Details

analyze1.3s (14.9%)

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
12.5%	87.4%	0.1%	6
15.6%	84.3%	0.1%	7
18.7%	81.1%	0.1%	8
25.7%	73.3%	0.9%	9
28.5%	60.8%	10.7%	10
30.2%	58.7%	11.1%	11
32.7%	52.2%	15.2%	12
33.5%	39.2%	27.4%	13
34.3%	37.8%	27.9%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample2.0s (22.8%)

Results

1.3s	8256×	body	128	valid
611.0ms	3807×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

614×	`*-commutative_binary64`
613×	`associate-l_binary64`
526×	`sqr-pow_binary64`
394×	`associate-*r/_binary64`
380×	`cube-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	18
2	55	17
3	104	17
4	225	17
5	591	17
6	1774	17
7	2466	17
8	2534	17
9	2692	17
10	2908	17
11	3166	17
12	3656	17
13	4497	17
14	5019	17

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	1.9b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series571.0ms (6.5%)

Counts

3 → 84

Calls

3 calls:

341.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
227.0ms	(*.f64 a (pow.f64 k m))
3.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

6.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
4.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
4.0ms	(*.f64 a (pow.f64 k m))

simplify120.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
543×	`fma-neg_binary64`
321×	`distribute-rgt-in_binary64`
285×	`cancel-sign-sub-inv_binary64`
191×	`associate-r_binary64`

Counts

156 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	223	2902
1	603	2584
2	2391	2295
3	4340	2291
4	4966	2291
5	4913	2291

prune166.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	4	152

Error

0.0b

Counts

152 → 4

Alt Table

Status	Error	Program
	13.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 3)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	26.4b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) (-.f64 (/.f64 99 k) 10)))
	2.0b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
▶	1.9b	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))

Compiler

Compiled 3783 to 1998 computations (47.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	0.4b	(/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
✓	1.5b	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))

series359.0ms (4.1%)

Counts

2 → 60

Calls

2 calls:

303.0ms	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
56.0ms	(/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
41×	`add-exp-log_binary64`
39×	`add-cube-cbrt_binary64`

Counts

2 → 131

Calls

2 calls:

19.0ms	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
6.0ms	(/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

simplify186.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
411×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l*_binary64`
250×	`associate-r_binary64`
199×	`associate-l_binary64`

Counts

191 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5939
1	822	5188
2	3284	4860
3	3852	4860
4	4955	4860
5	4982	4860

prune309.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	307	4	311

Error

0.0b

Counts

311 → 4

Alt Table

Status	Error	Program
	13.2b	(/.f64 (cbrt.f64 (pow.f64 (.f64 a (pow.f64 k m)) 3)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
▶	2.0b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
	26.5b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	1.9b	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))

Compiler

Compiled 9094 to 5114 computations (43.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
✓	1.9b	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

series566.0ms (6.4%)

Counts

2 → 72

Calls

2 calls:

291.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
275.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
36×	`times-frac_binary64`
26×	`div-exp_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

2 → 89

Calls

2 calls:

6.0ms	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m))))
4.0ms	(/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 a (pow.f64 k m)))

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-def_binary64`
360×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
214×	`associate-r_binary64`
162×	`neg-mul-1_binary64`

Counts

161 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	4810
1	696	4018
2	2746	3945
3	4282	3936
4	4879	3936

prune213.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	201	4	205

Error

0.0b

Counts

205 → 4

Alt Table

Status	Error	Program
▶	1.9b	(/.f64 (/.f64 1 (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 (*.f64 a (pow.f64 k m))))
✓	1.9b	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
	16.6b	(/.f64 1 (fma.f64 k (/.f64 k (.f64 a (pow.f64 k m))) (fma.f64 k (/.f64 10 (.f64 a (pow.f64 k m))) (/.f64 (pow.f64 k (neg.f64 m)) a))))
	2.0b	(/.f64 1 (/.f64 (fma.f64 k (+.f64 k 10) 1) (*.f64 (pow.f64 k m) a)))

Compiler

Compiled 5357 to 3043 computations (43.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (*.f64 a (pow.f64 k m)))
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.5b	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))
✓	1.5b	(/.f64 (/.f64 1 (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 (*.f64 a (pow.f64 k m))))

series547.0ms (6.2%)

Counts

3 → 84

Calls

3 calls:

293.0ms	(/.f64 (/.f64 1 (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 (*.f64 a (pow.f64 k m))))
251.0ms	(/.f64 1 (*.f64 a (pow.f64 k m)))
3.0ms	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))

rewrite46.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

217×	`times-frac_binary64`
186×	`add-exp-log_binary64`
120×	`div-exp_binary64`
97×	`*-un-lft-identity_binary64`
97×	`add-sqr-sqrt_binary64`

Counts

3 → 251

Calls

3 calls:

9.0ms	(/.f64 (/.f64 1 (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 (*.f64 a (pow.f64 k m))))
6.0ms	(/.f64 1 (*.f64 a (pow.f64 k m)))
2.0ms	(/.f64 1 (fma.f64 k (+.f64 k 10) 1))

simplify214.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

570×	`fma-def_binary64`
535×	`fma-neg_binary64`
352×	`cancel-sign-sub-inv_binary64`
193×	`associate-r_binary64`
177×	`distribute-rgt-in_binary64`

Counts

335 → 334

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	294	8914
1	743	7767
2	2550	7480
3	4108	7471
4	4918	7471

prune367.0ms (4.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	371	1	372
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	372	4	376

Error

0.0b

Counts

376 → 4

Alt Table

Status	Error	Program
✓	1.9b	(/.f64 (/.f64 1 (fma.f64 k (+.f64 k 10) 1)) (/.f64 1 (*.f64 a (pow.f64 k m))))
✓	1.9b	(.f64 (/.f64 a 1) (/.f64 (pow.f64 k m) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k))))
	16.6b	(/.f64 1 (fma.f64 k (/.f64 k (.f64 a (pow.f64 k m))) (fma.f64 k (/.f64 10 (.f64 a (pow.f64 k m))) (/.f64 (pow.f64 k (neg.f64 m)) a))))
	1.9b	(/.f64 (*.f64 (pow.f64 k m) a) (fma.f64 k (+.f64 k 10) 1))

Compiler

Compiled 10014 to 6179 computations (38.3% saved)

regimes1.4s (15.3%)

Accuracy

Total 0.1b remaining (53.3%)

Threshold costs 0.1b (53.3%)

Counts

213 → 2

Compiler

Compiled 16919 to 11782 computations (30.4% saved)

bsearch44.0ms (0.5%)

Steps

Iters	Range		Point
8	6.255524633154715e+77	4.749218810054733e+81	3.2317114830070396e+78

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-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	22	44
1	30	44
2	32	44
3	33	44
4	32	44

end82.0ms (0.9%)

Compiler: Compiled 149 to 97 computations (34.9% saved)

Details

analyze1.3s (14.9%)

sample2.0s (22.8%)

simplify104.0ms (1.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series571.0ms (6.5%)

rewrite18.0ms (0.2%)

simplify120.0ms (1.4%)

prune166.0ms (1.9%)

localize10.0ms (0.1%)

series359.0ms (4.1%)

rewrite45.0ms (0.5%)

simplify186.0ms (2.1%)

prune309.0ms (3.5%)

localize9.0ms (0.1%)

series566.0ms (6.4%)

rewrite20.0ms (0.2%)

simplify124.0ms (1.4%)

prune213.0ms (2.4%)

localize10.0ms (0.1%)

series547.0ms (6.2%)

rewrite46.0ms (0.5%)

simplify214.0ms (2.4%)

prune367.0ms (4.2%)

regimes1.4s (15.3%)

bsearch44.0ms (0.5%)

simplify3.0ms (0%)

end82.0ms (0.9%)

Profiling