Details

analyze10.0ms (0.3%)

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)

sample25.0ms (0.8%)

Algorithm

1×

intervals

Results

7.0ms	48×	body	640	valid
6.0ms	157×	body	80	valid
3.0ms	18×	body	1280	valid
3.0ms	25×	body	320	valid
1.0ms	8×	body	160	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify28.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

prune2.0ms (0.1%)

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: 7.2b

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))
2.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite93.0ms (2.8%)

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:

49.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
23.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))

series165.0ms (5%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(+.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))

simplify140.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5057	2633

prune209.0ms (6.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	3	152

Merged error: 0.0b

Counts

152 → 3

Compiler

Compiled 3301 to 2652 computations (19.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
16.5b	(+.f64 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (/.f64 1 (cbrt.f64 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite77.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
32×	`cbrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
10×	`distribute-lft-out_binary64`
9×	`flip3-+_binary64` `add-log-exp_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow1/3_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`frac-add_binary64` `add-exp-log_binary64`
5×	`frac-times_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `insert-posit16` `frac-sub_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `pow-plus_binary64` `prod-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

51.0ms	(+.f64 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (/.f64 1 (cbrt.f64 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
13.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
4.0ms	(cbrt.f64 (+.f64 1 x))
4.0ms	(cbrt.f64 (+.f64 1 x))

series250.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 (-.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (/.f64 1 (cbrt.f64 (+.f64 1 x)))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
54.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
42.0ms	(cbrt.f64 (+.f64 1 x))
41.0ms	(cbrt.f64 (+.f64 1 x))

simplify115.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4918	2323
1	4918	2323

prune228.0ms (6.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Merged error: 0.0b

Counts

122 → 3

Compiler

Compiled 3915 to 3201 computations (18.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (+.f64 1 x))
0.0b	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
0.2b	(-.f64 x (*.f64 (+.f64 1 x) 2))
14.8b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite44.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`associate-*r/_binary64`
16×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
13×	`flip3-+_binary64` `add-sqr-sqrt_binary64` `flip-+_binary64`
12×	`*-un-lft-identity_binary64` `frac-times_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-l_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`associate-*l/_binary64`
5×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `insert-posit16`
3×	`sub-neg_binary64`
2×	`associate-+l+_binary64` `difference-of-squares_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

14.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
13.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
8.0ms	(*.f64 x (+.f64 1 x))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series213.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
55.0ms	(*.f64 x (+.f64 1 x))
36.0ms	(-.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)))

simplify93.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5341	2919

prune206.0ms (6.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	115	3	118

Merged error: 0.0b

Counts

118 → 3

Compiler

Compiled 4259 to 2977 computations (30.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite42.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`pow1_binary64` `associate-l_binary64`
8×	`add-cube-cbrt_binary64` `associate-/r/_binary64` `frac-times_binary64`
7×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
6×	`flip3--_binary64` `flip--_binary64`
5×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `associate-*l/_binary64`
3×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64` `insert-posit16`
2×	`difference-of-squares_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `distribute-lft-out_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`

Counts

3 → 91

Calls

3 calls:

16.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
15.0ms	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))
8.0ms	(*.f64 x (+.f64 1 x))

series231.0ms (7%)

Counts

3 → 9

Calls

3 calls:

107.0ms	(.f64 (-.f64 x 1) (.f64 x (+.f64 1 x)))
64.0ms	(/.f64 2 (.f64 (-.f64 x 1) (.f64 x (+.f64 1 x))))
59.0ms	(*.f64 x (+.f64 1 x))

simplify119.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5329	1253

prune89.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	101	2	103

Merged error: 0b

Counts

103 → 2

Compiler

Compiled 1454 to 1034 computations (28.9% saved)

regimes8.0ms (0.2%)

Compiler: Compiled 20 to 17 computations (15% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	16
1	22	16

end0.0ms (0%)

sample852.0ms (25.9%)

Algorithm

1×

intervals

Results

266.0ms	1862×	body	640	valid
158.0ms	4103×	body	80	valid
107.0ms	984×	body	320	valid
101.0ms	557×	body	1280	valid
35.0ms	494×	body	160	valid
0.0ms	1×	body	80	invalid

Compiler

Compiled 54 to 46 computations (14.8% saved)

Details

analyze10.0ms (0.3%)

sample25.0ms (0.8%)

simplify28.0ms (0.9%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite93.0ms (2.8%)

series165.0ms (5%)

simplify140.0ms (4.3%)

prune209.0ms (6.3%)

localize14.0ms (0.4%)

rewrite77.0ms (2.3%)

series250.0ms (7.6%)

simplify115.0ms (3.5%)

prune228.0ms (6.9%)

localize12.0ms (0.4%)

rewrite44.0ms (1.3%)

series213.0ms (6.5%)

simplify93.0ms (2.8%)

prune206.0ms (6.3%)

localize7.0ms (0.2%)

rewrite42.0ms (1.3%)

series231.0ms (7%)

simplify119.0ms (3.6%)

prune89.0ms (2.7%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

simplify6.0ms (0.2%)

end0.0ms (0%)

sample852.0ms (25.9%)

Profiling