Details

analyze424.0ms (7.2%)

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%	68.6%	18.9%	6
18.7%	62.4%	18.9%	7
18.7%	59.3%	22%	8
28.1%	39%	32.9%	9
32.8%	34.3%	32.9%	10
32.8%	32%	35.3%	11
38.2%	20.7%	41.1%	12
41%	17.9%	41.1%	13
41%	16.6%	42.5%	14

Compiler

Compiled 38 to 24 computations (36.8% saved)

sample53.0ms (0.9%)

Algorithm

1×

intervals

Results

38.0ms	236×	body	256	valid
3.0ms	35×	body	128	nan
2.0ms	20×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify327.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (231.0ms)

Iter	Nodes	Cost
0	4834	48
1	4834	48

prune6.0ms (0.1%)

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: 37.3b

Counts

2 → 2

Compiler

Compiled 99 to 59 computations (40.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

9.6b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2457`
11×	`cbrt-prod_binary64_2464`
10×	`*-un-lft-identity_binary64_2436`
9×	`sqrt-prod_binary64_2451`
8×	`add-cube-cbrt_binary64_2468`
6×	`pow1_binary64_2494` `times-frac_binary64_2442`
4×	`add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `sqrt-div_binary64_2452` `difference-of-squares_binary64_2405`
2×	`pow1/3_binary64_2515` `pow1/2_binary64_2513` `flip3--_binary64_2440` `rem-sqrt-square_binary64_2449` `flip--_binary64_2411` `cbrt-div_binary64_2465` `sqrt-pow1_binary64_2453`
1×	`distribute-lft-out--_binary64_2390` `div-inv_binary64_2433` `associate-*l/_binary64_2381`

Counts

4 → 61

Calls

4 calls:

10.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
9.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series547.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
234.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
33.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5099	1656

prune169.0ms (2.9%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	53	20	73
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	20	75

Merged error: 33.0b

Counts

75 → 20

Compiler

Compiled 3549 to 1370 computations (61.4% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2457` `sqrt-prod_binary64_2451`
6×	`add-log-exp_binary64_2472` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
4×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `sqrt-div_binary64_2452`
3×	`flip3--_binary64_2440` `flip--_binary64_2411` `difference-of-squares_binary64_2405`
2×	`pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `sqrt-pow1_binary64_2453`
1×	`pow1/3_binary64_2515` `diff-log_binary64_2525` `cbrt-prod_binary64_2464` `associate-*l/_binary64_2381` `cbrt-div_binary64_2465` `sub-neg_binary64_2429`

Counts

4 → 54

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series322.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
30.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
22.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	1098
1	4946	1098

prune135.0ms (2.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	2	17	19
Picked	1	0	1
Done	0	0	0
Total	65	21	86

Merged error: 32.1b

Counts

86 → 21

Compiler

Compiled 3247 to 1309 computations (59.7% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
31.0b	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-div_binary64_2452`
8×	`pow1_binary64_2494`
6×	`add-sqr-sqrt_binary64_2457` `add-log-exp_binary64_2472`
5×	`flip3--_binary64_2440` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `sqrt-prod_binary64_2451` `flip--_binary64_2411`
4×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `frac-times_binary64_2446`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-*l/_binary64_2381` `sqrt-pow1_binary64_2453`
2×	`pow1/2_binary64_2513` `associate-*r/_binary64_2380` `difference-of-squares_binary64_2405`
1×	`pow1/3_binary64_2515` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `cbrt-prod_binary64_2464` `rem-sqrt-square_binary64_2449` `cbrt-div_binary64_2465` `sub-neg_binary64_2429`

Counts

4 → 57

Calls

4 calls:

8.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
6.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))

series341.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (.f64 (+.f64 g h) (-.f64 g h)))) a) -1/2))
42.0ms	(sqrt.f64 (*.f64 (+.f64 g h) (-.f64 g h)))
31.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
21.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4953	1275
1	4953	1275

prune134.0ms (2.3%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	2	18	20
Picked	1	0	1
Done	0	0	0
Total	69	21	90

Merged error: 32.1b

Counts

90 → 21

Compiler

Compiled 3433 to 1403 computations (59.1% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.6b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
31.0b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_2457` `sqrt-prod_binary64_2451`
6×	`add-log-exp_binary64_2472` `add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
4×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `sqrt-div_binary64_2452`
3×	`flip3--_binary64_2440` `flip--_binary64_2411` `difference-of-squares_binary64_2405`
2×	`pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `sqrt-pow1_binary64_2453`
1×	`pow1/3_binary64_2515` `diff-log_binary64_2525` `cbrt-prod_binary64_2464` `associate-*l/_binary64_2381` `cbrt-div_binary64_2465` `sub-neg_binary64_2429`

Counts

4 → 54

Calls

4 calls:

9.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
4.0ms	(-.f64 (.f64 g g) (.f64 h h))
4.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

series314.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
28.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
27.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
21.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4946	1098
1	4946	1098

prune91.0ms (1.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	19	20
Picked	1	0	1
Done	0	0	0
Total	66	21	87

Merged error: 32.1b

Counts

87 → 21

Compiler

Compiled 2430 to 851 computations (65% saved)

regimes230.0ms (3.9%)

Compiler: Compiled 3248 to 1886 computations (41.9% saved)

bsearch94.0ms (1.6%)

Steps

Iters	Range		Point
11	3.0019519371863446e-168	1.256773250423451e-143	2.2719417431808843e-159

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	82	97
1	82	97

end0.0ms (0%)

sample2.2s (37.1%)

Algorithm

1×

intervals

Results

1.2s	7559×	body	256	valid
103.0ms	1233×	body	128	nan
39.0ms	441×	body	128	valid

Compiler

Compiled 909 to 531 computations (41.6% saved)

Details

analyze424.0ms (7.2%)

sample53.0ms (0.9%)

simplify327.0ms (5.6%)

prune6.0ms (0.1%)

localize17.0ms (0.3%)

rewrite34.0ms (0.6%)

series547.0ms (9.3%)

simplify58.0ms (1%)

prune169.0ms (2.9%)

localize23.0ms (0.4%)

rewrite29.0ms (0.5%)

series322.0ms (5.5%)

simplify80.0ms (1.4%)

prune135.0ms (2.3%)

localize23.0ms (0.4%)

rewrite28.0ms (0.5%)

series341.0ms (5.8%)

simplify86.0ms (1.5%)

prune134.0ms (2.3%)

localize24.0ms (0.4%)

rewrite28.0ms (0.5%)

series314.0ms (5.3%)

simplify74.0ms (1.3%)

prune91.0ms (1.6%)

regimes230.0ms (3.9%)

bsearch94.0ms (1.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (37.1%)

Profiling