Details

analyze1.3s (17.3%)

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)

sample1.9s (24.6%)

Results

1.2s	8256×	body	128	valid
556.0ms	3823×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify105.0ms (1.4%)

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

1.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.1b	(/.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 10 k))
✓	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	1.1b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series513.0ms (6.6%)

Counts

4 → 96

Calls

4 calls:

285.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
224.0ms	(*.f64 a (pow.f64 k m))
2.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
1.0ms	(+.f64 1 (*.f64 10 k))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

7.0ms	(/.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))
2.0ms	(+.f64 1 (*.f64 10 k))

simplify125.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

528×	`fma-neg_binary64`
323×	`distribute-rgt-in_binary64`
302×	`cancel-sign-sub-inv_binary64`
278×	`distribute-lft-in_binary64`
213×	`associate-r_binary64`

Counts

184 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3078
1	661	2754
2	2555	2566
3	4343	2560
4	4999	2560
5	4912	2560

prune171.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	4	178

Error

0.2b

Counts

178 → 4

Alt Table

Status	Error	Program
	1.5b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
	32.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
▶	1.1b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
	27.2b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m)))

Compiler

Compiled 4361 to 2267 computations (48% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(fma.f64 k 10 (fma.f64 k k 1))
✓	0.3b	(/.f64 1 (fma.f64 k 10 (fma.f64 k k 1)))
✓	1.1b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))

series285.0ms (3.7%)

Counts

3 → 60

Calls

3 calls:

279.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
3.0ms	(/.f64 1 (fma.f64 k 10 (fma.f64 k k 1)))
2.0ms	(fma.f64 k 10 (fma.f64 k k 1))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
18×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`

Counts

3 → 90

Calls

3 calls:

7.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
2.0ms	(/.f64 1 (fma.f64 k 10 (fma.f64 k k 1)))
0.0ms	(fma.f64 k 10 (fma.f64 k k 1))

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-def_binary64`
514×	`fma-neg_binary64`
433×	`associate-/l*_binary64`
325×	`times-frac_binary64`
315×	`cancel-sign-sub-inv_binary64`

Counts

150 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	3293
1	544	2997
2	1901	2619
3	4537	2610
4	4924	2610

prune198.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	218	4	222

Error

0.2b

Counts

222 → 4

Alt Table

Status	Error	Program
▶	1.5b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
	32.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	1.1b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
	27.2b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m)))

Compiler

Compiled 5256 to 2951 computations (43.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k 10 (fma.f64 k k 1))
✓	1.1b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
✓	1.1b	(expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1))))
✓	14.8b	(log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))

series409.0ms (5.3%)

Counts

3 → 60

Calls

3 calls:

404.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
3.0ms	(log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))
2.0ms	(expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

6.0ms	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
0.0ms	(log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1))))

simplify224.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

648×	`times-frac_binary64`
548×	`fma-neg_binary64`
510×	`fma-def_binary64`
296×	`cancel-sign-sub-inv_binary64`
213×	`associate-/l/_binary64`

Counts

107 → 141

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	206	2424
1	548	2196
2	1884	1918
3	4478	1913
4	4951	1913
5	4987	1913

prune235.0ms (3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Error

0.2b

Counts

170 → 4

Alt Table

Status	Error	Program
✓	1.5b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
	32.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	1.1b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
▶	27.2b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m)))

Compiler

Compiled 3783 to 2145 computations (43.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 k 10 (fma.f64 k k 1))
✓	0.2b	(*.f64 (log.f64 k) m)
✓	1.1b	(.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m))
✓	3.5b	(/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))

series832.0ms (10.7%)

Counts

3 → 68

Calls

3 calls:

562.0ms	(.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m))
218.0ms	(*.f64 (log.f64 k) m)
52.0ms	(/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

6.0ms	(.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m))
4.0ms	(*.f64 (log.f64 k) m)
2.0ms	(/.f64 a (fma.f64 k 10 (fma.f64 k k 1)))

simplify117.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
438×	`fma-neg_binary64`
384×	`cancel-sign-sub-inv_binary64`
241×	`associate-r_binary64`
165×	`associate-l_binary64`

Counts

153 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	3463
1	638	3138
2	2404	2969
3	4499	2959
4	5048	2959

prune247.0ms (3.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	293	4	297

Error

0.2b

Counts

297 → 4

Alt Table

Status	Error	Program
✓	1.5b	(/.f64 (*.f64 a (pow.f64 k m)) (expm1.f64 (log1p.f64 (fma.f64 k 10 (fma.f64 k k 1)))))
	32.0b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	1.1b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (fma.f64 k 10 (fma.f64 k k 1))))
✓	27.2b	(+.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (/.f64 a (fma.f64 k 10 (fma.f64 k k 1))) (.f64 (log.f64 k) m)))

Compiler

Compiled 9696 to 5207 computations (46.3% saved)

regimes750.0ms (9.7%)

Accuracy

Total 1.9b remaining (97.5%)

Threshold costs 0b (0%)

Counts

169 → 1

Compiler

Compiled 13102 to 8916 computations (31.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
2	12	18

end88.0ms (1.1%)

Compiler: Compiled 118 to 74 computations (37.3% saved)

Details

analyze1.3s (17.3%)

sample1.9s (24.6%)

simplify105.0ms (1.4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series513.0ms (6.6%)

rewrite21.0ms (0.3%)

simplify125.0ms (1.6%)

prune171.0ms (2.2%)

localize9.0ms (0.1%)

series285.0ms (3.7%)

rewrite15.0ms (0.2%)

simplify103.0ms (1.3%)

prune198.0ms (2.5%)

localize13.0ms (0.2%)

series409.0ms (5.3%)

rewrite9.0ms (0.1%)

simplify224.0ms (2.9%)

prune235.0ms (3%)

localize11.0ms (0.1%)

series832.0ms (10.7%)

rewrite16.0ms (0.2%)

simplify117.0ms (1.5%)

prune247.0ms (3.2%)

regimes750.0ms (9.7%)

simplify2.0ms (0%)

end88.0ms (1.1%)

Profiling