Details

analyze1.1s (13.9%)

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
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)

sample46.0ms (0.6%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
12.0ms	170×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify219.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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: 5.9b

Counts

2 → 2

Compiler

Compiled 133 to 108 computations (18.8% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 2 (*.f64 r r))
4.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
7.0b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
9.2b	(.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:

26.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
14.0ms	(/.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))

series314.0ms (4%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
97.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
64.0ms	(.f64 r (.f64 w w))
39.0ms	(/.f64 2 (*.f64 r r))

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5261	3748

prune827.0ms (10.5%)

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: 2.0b

Counts

180 → 11

Compiler

Compiled 17285 to 11750 computations (32% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
1.0b	(/.f64 2 (*.f64 r r))
4.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
7.0b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite80.0ms (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:

25.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
13.0ms	(/.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))

series336.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.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)))
79.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
42.0ms	(/.f64 2 (*.f64 r r))

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5248	4160

prune899.0ms (11.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	189	13	202

Merged error: 0.0b

Counts

202 → 13

Compiler

Compiled 18520 to 13033 computations (29.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
1.0b	(/.f64 2 (*.f64 r r))
2.5b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.8b	(.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))))

rewrite108.0ms (1.4%)

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:

42.0ms	(.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))))
13.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
4.0ms	(cbrt.f64 (-.f64 1 v))

series402.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
138.0ms	(.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))))
53.0ms	(cbrt.f64 (-.f64 1 v))
36.0ms	(/.f64 2 (*.f64 r r))

simplify141.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4995	6289
1	4995	6289

prune715.0ms (9.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	248	13	261

Merged error: 0.0b

Counts

261 → 13

Compiler

Compiled 11012 to 7071 computations (35.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
1.0b	(/.f64 2 (*.f64 r r))
4.4b	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.2b	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))

rewrite60.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

18.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
15.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.0ms	(.f64 (.f64 r w) w)
5.0ms	(/.f64 2 (*.f64 r r))

series315.0ms (4%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
97.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
44.0ms	(.f64 (.f64 r w) w)
36.0ms	(/.f64 2 (*.f64 r r))

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5907	2537

prune276.0ms (3.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	140	12	152

Merged error: 0.0b

Counts

152 → 12

Compiler

Compiled 5960 to 3855 computations (35.3% saved)

regimes131.0ms (1.7%)

Compiler: Compiled 1549 to 1235 computations (20.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	55
1	130	55

end0.0ms (0%)

sample1.5s (19.5%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	128	valid
341.0ms	4819×	body	128	invalid

Compiler

Compiled 424 to 338 computations (20.3% saved)

Details

analyze1.1s (13.9%)

sample46.0ms (0.6%)

simplify219.0ms (2.8%)

prune10.0ms (0.1%)

localize25.0ms (0.3%)

rewrite78.0ms (1%)

series314.0ms (4%)

simplify67.0ms (0.9%)

prune827.0ms (10.5%)

localize16.0ms (0.2%)

rewrite80.0ms (1%)

series336.0ms (4.3%)

simplify90.0ms (1.1%)

prune899.0ms (11.4%)

localize21.0ms (0.3%)

rewrite108.0ms (1.4%)

series402.0ms (5.1%)

simplify141.0ms (1.8%)

prune715.0ms (9.1%)

localize17.0ms (0.2%)

rewrite60.0ms (0.8%)

series315.0ms (4%)

simplify58.0ms (0.7%)

prune276.0ms (3.5%)

regimes131.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.5s (19.5%)

Profiling