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)

sample28.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	51×	body	512	valid
7.0ms	43×	body	1024	valid
5.0ms	141×	body	128	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	192	22
1	192	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: 9.9b

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))
2.4b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite96.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 159

Calls

4 calls:

44.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
24.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))

series166.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
33.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
19.0ms	(/.f64 1 (-.f64 x 1))
17.0ms	(/.f64 1 (+.f64 x 1))

simplify73.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4919	2783
1	4919	2783

prune515.0ms (17.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	169	3	172

Merged error: 0.1b

Counts

172 → 3

Compiler

Compiled 9523 to 7754 computations (18.6% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.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) (neg.f64 x)))
17.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite78.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`associate-*r/_binary64`
41×	`*-un-lft-identity_binary64`
32×	`frac-add_binary64`
31×	`flip3--_binary64` `flip--_binary64`
24×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
20×	`frac-times_binary64`
19×	`flip3-+_binary64` `flip-+_binary64`
18×	`associate-/l/_binary64` `add-cube-cbrt_binary64`
10×	`associate-*l/_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64` `distribute-rgt-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow3_binary64`
7×	`associate-/r_binary64` `associate-l*_binary64`
6×	`pow1_binary64`
5×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64`
4×	`associate-+l+_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
3×	`associate-r_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64` `difference-of-squares_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` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 142

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) (neg.f64 x)))
15.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
10.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
4.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series119.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (+.f64 (pow.f64 x 3) (neg.f64 x)))
27.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
23.0ms	(.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)))

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4958	6082
1	4958	6082

prune360.0ms (12.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	1	0	1
Picked	1	0	1
Done	1	0	1
Total	155	2	157

Merged error: 0.1b

Counts

157 → 2

Compiler

Compiled 7023 to 4867 computations (30.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`distribute-lft-out_binary64` `distribute-rgt-out_binary64` `unpow3_binary64`
7×	`associate-/r*_binary64`
4×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

1 → 45

Calls

1 calls:

13.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

series56.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

56.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify58.0ms (2%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5193	775

prune136.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Merged error: 0b

Counts

50 → 3

Compiler

Compiled 1984 to 1566 computations (21.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
15×	`difference-of-sqr--1_binary64`
13×	`associate-/l*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`div-inv_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `pow1_binary64` `associate-/r/_binary64` `flip-+_binary64`
1×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 98

Calls

2 calls:

10.0ms	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))
4.0ms	(+.f64 (*.f64 x x) -1)

series108.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (/.f64 2 x) (+.f64 (*.f64 x x) -1))
51.0ms	(+.f64 (*.f64 x x) -1)

simplify65.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5237	2363

prune96.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Merged error: 0b

Counts

107 → 3

Compiler

Compiled 1861 to 1207 computations (35.1% saved)

regimes9.0ms (0.3%)

Compiler: Compiled 29 to 25 computations (13.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms (0%)

sample798.0ms (27.1%)

Algorithm

1×

intervals

Results

197.0ms	1350×	body	1024	valid
175.0ms	4393×	body	128	valid
166.0ms	1487×	body	512	valid
59.0ms	770×	body	256	valid

Compiler

Compiled 61 to 52 computations (14.8% saved)

Details

analyze6.0ms (0.2%)

sample28.0ms (1%)

simplify14.0ms (0.5%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite96.0ms (3.3%)

series166.0ms (5.7%)

simplify73.0ms (2.5%)

prune515.0ms (17.5%)

localize13.0ms (0.5%)

rewrite78.0ms (2.6%)

series119.0ms (4.1%)

simplify83.0ms (2.8%)

prune360.0ms (12.2%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series56.0ms (1.9%)

simplify58.0ms (2%)

prune136.0ms (4.6%)

localize5.0ms (0.2%)

rewrite25.0ms (0.8%)

series108.0ms (3.7%)

simplify65.0ms (2.2%)

prune96.0ms (3.3%)

regimes9.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample798.0ms (27.1%)

Profiling