Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	51×	body	640	valid
5.0ms	137×	body	80	valid
4.0ms	39×	body	320	valid
3.0ms	15×	body	1280	valid
1.0ms	14×	body	160	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify30.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

prune7.0ms (0.2%)

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

Merged error: 10.5b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.7b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite92.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64` `insert-posit16`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
25.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))

series163.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
26.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
19.0ms	(/.f64 1 (-.f64 x 1))
18.0ms	(/.f64 1 (+.f64 x 1))

simplify145.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	5044	2633

prune220.0ms (6.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	4	152

Merged error: 0.0b

Counts

152 → 4

Compiler

Compiled 3319 to 2668 computations (19.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 (pow.f64 x 3) x)
15.1b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite68.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-sqr-sqrt_binary64`
42×	`associate-*r/_binary64`
38×	`*-un-lft-identity_binary64`
32×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
27×	`times-frac_binary64`
22×	`difference-of-squares_binary64`
20×	`add-cube-cbrt_binary64` `frac-times_binary64`
18×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64` `distribute-lft-out--_binary64`
5×	`sub-neg_binary64` `distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64`
4×	`insert-posit16`
3×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 155

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
14.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
12.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
8.0ms	(-.f64 (pow.f64 x 3) x)

series189.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(-.f64 (pow.f64 x 3) x)
62.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
27.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify174.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4941	6743
1	4941	6743

prune561.0ms (16.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	168	3	171

Merged error: 0.0b

Counts

171 → 3

Compiler

Compiled 7093 to 4955 computations (30.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.0b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
20×	`difference-of-squares_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-/r*_binary64`
5×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `distribute-lft-out--_binary64` `unpow3_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `insert-posit16` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 72

Calls

2 calls:

11.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
9.0ms	(-.f64 (pow.f64 x 3) x)

series143.0ms (4.3%)

Counts

2 → 6

Calls

2 calls:

93.0ms	(-.f64 (pow.f64 x 3) x)
50.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify107.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4925	1333
1	4925	1333

prune79.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

Compiler

Compiled 1157 to 846 computations (26.9% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
0.7b	(/.f64 2 (-.f64 (*.f64 x x) 1))

rewrite35.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
39×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`
24×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-l_binary64`
9×	`div-exp_binary64`
8×	`prod-exp_binary64`
7×	`difference-of-sqr-1_binary64`
6×	`associate-/r*_binary64` `unswap-sqr_binary64`
5×	`cbrt-undiv_binary64`
4×	`pow1_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`add-log-exp_binary64` `flip3--_binary64` `1-exp_binary64` `rec-exp_binary64` `insert-posit16` `flip--_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

2 → 110

Calls

2 calls:

21.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
8.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

series104.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

59.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
45.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

simplify137.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4974	1946
1	4974	1946

prune110.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	116	4	120

Merged error: 0b

Counts

120 → 4

Compiler

Compiled 1945 to 1362 computations (30% saved)

regimes10.0ms (0.3%)

Compiler: Compiled 40 to 34 computations (15% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms (0%)

sample888.0ms (26.4%)

Algorithm

1×

intervals

Results

258.0ms	1824×	body	640	valid
175.0ms	4208×	body	80	valid
103.0ms	578×	body	1280	valid
98.0ms	904×	body	320	valid
38.0ms	486×	body	160	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 70 to 60 computations (14.3% saved)

Details

analyze6.0ms (0.2%)

sample26.0ms (0.8%)

simplify30.0ms (0.9%)

prune7.0ms (0.2%)

localize9.0ms (0.3%)

rewrite92.0ms (2.7%)

series163.0ms (4.9%)

simplify145.0ms (4.3%)

prune220.0ms (6.5%)

localize12.0ms (0.4%)

rewrite68.0ms (2%)

series189.0ms (5.6%)

simplify174.0ms (5.2%)

prune561.0ms (16.7%)

localize5.0ms (0.2%)

rewrite24.0ms (0.7%)

series143.0ms (4.3%)

simplify107.0ms (3.2%)

prune79.0ms (2.3%)

localize9.0ms (0.3%)

rewrite35.0ms (1%)

series104.0ms (3.1%)

simplify137.0ms (4.1%)

prune110.0ms (3.3%)

regimes10.0ms (0.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample888.0ms (26.4%)

Profiling