Details

analyze1.1s (14.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

Compiler

Compiled 30 to 25 computations (16.7% saved)

sample40.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
8.0ms	112×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify226.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4993	37
1	4993	37

prune10.0ms (0.1%)

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: 7.9b

Counts

2 → 2

Compiler

Compiled 133 to 108 computations (18.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (*.f64 r r))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
5.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
8.6b	(.f64 r (.f64 w w))

rewrite78.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
48×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`div-inv_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64`

Counts

4 → 166

Calls

4 calls:

25.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
19.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
8.0ms	(.f64 r (.f64 w w))
5.0ms	(/.f64 2 (*.f64 r r))

series300.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
95.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
64.0ms	(.f64 r (.f64 w w))
31.0ms	(/.f64 2 (*.f64 r r))

simplify69.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5261	3748

prune791.0ms (10.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	167	11	178
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Merged error: 2.5b

Counts

180 → 11

Compiler

Compiled 16002 to 11145 computations (30.4% saved)

localize49.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
0.5b	(/.f64 2 (*.f64 r r))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
5.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite77.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`add-cube-cbrt_binary64`
35×	`associate-r_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`difference-of-squares_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 179

Calls

4 calls:

24.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
10.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))

series337.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
95.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
88.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
32.0ms	(/.f64 2 (*.f64 r r))

simplify90.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5248	4160

prune1.0s (13.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	191	11	202

Merged error: 0.0b

Counts

202 → 11

Compiler

Compiled 20923 to 14973 computations (28.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
0.5b	(/.f64 2 (*.f64 r r))
3.4b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite104.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64`
143×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
100×	`add-exp-log_binary64`
82×	`add-cbrt-cube_binary64`
78×	`cbrt-prod_binary64`
44×	`cbrt-unprod_binary64` `prod-exp_binary64`
32×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
26×	`difference-of-squares_binary64`
13×	`distribute-lft-out--_binary64`
9×	`pow1_binary64` `frac-times_binary64`
6×	`associate-r/_binary64` `associate-/l_binary64` `div-inv_binary64`
5×	`associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64`
2×	`cbrt-div_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-/r/_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 236

Calls

4 calls:

38.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
16.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
4.0ms	(cbrt.f64 (-.f64 1 v))

series380.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
131.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
44.0ms	(cbrt.f64 (-.f64 1 v))
41.0ms	(/.f64 2 (*.f64 r r))

simplify138.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4995	6289
1	4995	6289

prune696.0ms (9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	248	11	259

Merged error: 0.0b

Counts

259 → 11

Compiler

Compiled 10942 to 7016 computations (35.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
0.2b	(/.f64 1 (.f64 (.f64 r w) w))
0.5b	(/.f64 2 (*.f64 r r))
5.2b	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
39×	`times-frac_binary64`
37×	`add-cbrt-cube_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`div-exp_binary64`
22×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`cbrt-undiv_binary64`
10×	`cbrt-unprod_binary64`
9×	`associate-/r_binary64` `associate-/l_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`associate-/r/_binary64` `associate-l_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

10.0ms	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))
7.0ms	(/.f64 1 (.f64 (.f64 r w) w))
6.0ms	(.f64 (.f64 r w) w)
5.0ms	(/.f64 2 (*.f64 r r))

series165.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(.f64 (.f64 r w) w)
47.0ms	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))
33.0ms	(/.f64 2 (*.f64 r r))
31.0ms	(/.f64 1 (.f64 (.f64 r w) w))

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5392	1609

prune256.0ms (3.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	139	12	151

Merged error: 0.0b

Counts

151 → 12

Compiler

Compiled 5340 to 3472 computations (35% saved)

regimes139.0ms (1.8%)

Compiler: Compiled 1698 to 1329 computations (21.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	34
1	92	34

end0.0ms (0%)

sample1.5s (19.2%)

Algorithm

1×

intervals

Results

539.0ms	8000×	body	128	valid
320.0ms	4708×	body	128	invalid

Compiler

Compiled 439 to 346 computations (21.2% saved)

Details

analyze1.1s (14.2%)

sample40.0ms (0.5%)

simplify226.0ms (2.9%)

prune10.0ms (0.1%)

localize17.0ms (0.2%)

rewrite78.0ms (1%)

series300.0ms (3.9%)

simplify69.0ms (0.9%)

prune791.0ms (10.2%)

localize49.0ms (0.6%)

rewrite77.0ms (1%)

series337.0ms (4.3%)

simplify90.0ms (1.2%)

prune1.0s (13.1%)

localize20.0ms (0.3%)

rewrite104.0ms (1.3%)

series380.0ms (4.9%)

simplify138.0ms (1.8%)

prune696.0ms (9%)

localize20.0ms (0.3%)

rewrite42.0ms (0.5%)

series165.0ms (2.1%)

simplify104.0ms (1.3%)

prune256.0ms (3.3%)

regimes139.0ms (1.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (19.2%)

Profiling