Details

analyze431.0ms (5.7%)

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
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)

sample56.0ms (0.7%)

Algorithm

1×

intervals

Results

41.0ms	247×	body	256	valid
3.0ms	34×	body	128	nan
1.0ms	9×	body	128	valid

Compiler

Compiled 75 to 50 computations (33.3% saved)

simplify204.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	4882	48
1	4882	48

prune9.0ms (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: 31.4b

Counts

2 → 2

Compiler

Compiled 167 to 100 computations (40.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

8.1b	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
9.0b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
9×	`sqrt-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `sqrt-div_binary64`
2×	`cbrt-div_binary64` `pow1/2_binary64` `flip3--_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`distribute-lft-out--_binary64` `div-inv_binary64` `associate-*l/_binary64`

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)))

series1.0s (13.5%)

Counts

4 → 12

Calls

4 calls:

460.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
458.0ms	(cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))) g) (*.f64 2 a)))
55.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
54.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4994	1656
1	4994	1656

prune767.0ms (10.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	60	13	73
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	14	75

Merged error: 27.5b

Counts

75 → 14

Compiler

Compiled 17850 to 8927 computations (50% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.0b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `cancel-sign-sub-inv_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 55

Calls

4 calls:

10.0ms	(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)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))

series595.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

436.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
58.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
58.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
43.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4854	1101
1	4854	1101

prune349.0ms (4.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	65	16	81

Merged error: 26.9b

Counts

81 → 16

Compiler

Compiled 8498 to 4039 computations (52.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
3.4b	(-.f64 (.f64 g g) (.f64 h h))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))

series201.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
51.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
48.0ms	(-.f64 (.f64 g g) (.f64 h h))
39.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4948	960
1	4948	960

prune250.0ms (3.3%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	69	17	86

Merged error: 26.9b

Counts

86 → 17

Compiler

Compiled 6147 to 2819 computations (54.1% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

3.4b	(-.f64 (.f64 g g) (.f64 h h))
9.0b	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
25.9b	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64` `cancel-sign-sub-inv_binary64` `cbrt-prod_binary64` `associate-*l/_binary64`

Counts

4 → 55

Calls

4 calls:

10.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
6.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
5.0ms	(-.f64 (.f64 g g) (.f64 h h))

series596.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

450.0ms	(cbrt.f64 (.f64 (/.f64 (+.f64 g (sqrt.f64 (-.f64 (.f64 g g) (*.f64 h h)))) a) -1/2))
55.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
50.0ms	(sqrt.f64 (-.f64 (.f64 g g) (.f64 h h)))
41.0ms	(-.f64 (.f64 g g) (.f64 h h))

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4854	1101
1	4854	1101

prune186.0ms (2.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	1	14	15
Picked	1	0	1
Done	0	1	1
Total	67	17	84

Merged error: 26.9b

Counts

84 → 17

Compiler

Compiled 4583 to 2013 computations (56.1% saved)

regimes331.0ms (4.3%)

Compiler: Compiled 4960 to 2742 computations (44.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	52
1	51	52

end0.0ms (0%)

sample2.1s (28%)

Algorithm

1×

intervals

Results

1.3s	7549×	body	256	valid
108.0ms	1258×	body	128	nan
39.0ms	451×	body	128	valid

Compiler

Compiled 765 to 425 computations (44.4% saved)

Details

analyze431.0ms (5.7%)

sample56.0ms (0.7%)

simplify204.0ms (2.7%)

prune9.0ms (0.1%)

localize21.0ms (0.3%)

rewrite36.0ms (0.5%)

series1.0s (13.5%)

simplify55.0ms (0.7%)

prune767.0ms (10.1%)

localize19.0ms (0.2%)

rewrite30.0ms (0.4%)

series595.0ms (7.8%)

simplify82.0ms (1.1%)

prune349.0ms (4.6%)

localize20.0ms (0.3%)

rewrite26.0ms (0.3%)

series201.0ms (2.6%)

simplify55.0ms (0.7%)

prune250.0ms (3.3%)

localize22.0ms (0.3%)

rewrite32.0ms (0.4%)

series596.0ms (7.8%)

simplify81.0ms (1.1%)

prune186.0ms (2.4%)

regimes331.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (28%)

Profiling