Details

analyze579.0ms (8.6%)

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%	90.5%	6.3%	6
4.7%	85.9%	9.5%	7
21.1%	64%	14.9%	8
23.4%	58.9%	17.7%	9
27.7%	51.3%	21%	10
28.9%	48.5%	22.6%	11
31.1%	44.4%	24.5%	12
31.7%	42.9%	25.4%	13
32.7%	41%	26.3%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample77.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	57×	body	1024	valid
13.0ms	32×	body	512	valid
11.0ms	144×	body	128	valid
6.0ms	7×	body	2048	valid
3.0ms	7×	body	1024	invalid
3.0ms	16×	body	256	valid
2.0ms	6×	body	512	invalid
1.0ms	8×	body	256	invalid
0.0ms	4×	body	128	invalid
0.0ms	1×	body	128	nan

Compiler

Compiled 23 to 19 computations (17.4% saved)

simplify163.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4941	13
1	4941	13

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

9.7b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 6 expressions with local error:

5.6b	(pow.f64 (/.f64 x (+.f64 x y)) x)
0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
0.0b	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
0.0b	(/.f64 x (+.f64 x y))
5.6b	(pow.f64 (/.f64 x (+.f64 x y)) x)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_13042`
118×	`*-un-lft-identity_binary64_13036`
90×	`unpow-prod-down_binary64_13115`
80×	`add-sqr-sqrt_binary64_13058` `add-cube-cbrt_binary64_13071`
25×	`associate-/l*_binary64_12981`
19×	`distribute-lft-out_binary64_12987`
16×	`add-exp-log_binary64_13074`
12×	`associate-/r/_binary64_12982`
7×	`div-inv_binary64_13033` `div-exp_binary64_13087` `associate-/r*_binary64_12980` `add-cbrt-cube_binary64_13072`
6×	`flip3-+_binary64_13039` `flip-+_binary64_13010`
5×	`sqr-pow_binary64_13008`
4×	`pow-exp_binary64_13104` `pow1_binary64_13097`
3×	`add-log-exp_binary64_13075` `pow-unpow_binary64_13113`
2×	`clear-num_binary64_13035` `cbrt-undiv_binary64_13070` `pow-to-exp_binary64_13105` `frac-2neg_binary64_13047`
1×	`pow-pow_binary64_13108`

Counts

3 → 172

Calls

6 calls:

11.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
7.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
5.0ms	(/.f64 x (+.f64 x y))
0.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
0.0ms	(/.f64 x (+.f64 x y))

series275.0ms (4.1%)

Counts

3 → 38

Calls

3 calls:

119.0ms	(/.f64 (pow.f64 (/.f64 x (+.f64 x y)) x) x)
91.0ms	(pow.f64 (/.f64 x (+.f64 x y)) x)
64.0ms	(/.f64 x (+.f64 x y))

Compiler

Compiled 877 to 687 computations (21.7% saved)

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4993	4446
1	4993	4446

prune184.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	206	4	210
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	207	4	211

Error

Counts

211 → 4

Compiler

Compiled 3775 to 827 computations (78.1% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

Counts

4 → 4

Compiler

Compiled 67 to 46 computations (31.3% saved)

localize22.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 1/3 (pow.f64 (/.f64 y x) 3))
0.0b	(+.f64 (/.f64 1/2 x) 1/6)
0.0b	(+.f64 (/.f64 1 x) (.f64 (/.f64 (.f64 y y) x) (+.f64 1/2 (/.f64 1/2 x))))
0.0b	(+.f64 (/.f64 y x) (+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6))))
5.2b	(+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))
6.2b	(/.f64 (pow.f64 y 3) x)
6.6b	(/.f64 (*.f64 y y) x)
13.8b	(-.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 (.f64 y y) x) (+.f64 1/2 (/.f64 1/2 x)))) (+.f64 (/.f64 y x) (+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))))

rewrite116.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`frac-add_binary64_13044`
74×	`associate-*r/_binary64_12978`
63×	`frac-sub_binary64_13045`
58×	`flip3-+_binary64_13039` `flip-+_binary64_13010`
40×	`cube-div_binary64_13065`
39×	`*-un-lft-identity_binary64_13036` `times-frac_binary64_13042`
34×	`add-sqr-sqrt_binary64_13058` `frac-times_binary64_13046`
32×	`add-cube-cbrt_binary64_13071`
27×	`add-log-exp_binary64_13075`
17×	`associate-*l/_binary64_12979`
14×	`add-exp-log_binary64_13074`
13×	`associate-/l*_binary64_12981`
12×	`cube-prod_binary64_13064` `unpow-prod-down_binary64_13115`
11×	`add-cbrt-cube_binary64_13072`
10×	`sum-log_binary64_13127`
6×	`associate-/r*_binary64_12980` `diff-log_binary64_13128`
5×	`div-exp_binary64_13087`
4×	`unpow3_binary64_13102` `cube-mult_binary64_13066` `pow1_binary64_13097` `cancel-sign-sub-inv_binary64_13002` `sqr-pow_binary64_13008`
3×	`cbrt-undiv_binary64_13070`
2×	`clear-num_binary64_13035` `div-inv_binary64_13033` `distribute-lft-out--_binary64_12988` `distribute-lft-out_binary64_12987` `associate-+r+_binary64_12968` `frac-2neg_binary64_13047`
1×	`flip--_binary64_13011` `distribute-rgt-in_binary64_12986` `distribute-lft-in_binary64_12985` `pow-exp_binary64_13104` `sub-neg_binary64_13029` `flip3--_binary64_13040` `associate--r+_binary64_12972` `prod-exp_binary64_13085` `difference-of-squares_binary64_13005` `pow-to-exp_binary64_13105` `associate--l+_binary64_12973` `cbrt-unprod_binary64_13069` `+-commutative_binary64_12966`

Counts

4 → 192

Calls

8 calls:

35.0ms	(-.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 (.f64 y y) x) (+.f64 1/2 (/.f64 1/2 x)))) (+.f64 (/.f64 y x) (+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))))
12.0ms	(+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))
6.0ms	(/.f64 (pow.f64 y 3) x)
4.0ms	(/.f64 (*.f64 y y) x)
0.0ms	(+.f64 (/.f64 y x) (+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6))))

series691.0ms (10.2%)

Counts

4 → 35

Calls

4 calls:

306.0ms	(-.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 (.f64 y y) x) (+.f64 1/2 (/.f64 1/2 x)))) (+.f64 (/.f64 y x) (+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))))
221.0ms	(+.f64 (.f64 1/3 (pow.f64 (/.f64 y x) 3)) (.f64 (/.f64 (pow.f64 y 3) x) (+.f64 (/.f64 1/2 x) 1/6)))
92.0ms	(/.f64 (pow.f64 y 3) x)
71.0ms	(/.f64 (*.f64 y y) x)

Compiler

Compiled 2104 to 1624 computations (22.8% saved)

simplify186.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	17661
1	4981	17661

prune1.2s (17.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	227	4	231

Error

Counts

231 → 4

Compiler

Compiled 16215 to 10049 computations (38% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
0.3b	(/.f64 (cbrt.f64 x) (+.f64 x y))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y))) x) x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
21.2b	(pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y))) x)

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_13074`
10×	`pow1_binary64_13097`
9×	`cbrt-prod_binary64_13067`
8×	`*-un-lft-identity_binary64_13036` `add-sqr-sqrt_binary64_13058` `add-cube-cbrt_binary64_13071`
6×	`prod-exp_binary64_13085`
5×	`pow-exp_binary64_13104`
4×	`add-log-exp_binary64_13075` `add-cbrt-cube_binary64_13072`
3×	`pow-pow_binary64_13108` `pow-unpow_binary64_13113` `pow1/3_binary64_13118` `pow-prod-down_binary64_13107`
2×	`div-exp_binary64_13087`
1×	`pow-to-exp_binary64_13105` `unpow-prod-down_binary64_13115` `sqr-pow_binary64_13008`

Counts

4 → 54

Calls

8 calls:

13.0ms	(pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y))) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(/.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y))) x) x)

series321.0ms (4.7%)

Counts

4 → 19

Calls

4 calls:

92.0ms	(pow.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y))) x)
79.0ms	(cbrt.f64 x)
78.0ms	(cbrt.f64 x)
71.0ms	(cbrt.f64 x)

Compiler

Compiled 623 to 459 computations (26.3% saved)

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4908	622
1	4908	622

prune50.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	73	4	77

Error

Counts

77 → 4

Compiler

Compiled 1205 to 302 computations (74.9% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	416	821
1	416	821

regimes289.0ms (4.3%)

Compiler: Compiled 1685 to 1065 computations (36.8% saved)

bsearch60.0ms (0.9%)

Steps

Iters	Range		Point
10	8.738804090705715e-13	4.619368253140821	0.4586887196655391
7	-5.540770461868965e+22	-2.2840129458104726e+21	-2.3049130861507487e+21

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes26.0ms (0.4%)

Compiler: Compiled 16 to 34 computations (-112.5% saved)

bsearch25.0ms (0.4%)

Steps

Iters	Range		Point
7	7.810305127225359e+146	1.6722730755572225e+148	3.670486696812112e+147

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes18.0ms (0.3%)

Accuracy

Total 0.4b remaining (94.4%)

Threshold costs 0.4b (94.4%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch3.0ms (0%)

Compiler: Compiled 31 to 27 computations (12.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	39
1	28	39

end0.0ms (0%)

sample2.2s (33.1%)

Algorithm

1×

intervals

Results

621.0ms	1671×	body	1024	valid
274.0ms	4613×	body	128	valid
230.0ms	1022×	body	512	valid
92.0ms	145×	body	2048	valid
76.0ms	549×	body	256	valid
61.0ms	181×	body	1024	invalid
51.0ms	235×	body	512	invalid
22.0ms	147×	body	256	invalid
12.0ms	193×	body	128	invalid
8.0ms	193×	body	128	nan

Compiler

Compiled 624 to 400 computations (35.9% saved)

Pareto

0.7931202672605782

Details

analyze579.0ms (8.6%)

sample77.0ms (1.1%)

simplify163.0ms (2.4%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

rewrite41.0ms (0.6%)

series275.0ms (4.1%)

simplify92.0ms (1.4%)

prune184.0ms (2.7%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize22.0ms (0.3%)

rewrite116.0ms (1.7%)

series691.0ms (10.2%)

simplify186.0ms (2.8%)

prune1.2s (17.4%)

localize13.0ms (0.2%)

rewrite21.0ms (0.3%)

series321.0ms (4.7%)

simplify55.0ms (0.8%)

prune50.0ms (0.7%)

simplify16.0ms (0.2%)

regimes289.0ms (4.3%)

bsearch60.0ms (0.9%)

regimes26.0ms (0.4%)

bsearch25.0ms (0.4%)

regimes18.0ms (0.3%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (33.1%)

Profiling