Details

analyze149.0ms (1.9%)

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 (0.3%)

Algorithm

1×

intervals

Results

7.0ms	50×	body	1024	valid
6.0ms	48×	body	512	valid
5.0ms	141×	body	128	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune2.0ms (0%)

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: 10.3b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (-.f64 x 1))
1.3b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite90.0ms (1.2%)

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`
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 → 135

Calls

4 calls:

45.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
7.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))

series174.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.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))
18.0ms	(/.f64 1 (+.f64 x 1))
18.0ms	(/.f64 1 (-.f64 x 1))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5051	2576

prune199.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	144	4	148

Merged error: 0.4b

Counts

148 → 4

Compiler

Compiled 3289 to 2641 computations (19.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))
0.2b	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
3.9b	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
14.8b	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))

rewrite446.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Rules

774×	`*-un-lft-identity_binary64`
753×	`times-frac_binary64`
635×	`add-sqr-sqrt_binary64`
260×	`distribute-lft-out--_binary64`
245×	`difference-of-squares_binary64`
150×	`add-cube-cbrt_binary64`
81×	`div-inv_binary64`
58×	`frac-sub_binary64`
52×	`difference-of-sqr-1_binary64`
37×	`flip3--_binary64` `flip--_binary64`
35×	`associate-/l*_binary64`
27×	`frac-times_binary64`
24×	`distribute-lft-out_binary64`
23×	`associate-/r*_binary64` `associate-/r/_binary64`
21×	`swap-sqr_binary64`
18×	`associate-/l/_binary64`
17×	`add-exp-log_binary64`
14×	`pow1_binary64`
13×	`associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`associate-r/_binary64` `associate-l/_binary64`
7×	`div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`sub-neg_binary64`
4×	`cbrt-undiv_binary64`
2×	`pow-div_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `1-exp_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `inv-pow_binary64` `prod-exp_binary64` `rec-exp_binary64` `pow-sqr_binary64` `pow-flip_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 544

Calls

4 calls:

146.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))
97.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
50.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
17.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))

series495.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(/.f64 (-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))) (-.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1))))
121.0ms	(-.f64 (*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) (/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1)))
35.0ms	(*.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)))
24.0ms	(/.f64 (/.f64 1 (-.f64 x 1)) (-.f64 x 1))

simplify240.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

556 → 556

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5289	25568

prune3.5s (45.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	555	1	556
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	555	5	560

Merged error: 0.3b

Counts

560 → 5

Compiler

Compiled 31680 to 25315 computations (20.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (+.f64 1 x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.1b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

12.0ms	(+.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)))
7.0ms	(*.f64 x (+.f64 1 x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))

series122.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(*.f64 x (+.f64 1 x))
32.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
28.0ms	(.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)))

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4997	3152
1	4997	3152

prune183.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	109	5	114

Merged error: 0.3b

Counts

114 → 5

Compiler

Compiled 3896 to 2719 computations (30.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
0.2b	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
6.2b	(+.f64 (*.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)
12.3b	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))

rewrite158.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`flip3-+_binary64` `flip-+_binary64`
12×	`frac-times_binary64`
11×	`associate-/l/_binary64` `associate-/r/_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
9×	`times-frac_binary64`
8×	`frac-add_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
4×	`pow1_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64` `div-exp_binary64` `flip--_binary64`
3×	`div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`
2×	`sub-neg_binary64` `associate-+l+_binary64`
1×	`associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 88

Calls

4 calls:

75.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
31.0ms	(+.f64 (*.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)
19.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
19.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))

series292.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(/.f64 (.f64 (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x)) (+.f64 (.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)) (*.f64 (-.f64 x 1) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))))
66.0ms	(+.f64 (*.f64 (-.f64 x 1) (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))) 1)
26.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))
26.0ms	(+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 2 x))

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5231	3120

prune245.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 4564 to 3621 computations (20.7% saved)

regimes33.0ms (0.4%)

Compiler: Compiled 200 to 164 computations (18% saved)

bsearch47.0ms (0.6%)

Steps

Iters	Range		Point
9	0.010202949254377256	24399092.24294659	7216120.091792685
8	-4012917671.3003016	-13249224.75806342	-35323144.403240085

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	109
1	119	109

end0.0ms (0%)

sample941.0ms (12.2%)

Algorithm

1×

intervals

Results

180.0ms	1295×	body	1024	valid
174.0ms	4490×	body	128	valid
158.0ms	1512×	body	512	valid
54.0ms	703×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 296 to 240 computations (18.9% saved)

Details

analyze149.0ms (1.9%)

sample26.0ms (0.3%)

simplify14.0ms (0.2%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite90.0ms (1.2%)

series174.0ms (2.3%)

simplify79.0ms (1%)

prune199.0ms (2.6%)

localize15.0ms (0.2%)

rewrite446.0ms (5.8%)

series495.0ms (6.4%)

simplify240.0ms (3.1%)

prune3.5s (45.8%)

localize13.0ms (0.2%)

rewrite46.0ms (0.6%)

series122.0ms (1.6%)

simplify74.0ms (1%)

prune183.0ms (2.4%)

localize17.0ms (0.2%)

rewrite158.0ms (2.1%)

series292.0ms (3.8%)

simplify64.0ms (0.8%)

prune245.0ms (3.2%)

regimes33.0ms (0.4%)

bsearch47.0ms (0.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample941.0ms (12.2%)

Profiling