Details

analyze118.0ms (4.9%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample15.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	80	valid
0.0ms	9×	body	80	invalid

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify164.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4936	16
1	4936	16

prune6.0ms (0.3%)

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: 8.4b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 x y) 1)
0.1b	(*.f64 x (+.f64 (/.f64 x y) 1))
7.8b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

rewrite34.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-r/_binary64` `times-frac_binary64` `flip-+_binary64`
3×	`associate-l_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 62

Calls

3 calls:

13.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
10.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))
9.0ms	(+.f64 (/.f64 x y) 1)

series15.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
5.0ms	(*.f64 x (+.f64 (/.f64 x y) 1))
3.0ms	(+.f64 (/.f64 x y) 1)

simplify61.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5107	997

prune65.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	8	72

Merged error: 0b

Counts

72 → 8

Compiler

Compiled 1252 to 753 computations (39.9% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 x y) 1)
0.0b	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1)))
0.1b	(/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1))

rewrite48.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`*-un-lft-identity_binary64`
146×	`times-frac_binary64`
72×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
43×	`distribute-lft-out_binary64`
26×	`associate-/r*_binary64`
11×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
6×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`+-commutative_binary64` `sum-log_binary64`

Counts

3 → 158

Calls

3 calls:

18.0ms	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1)))
14.0ms	(/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1))
7.0ms	(+.f64 (/.f64 x y) 1)

series17.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

8.0ms	(/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1))
7.0ms	(/.f64 x (/.f64 (+.f64 x 1) (+.f64 (/.f64 x y) 1)))
3.0ms	(+.f64 (/.f64 x y) 1)

simplify115.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5339	4122

prune124.0ms (5.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	168	7	175

Merged error: 0b

Counts

175 → 7

Compiler

Compiled 3515 to 2047 computations (41.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (/.f64 x y))
0.0b	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y))))
0.0b	(/.f64 x (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y)))))
0.1b	(/.f64 1 (+.f64 1 (/.f64 x y)))

rewrite50.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
32×	`add-exp-log_binary64`
31×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`
18×	`associate-r_binary64`
11×	`div-exp_binary64`
10×	`associate-/r/_binary64`
9×	`distribute-lft-out_binary64`
8×	`prod-exp_binary64`
7×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
5×	`associate-/r*_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`1-exp_binary64` `unswap-sqr_binary64` `rec-exp_binary64` `div-inv_binary64`
2×	`associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64`
1×	`pow-prod-down_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

16.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y))))
15.0ms	(/.f64 x (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y)))))
9.0ms	(/.f64 1 (+.f64 1 (/.f64 x y)))
6.0ms	(+.f64 1 (/.f64 x y))

series25.0ms (1%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 x (*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y)))))
8.0ms	(*.f64 (+.f64 x 1) (/.f64 1 (+.f64 1 (/.f64 x y))))
5.0ms	(/.f64 1 (+.f64 1 (/.f64 x y)))
3.0ms	(+.f64 1 (/.f64 x y))

simplify94.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5202	2035

prune122.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	138	7	145

Merged error: 0b

Counts

145 → 7

Compiler

Compiled 2454 to 1550 computations (36.8% saved)

localize11.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 x y) 1)
0.1b	(/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1))
0.2b	(*.f64 x (/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1)))

rewrite43.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
33×	`times-frac_binary64`
28×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`
19×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`flip3-+_binary64` `associate-/r_binary64` `associate-/r/_binary64` `associate-/l_binary64` `flip-+_binary64`
3×	`associate-l_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 93

Calls

3 calls:

19.0ms	(*.f64 x (/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1)))
12.0ms	(/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1))
9.0ms	(+.f64 (/.f64 x y) 1)

series15.0ms (0.6%)

Counts

3 → 9

Calls

3 calls:

7.0ms	(*.f64 x (/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1)))
5.0ms	(/.f64 (+.f64 (/.f64 x y) 1) (+.f64 x 1))
3.0ms	(+.f64 (/.f64 x y) 1)

simplify105.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4958	1800
1	4958	1800

prune63.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	102	7	109

Merged error: 0b

Counts

109 → 7

Compiler

Compiled 1839 to 1115 computations (39.4% saved)

regimes60.0ms (2.5%)

Compiler: Compiled 212 to 170 computations (19.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	13	16

end0.0ms (0%)

sample1.0s (42.1%)

Algorithm

1×

intervals

Results

257.0ms	8000×	body	80	valid
9.0ms	291×	body	80	invalid

Compiler

Compiled 140 to 113 computations (19.3% saved)

Details

analyze118.0ms (4.9%)

sample15.0ms (0.6%)

simplify164.0ms (6.8%)

prune6.0ms (0.3%)

localize6.0ms (0.3%)

rewrite34.0ms (1.4%)

series15.0ms (0.6%)

simplify61.0ms (2.5%)

prune65.0ms (2.7%)

localize6.0ms (0.3%)

rewrite48.0ms (2%)

series17.0ms (0.7%)

simplify115.0ms (4.8%)

prune124.0ms (5.2%)

localize8.0ms (0.3%)

rewrite50.0ms (2.1%)

series25.0ms (1%)

simplify94.0ms (3.9%)

prune122.0ms (5.1%)

localize11.0ms (0.5%)

rewrite43.0ms (1.8%)

series15.0ms (0.6%)

simplify105.0ms (4.3%)

prune63.0ms (2.6%)

regimes60.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (42.1%)

Profiling