Details

analyze1.1s (14.5%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
10.0ms	123×	body	128	invalid
2.0ms	52×	body	128	nan

Compiler

Compiled 40 to 28 computations (30% saved)

simplify118.0ms (1.5%)

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 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	27	19
2	50	19
3	94	19
4	214	19
5	580	19
6	1763	19
7	2455	19
8	2523	19
9	2681	19
10	2897	19
11	3155	19
12	3645	19
13	4486	19
14	5008	19

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.9b

Counts

2 → 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 52 to 35 computations (32.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (*.f64 10 k))
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)))

rewrite126.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

19×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`associate-r_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
5.0ms	(*.f64 a (pow.f64 k m))
5.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
3.0ms	(+.f64 1 (*.f64 10 k))

Compiler

Compiled 1731 to 842 computations (51.4% saved)

series188.0ms (2.4%)

Error

1.9b

Counts

4 → 44

Calls

4 calls:

79.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 (+.f64 1 (.f64 10 k)) (*.f64 k k)))
44.0ms	(*.f64 a (pow.f64 k m))
16.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
9.0ms	(+.f64 1 (*.f64 10 k))

Compiler

Compiled 2087 to 1387 computations (33.5% saved)

simplify129.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

979×	`times-frac_binary64`
244×	`distribute-rgt-in_binary64`
197×	`cancel-sign-sub-inv_binary64`
181×	`associate-r_binary64`
162×	`associate-l_binary64`

Counts

118 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	2204
1	548	2007
2	2002	1927
3	4432	1903
4	4888	1903
5	4972	1903

prune96.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

1.8b

Counts

87 → 4

Alt Table

Status	Error	Program
	2.2b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
▶	1.9b	(/.f64 (.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
	1.9b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
	32.1b	(+.f64 (+.f64 (/.f64 a (+.f64 1 (.f64 k (+.f64 k 10)))) (.f64 (/.f64 a (+.f64 1 (.f64 k (+.f64 k 10)))) (log.f64 (pow.f64 k m)))) (.f64 1/2 (.f64 (/.f64 a (+.f64 1 (.f64 k (+.f64 k 10)))) (.f64 (.f64 m m) (pow.f64 (log.f64 k) 2)))))

Compiler

Compiled 1478 to 842 computations (43% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 a (sqrt.f64 (pow.f64 k m)))
0.0b	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))
0.0b	(.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2)))
1.9b	(/.f64 (.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

rewrite165.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

40×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
19×	`prod-exp_binary64` `add-sqr-sqrt_binary64`
17×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`

Counts

4 → 94

Calls

4 calls:

13.0ms	(/.f64 (.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
8.0ms	(.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2)))
6.0ms	(*.f64 a (sqrt.f64 (pow.f64 k m)))
5.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

Compiler

Compiled 2833 to 1387 computations (51% saved)

series331.0ms (4.3%)

Error

1.8b

Counts

4 → 50

Calls

4 calls:

120.0ms	(/.f64 (.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))
87.0ms	(.f64 (.f64 a (sqrt.f64 (pow.f64 k m))) (pow.f64 k (/.f64 m 2)))
53.0ms	(*.f64 a (sqrt.f64 (pow.f64 k m)))
18.0ms	(+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k))

Compiler

Compiled 3564 to 2439 computations (31.6% saved)

simplify161.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-/r/_binary64`
289×	`associate-l_binary64`
287×	`associate-r_binary64`
245×	`distribute-rgt-in_binary64`
220×	`distribute-lft-in_binary64`

Counts

144 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	3839
1	697	3436
2	2743	2483
3	4510	2473
4	4980	2473
5	4975	2473

prune121.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Error

1.8b

Counts

131 → 3

Alt Table

Status	Error	Program
	2.2b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
▶	1.9b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
	31.1b	(/.f64 (+.f64 (.f64 (.f64 m (log.f64 k)) a) (+.f64 a (.f64 a (+.f64 (.f64 1/2 (.f64 (.f64 m m) (pow.f64 (log.f64 k) 2))) (.f64 1/6 (.f64 (pow.f64 m 3) (pow.f64 (log.f64 k) 3))))))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

Compiler

Compiled 2138 to 1136 computations (46.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite210.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

45×	`times-frac_binary64`
44×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
27×	`associate-r_binary64`
22×	`unpow-prod-down_binary64`

Counts

3 → 110

Calls

3 calls:

12.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
6.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

Compiler

Compiled 2746 to 1631 computations (40.6% saved)

series179.0ms (2.3%)

Error

1.8b

Counts

3 → 40

Calls

3 calls:

80.0ms	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
41.0ms	(/.f64 (pow.f64 k m) (+.f64 1 (*.f64 k (+.f64 k 10))))
18.0ms	(+.f64 1 (*.f64 k (+.f64 k 10)))

Compiler

Compiled 2208 to 1542 computations (30.2% saved)

simplify182.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

399×	`associate-/l/_binary64`
356×	`distribute-rgt-in_binary64`
339×	`distribute-lft-in_binary64`
288×	`cancel-sign-sub-inv_binary64`
216×	`associate-r_binary64`

Counts

150 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	4009
1	639	3770
2	2333	3667
3	4701	3619
4	4954	3619
5	5010	3619

prune101.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	96	3	99

Error

1.8b

Counts

99 → 3

Alt Table

Status	Error	Program
▶	2.2b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
✓	1.9b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
	31.1b	(/.f64 (+.f64 (.f64 (.f64 m (log.f64 k)) a) (+.f64 a (.f64 a (+.f64 (.f64 1/2 (.f64 (.f64 m m) (pow.f64 (log.f64 k) 2))) (.f64 1/6 (.f64 (pow.f64 m 3) (pow.f64 (log.f64 k) 3))))))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

Compiler

Compiled 1703 to 979 computations (42.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.1b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
13.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
13.0b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite323.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

131×	`add-sqr-sqrt_binary64`
110×	`times-frac_binary64`
64×	`sqrt-prod_binary64`
61×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
48×	`associate-r_binary64`

Counts

4 → 188

Calls

4 calls:

34.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
8.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
2.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

Compiler

Compiled 5910 to 3989 computations (32.5% saved)

series206.0ms (2.7%)

Error

1.8b

Counts

4 → 49

Calls

4 calls:

81.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
42.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
15.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
14.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

Compiler

Compiled 2846 to 1981 computations (30.4% saved)

simplify286.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

889×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`
245×	`associate-*l/_binary64`
230×	`associate-r_binary64`
224×	`associate-/l*_binary64`

Counts

237 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	326	8164
1	900	7309
2	2930	7281
3	4635	7253
4	4926	7253
5	4979	7253

prune174.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	166	3	169

Error

1.8b

Counts

169 → 3

Alt Table

Status	Error	Program
	2.2b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
	1.9b	(.f64 a (/.f64 (pow.f64 k m) (+.f64 1 (.f64 k (+.f64 k 10)))))
	31.1b	(/.f64 (+.f64 (.f64 (.f64 m (log.f64 k)) a) (+.f64 a (.f64 a (+.f64 (.f64 1/2 (.f64 (.f64 m m) (pow.f64 (log.f64 k) 2))) (.f64 1/6 (.f64 (pow.f64 m 3) (pow.f64 (log.f64 k) 3))))))) (+.f64 (+.f64 1 (.f64 10 k)) (.f64 k k)))

Compiler

Compiled 3552 to 2270 computations (36.1% saved)

regimes1.9s (24.9%)

Accuracy

Total 0.1b remaining (3.8%)

Threshold costs 0.1b (3.8%)

Compiler

Compiled 30962 to 21082 computations (31.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64` `*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	18	22
2	17	22

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.5s (19.4%)

Algorithm

1×

intervals

Results

518.0ms	8000×	body	128	valid
286.0ms	3301×	body	128	invalid
101.0ms	2078×	body	128	nan

Compiler

Compiled 127 to 88 computations (30.7% saved)

Details

analyze1.1s (14.5%)

sample48.0ms (0.6%)

simplify118.0ms (1.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite126.0ms (1.6%)

series188.0ms (2.4%)

simplify129.0ms (1.7%)

prune96.0ms (1.2%)

localize15.0ms (0.2%)

rewrite165.0ms (2.1%)

series331.0ms (4.3%)

simplify161.0ms (2.1%)

prune121.0ms (1.6%)

localize9.0ms (0.1%)

rewrite210.0ms (2.7%)

series179.0ms (2.3%)

simplify182.0ms (2.3%)

prune101.0ms (1.3%)

localize12.0ms (0.2%)

rewrite323.0ms (4.2%)

series206.0ms (2.7%)

simplify286.0ms (3.7%)

prune174.0ms (2.2%)

regimes1.9s (24.9%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.5s (19.4%)

Profiling