Details

analyze1.1s (13.7%)

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)

sample45.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
9.0ms	138×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify143.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	37

prune13.0ms (0.2%)

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

Error

8.6b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
5.0b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
8.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.4b	(.f64 r (.f64 w w))

rewrite78.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

22.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
8.0ms	(.f64 r (.f64 w w))

series194.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
52.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
48.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
33.0ms	(.f64 r (.f64 w w))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5250	4089

prune343.0ms (4.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	180	9	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Error

3.5b

Counts

191 → 9

Compiler

Compiled 6382 to 3700 computations (42% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (*.f64 r r))
1.2b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
8.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite67.0ms (0.9%)

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:

22.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
11.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
9.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.0ms	(/.f64 2 (*.f64 r r))

series180.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
56.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
42.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
19.0ms	(/.f64 2 (*.f64 r r))

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4950	4154
1	4950	4154

prune364.0ms (4.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	188	12	200

Error

0.0b

Counts

200 → 12

Compiler

Compiled 6451 to 3814 computations (40.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
0.7b	(/.f64 2 (*.f64 r r))
3.0b	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.7b	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))

rewrite55.0ms (0.7%)

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:

16.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
13.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.0ms	(.f64 (.f64 r w) w)
4.0ms	(/.f64 2 (*.f64 r r))

series174.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
48.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
26.0ms	(.f64 (.f64 r w) w)
16.0ms	(/.f64 2 (*.f64 r r))

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5439	2537

prune212.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	140	11	151

Error

0.0b

Counts

151 → 11

Compiler

Compiled 4506 to 2717 computations (39.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 w (.f64 r w))
0.7b	(/.f64 2 (*.f64 r r))
5.0b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
5.7b	(.f64 r (.f64 w (*.f64 r w)))

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
65×	`add-cbrt-cube_binary64`
39×	`cbrt-unprod_binary64`
38×	`pow1_binary64`
24×	`pow-prod-down_binary64`
10×	`div-exp_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-undiv_binary64`
5×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`associate-r_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 108

Calls

4 calls:

21.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
9.0ms	(.f64 r (.f64 w (*.f64 r w)))
5.0ms	(.f64 w (.f64 r w))
4.0ms	(/.f64 2 (*.f64 r r))

series130.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
27.0ms	(.f64 r (.f64 w (*.f64 r w)))
23.0ms	(/.f64 2 (*.f64 r r))
16.0ms	(.f64 w (.f64 r w))

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5129	1974

prune161.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	120	11	131

Error

0.0b

Counts

131 → 11

Compiler

Compiled 3516 to 2121 computations (39.7% saved)

regimes1.1s (13.8%)

Accuracy

Total 0.7b remaining (97.1%)

Threshold costs 0.7b (97.1%)

Compiler

Compiled 17352 to 13035 computations (24.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	55
1	130	55

end0.0ms (0%)

sample3.1s (39.7%)

Algorithm

1×

intervals

Results

545.0ms	8000×	body	128	valid
327.0ms	4854×	body	128	invalid

Compiler

Compiled 2739 to 2063 computations (24.7% saved)

Details

analyze1.1s (13.7%)

sample45.0ms (0.6%)

simplify143.0ms (1.8%)

prune13.0ms (0.2%)

localize18.0ms (0.2%)

rewrite78.0ms (1%)

series194.0ms (2.5%)

simplify73.0ms (0.9%)

prune343.0ms (4.3%)

localize16.0ms (0.2%)

rewrite67.0ms (0.9%)

series180.0ms (2.3%)

simplify126.0ms (1.6%)

prune364.0ms (4.6%)

localize16.0ms (0.2%)

rewrite55.0ms (0.7%)

series174.0ms (2.2%)

simplify61.0ms (0.8%)

prune212.0ms (2.7%)

localize16.0ms (0.2%)

rewrite52.0ms (0.7%)

series130.0ms (1.6%)

simplify51.0ms (0.6%)

prune161.0ms (2%)

regimes1.1s (13.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.1s (39.7%)

Profiling