Details

analyze1.8s (14.3%)

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
49.9%	49.9%	0.1%	3
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
49.9%	49.9%	0.1%	7
49.9%	49.9%	0.1%	8
49.9%	49.9%	0.1%	9
49.9%	43.9%	6.2%	10
49.9%	43.8%	6.3%	11
49.9%	40.8%	9.3%	12
49.9%	30.8%	19.3%	13
49.9%	30.6%	19.5%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.7s (13.7%)

Results

1.4s	8256×	body	128	valid
203.0ms	1549×	body	128	invalid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify133.0ms (1.1%)

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

5.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.7b	(/.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 a (pow.f64 k m))
✓	0.0b	(+.f64 1 (*.f64 10 k))
✓	0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
✓	5.3b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))

series650.0ms (5.1%)

Counts

4 → 96

Calls

4 calls:

360.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
286.0ms	(*.f64 a (pow.f64 k m))
3.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
2.0ms	(+.f64 1 (*.f64 10 k))

rewrite21.0ms (0.2%)

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))

simplify137.0ms (1.1%)

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

prune165.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	173	5	178

Error

0.0b

Counts

178 → 5

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
▶	5.7b	(/.f64 1 (/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m))))
✓	5.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	13.6b	(*.f64 a (pow.f64 k m))
	6.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k 10 (fma.f64 k k 1))) (cbrt.f64 (fma.f64 k 10 (fma.f64 k k 1))))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k 10 (fma.f64 k k 1)))))

Compiler

Compiled 4375 to 2277 computations (48% saved)

localize17.0ms (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))
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m))))
✓	5.6b	(/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m)))

series868.0ms (6.9%)

Counts

3 → 84

Calls

3 calls:

448.0ms	(/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m)))
417.0ms	(/.f64 1 (/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m))))
3.0ms	(fma.f64 k 10 (fma.f64 k k 1))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

10.0ms	(/.f64 1 (/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m))))
4.0ms	(/.f64 (fma.f64 k 10 (fma.f64 k k 1)) (*.f64 a (pow.f64 k m)))
0.0ms	(fma.f64 k 10 (fma.f64 k k 1))

simplify311.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

804×	`fma-def_binary64`
392×	`fma-neg_binary64`
363×	`cancel-sign-sub-inv_binary64`
213×	`associate-r_binary64`
155×	`associate-/l*_binary64`

Counts

183 → 204

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	5018
1	697	4377
2	2826	4127
3	4305	4127
4	4985	4127
5	5041	4127

prune546.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	243	4	247

Error

0.0b

Counts

247 → 4

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
▶	6.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	5.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
	12.3b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))

Compiler

Compiled 6386 to 3508 computations (45.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))
✓	2.0b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	3.2b	(/.f64 a (*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	15.9b	(cbrt.f64 (fma.f64 k (+.f64 k 10) 1))

series2.0s (15.6%)

Counts

4 → 84

Calls

4 calls:

1.5s	(/.f64 a (*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
416.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
9.0ms	(cbrt.f64 (fma.f64 k (+.f64 k 10) 1))
9.0ms	(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))

rewrite91.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
53×	`add-exp-log_binary64`
52×	`associate-r_binary64`
46×	`cbrt-prod_binary64`

Counts

4 → 177

Calls

4 calls:

30.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
9.0ms	(/.f64 a (*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
8.0ms	(*.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))
1.0ms	(cbrt.f64 (fma.f64 k (+.f64 k 10) 1))

simplify316.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
304×	`associate-r_binary64`
272×	`associate-*r/_binary64`
253×	`associate-l_binary64`
248×	`associate-/l*_binary64`

Counts

261 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	416	9761
1	1130	8036
2	4237	7964
3	4991	7964

prune577.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	350	4	354

Error

0.0b

Counts

354 → 4

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	6.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
✓	5.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
▶	12.3b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))

Compiler

Compiled 13337 to 8793 computations (34.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (pow.f64 k m))
✓	0.0b	(/.f64 k (*.f64 a (pow.f64 k m)))
✓	0.0b	(.f64 k (/.f64 k (.f64 a (pow.f64 k m))))
✓	0.1b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))

series1.2s (9.7%)

Counts

3 → 108

Calls

3 calls:

466.0ms	(.f64 k (/.f64 k (.f64 a (pow.f64 k m))))
387.0ms	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
377.0ms	(/.f64 k (*.f64 a (pow.f64 k m)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-exp-log_binary64`
35×	`prod-exp_binary64`
32×	`div-exp_binary64`
31×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

3 → 101

Calls

3 calls:

7.0ms	(.f64 k (/.f64 k (.f64 a (pow.f64 k m))))
7.0ms	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))
4.0ms	(/.f64 k (*.f64 a (pow.f64 k m)))

simplify134.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-neg_binary64`
517×	`associate-/r/_binary64`
444×	`*-commutative_binary64`
393×	`associate-/l/_binary64`
146×	`associate-r_binary64`

Counts

209 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	3395
1	462	3049
2	1840	2938
3	3987	2912
4	4892	2912
5	5078	2912

prune161.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	196	5	201

Error

0.0b

Counts

201 → 5

Alt Table

Status	Error	Program
	32.9b	(fma.f64 (/.f64 a k) (/.f64 (pow.f64 k m) k) (.f64 (/.f64 (.f64 a (pow.f64 k m)) (pow.f64 k 3)) -10))
✓	6.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1)))) (/.f64 (pow.f64 k m) (cbrt.f64 (fma.f64 k (+.f64 k 10) 1))))
	12.3b	(/.f64 (/.f64 1 k) (/.f64 k (*.f64 a (pow.f64 k m))))
✓	5.7b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
✓	12.3b	(/.f64 1 (.f64 k (/.f64 k (.f64 a (pow.f64 k m)))))

Compiler

Compiled 3674 to 1322 computations (64% saved)

regimes1.6s (12.5%)

Accuracy

Total 0.2b remaining (85.8%)

Threshold costs 0.2b (85.8%)

Counts

199 → 2

Compiler

Compiled 15839 to 10863 computations (31.4% saved)

bsearch10.0ms (0.1%)

Steps

Iters	Range		Point
1	5.4623296535475865e-24	1.747935423630934e-23	9.832168212624921e-24

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	61
1	30	61
2	40	61
3	44	61
4	46	61
5	44	61

end90.0ms (0.7%)

Compiler: Compiled 191 to 108 computations (43.5% saved)

Details

analyze1.8s (14.3%)

sample1.7s (13.7%)

simplify133.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series650.0ms (5.1%)

rewrite21.0ms (0.2%)

simplify137.0ms (1.1%)

prune165.0ms (1.3%)

localize17.0ms (0.1%)

series868.0ms (6.9%)

rewrite22.0ms (0.2%)

simplify311.0ms (2.5%)

prune546.0ms (4.3%)

localize24.0ms (0.2%)

series2.0s (15.6%)

rewrite91.0ms (0.7%)

simplify316.0ms (2.5%)

prune577.0ms (4.6%)

localize17.0ms (0.1%)

series1.2s (9.7%)

rewrite25.0ms (0.2%)

simplify134.0ms (1.1%)

prune161.0ms (1.3%)

regimes1.6s (12.5%)

bsearch10.0ms (0.1%)

simplify4.0ms (0%)

end90.0ms (0.7%)

Profiling