Details

analyze804.0ms (7%)

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
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample199.0ms (1.7%)

Algorithm

1×

intervals

Results

86.0ms	102×	body	1280	valid
61.0ms	27×	body	2560	valid
19.0ms	46×	body	640	valid
6.0ms	10×	body	640	invalid
5.0ms	26×	body	320	valid
4.0ms	49×	body	80	valid
3.0ms	4×	body	1280	invalid
1.0ms	14×	body	80	invalid
1.0ms	6×	body	160	invalid
1.0ms	6×	body	160	valid
1.0ms	2×	body	320	invalid
0.0ms	8×	body	80	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4923	22
1	4923	22

prune4.0ms (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

Merged error: 46.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
0.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite128.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64`
485×	`add-sqr-sqrt_binary64`
366×	`*-un-lft-identity_binary64`
224×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`
168×	`difference-of-squares_binary64`
88×	`unpow-prod-down_binary64`
85×	`sqr-pow_binary64`
84×	`difference-of-sqr-1_binary64`
29×	`div-inv_binary64`
28×	`distribute-lft-out--_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
13×	`associate-/r_binary64` `associate-/l_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 448

Calls

4 calls:

54.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
21.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series209.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
71.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
37.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
29.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify189.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5075	14743

prune677.0ms (5.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	452	8	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	453	8	461

Merged error: 17.2b

Counts

461 → 8

Compiler

Compiled 14009 to 7361 computations (47.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
0.1b	(*.f64 (pow.f64 i 3) 1/6)
6.5b	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
16.8b	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
102×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
47×	`associate-r_binary64`
23×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
15×	`associate-l_binary64`
13×	`associate-/r*_binary64`
9×	`add-log-exp_binary64` `div-inv_binary64`
7×	`unswap-sqr_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-/l*_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `associate-+r+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 182

Calls

4 calls:

20.0ms	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
13.0ms	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))
9.0ms	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
6.0ms	(*.f64 (pow.f64 i 3) 1/6)

series35.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(.f64 100 (/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2))) (/.f64 i n)))
12.0ms	(/.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))) (/.f64 i n))
4.0ms	(+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2)))
4.0ms	(*.f64 (pow.f64 i 3) 1/6)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5456	6239

prune292.0ms (2.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	180	14	194
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	181	21	202

Merged error: 7.8b

Counts

202 → 21

Compiler

Compiled 6779 to 3992 computations (41.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 i n) 50)
0.3b	(.f64 (.f64 i i) 50/3)
2.4b	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
3.7b	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`associate-l_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate-+r+_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(.f64 (.f64 i i) 50/3)
6.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))
6.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
5.0ms	(.f64 (.f64 i n) 50)

series30.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3)))
10.0ms	(+.f64 (.f64 (.f64 i n) 50) (.f64 n (+.f64 100 (.f64 (*.f64 i i) 50/3))))
4.0ms	(.f64 (.f64 i n) 50)
3.0ms	(.f64 (.f64 i i) 50/3)

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4911	1133
1	4911	1133

prune100.0ms (0.9%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	3	17	20
Picked	0	1	1
Done	0	0	0
Total	84	21	105

Merged error: 7.7b

Counts

105 → 21

Compiler

Compiled 2154 to 1361 computations (36.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.3b	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2)))) (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))) i)
13.5b	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
13.5b	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
13.5b	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64`
9×	`flip3-+_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64` `cbrt-prod_binary64`
8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `frac-times_binary64`
3×	`associate-/r*_binary64` `pow1/3_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `associate-r/_binary64` `div-exp_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 68

Calls

4 calls:

19.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2)))) (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))) i)
7.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
7.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
7.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))

series42.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (.f64 i i) 1/2)))) (cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))) i)
9.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
9.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))
9.0ms	(cbrt.f64 (+.f64 (.f64 (pow.f64 i 3) 1/6) (+.f64 i (.f64 (*.f64 i i) 1/2))))

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5491	2517

prune157.0ms (1.4%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	3	16	19
Picked	1	0	1
Done	0	1	1
Total	77	24	101

Merged error: 7.7b

Counts

101 → 24

Compiler

Compiled 4639 to 3069 computations (33.8% saved)

regimes239.0ms (2.1%)

Compiler: Compiled 1568 to 1148 computations (26.8% saved)

bsearch320.0ms (2.8%)

Steps

Iters	Range		Point
10	1983.7294034763543	1245091847839766.8	2003.3137174584608
9	-3.88832786057446e-31	-1.2603450300680378e-40	-3.827469972222611e-31

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	54
1	35	54

end0.0ms (0%)

sample7.5s (65.3%)

Algorithm

1×

intervals

Results

2.4s	2856×	body	1280	valid
2.0s	954×	body	2560	valid
621.0ms	1530×	body	640	valid
168.0ms	700×	body	320	valid
123.0ms	244×	body	640	invalid
112.0ms	1621×	body	80	valid
94.0ms	118×	body	1280	invalid
58.0ms	184×	body	320	invalid
50.0ms	329×	body	160	valid
38.0ms	426×	body	80	invalid
38.0ms	10×	body	5120	valid
35.0ms	18×	body	2560	invalid
20.0ms	103×	body	160	invalid
15.0ms	303×	body	80	nan

Compiler

Compiled 875 to 634 computations (27.5% saved)

Details

analyze804.0ms (7%)

sample199.0ms (1.7%)

simplify59.0ms (0.5%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite128.0ms (1.1%)

series209.0ms (1.8%)

simplify189.0ms (1.6%)

prune677.0ms (5.9%)

localize12.0ms (0.1%)

rewrite59.0ms (0.5%)

series35.0ms (0.3%)

simplify96.0ms (0.8%)

prune292.0ms (2.5%)

localize9.0ms (0.1%)

rewrite27.0ms (0.2%)

series30.0ms (0.3%)

simplify87.0ms (0.8%)

prune100.0ms (0.9%)

localize20.0ms (0.2%)

rewrite43.0ms (0.4%)

series42.0ms (0.4%)

simplify141.0ms (1.2%)

prune157.0ms (1.4%)

regimes239.0ms (2.1%)

bsearch320.0ms (2.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.5s (65.3%)

Profiling