5) (pow.f64 (+.f64 eps x) 5)))

Compiler

Compiled 14564 to 6977 computations (52.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

23.0ms

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

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

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

735×	`fma-def_binary64`
638×	`distribute-rgt-in_binary64`
634×	`distribute-lft-in_binary64`
273×	`associate-l_binary64`
262×	`exp-prod_binary64`

Counts

34 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	1015
1	103	866
2	294	866
3	1227	841
4	4922	841
5	4997	841
6	4970	841

prune216.0ms (4.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	141	6	147

Error

0.0b

Counts

147 → 6

Alt Table

Status	Error	Program
	13.2b	(.f64 (sqrt.f64 (.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 eps (.f64 10 (+.f64 eps x))))))) (sqrt.f64 (.f64 eps (+.f64 (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 eps (*.f64 10 (+.f64 eps x))))))))
✓	8.3b	(+.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 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 5)) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5) (.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 5))))
✓	9.7b	(fma.f64 eps (.f64 5 (pow.f64 x 4)) (.f64 (.f64 x x) (.f64 (.f64 10 (.f64 eps eps)) (+.f64 eps x))))
	9.8b	(fma.f64 5 (.f64 eps (pow.f64 x 4)) (.f64 10 (.f64 (.f64 eps eps) (pow.f64 x 3))))
✓	8.3b	(+.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)))))
	53.1b	(/.f64 (-.f64 (pow.f64 (+.f64 eps x) 10) (pow.f64 x 10)) (+.f64 (pow.f64 x 5) (pow.f64 (+.f64 eps x) 5)))

Compiler

Compiled 4048 to 1949 computations (51.9% saved)

regimes938.0ms (18.1%)

Accuracy

Total 0.4b remaining (88.7%)

Threshold costs 0.4b (88.7%)

Counts

168 → 3

Compiler

Compiled 13771 to 9414 computations (31.6% saved)

bsearch7.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	85
1	36	85
2	40	85
3	42	85
4	43	85
5	42	85

end161.0ms (3.1%)

Compiler: Compiled 309 to 197 computations (36.2% saved)

Details

analyze2.0ms (0%)

sample1.6s (31.7%)

simplify60.0ms (1.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series39.0ms (0.7%)

rewrite25.0ms (0.5%)

simplify135.0ms (2.6%)

prune221.0ms (4.3%)

localize15.0ms (0.3%)

series56.0ms (1.1%)

rewrite35.0ms (0.7%)

simplify79.0ms (1.5%)

prune330.0ms (6.4%)

localize20.0ms (0.4%)

series445.0ms (8.6%)

rewrite10.0ms (0.2%)

simplify164.0ms (3.2%)

prune455.0ms (8.8%)

localize13.0ms (0.2%)

series23.0ms (0.4%)

rewrite1.0ms (0%)

simplify82.0ms (1.6%)

prune216.0ms (4.2%)

regimes938.0ms (18.1%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end161.0ms (3.1%)

Profiling