Details

analyze1.3s (8.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5367	148
0	3	3
1	3	3

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

Symmetry

Compiler

Compiled 30 to 25 computations (16.7% saved)

sample52.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
12.0ms	172×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	37

prune8.0ms (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

Error

6.6b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (*.f64 r r))
5.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
5.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
9.3b	(.f64 r (.f64 w w))

rewrite369.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

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×	`div-exp_binary64` `cbrt-undiv_binary64`
15×	`prod-exp_binary64` `cbrt-unprod_binary64`
14×	`difference-of-squares_binary64`
11×	`pow1_binary64` `associate-/r*_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×	`-commutative_binary64` `flip3-+_binary64` `frac-times_binary64` `flip-+_binary64` `associate-l/_binary64` `associate-/r/_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`associate-*r/_binary64`

Counts

4 → 166

Calls

4 calls:

23.0ms	(.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))))
8.0ms	(.f64 r (.f64 w w))
4.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 5846 to 3308 computations (43.4% saved)

series580.0ms (4.1%)

Error

6.6b

Counts

4 → 33

Calls

4 calls:

263.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
180.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
67.0ms	(.f64 r (.f64 w w))
28.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 2465 to 1988 computations (19.4% saved)

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4960	4018
1	4960	4018

prune342.0ms (2.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	187	12	199
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	189	12	201

Error

2.6b

Counts

201 → 12

Compiler

Compiled 6500 to 3725 computations (42.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (-.f64 1 v) (.f64 (.f64 w r) w))
0.7b	(/.f64 2 (*.f64 r r))
5.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 w r) w)))
5.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 w r) w))))

rewrite395.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`div-exp_binary64` `cbrt-undiv_binary64`
18×	`difference-of-squares_binary64`
15×	`prod-exp_binary64` `cbrt-unprod_binary64`
12×	`associate-/l_binary64` `associate-/r_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `frac-2neg_binary64` `clear-num_binary64`
2×	`flip3-+_binary64` `frac-times_binary64` `flip-+_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `associate-/r/_binary64` `associate-/l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `div-sub_binary64` `flip3--_binary64` `flip--_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 w r) w))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 w r) w)))
9.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 w r) w))
4.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 6318 to 3604 computations (43% saved)

series734.0ms (5.2%)

Error

2.6b

Counts

4 → 39

Calls

4 calls:

264.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 w r) w))))
207.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 w r) w))
183.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 w r) w)))
30.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 2890 to 2313 computations (20% saved)

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4974	4593
1	4974	4593

prune371.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	212	6	218
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	219	11	230

Error

0.0b

Counts

230 → 11

Compiler

Compiled 7029 to 4011 computations (42.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v))))
0.7b	(/.f64 2 (*.f64 r r))
1.8b	(*.f64 w (/.f64 r (-.f64 1 v)))
5.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))

rewrite257.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 127

Calls

4 calls:

19.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))
12.0ms	(.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v))))
12.0ms	(*.f64 w (/.f64 r (-.f64 1 v)))
4.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 4415 to 2657 computations (39.8% saved)

series684.0ms (4.9%)

Error

0.0b

Counts

4 → 45

Calls

4 calls:

260.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))
187.0ms	(.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v))))
151.0ms	(*.f64 w (/.f64 r (-.f64 1 v)))
28.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 3297 to 2443 computations (25.9% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5006	2965

prune249.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	172	11	183

Error

0.0b

Counts

183 → 11

Compiler

Compiled 5322 to 3132 computations (41.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.8b	(*.f64 w (/.f64 r (-.f64 1 v)))
5.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))
10.4b	(sqrt.f64 (/.f64 2 (*.f64 r r)))
10.4b	(sqrt.f64 (/.f64 2 (*.f64 r r)))

rewrite285.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

38×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
26×	`pow1_binary64`
25×	`associate-r_binary64`
22×	`prod-exp_binary64` `cbrt-unprod_binary64`
20×	`add-cube-cbrt_binary64`
14×	`sqrt-prod_binary64` `pow-prod-down_binary64`
8×	`associate-*r/_binary64`
6×	`associate-l_binary64` `difference-of-squares_binary64`
4×	`add-log-exp_binary64` `rem-sqrt-square_binary64`
3×	`div-inv_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64` `flip3-+_binary64` `frac-times_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64` `unswap-sqr_binary64` `associate-/r/_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 117

Calls

4 calls:

19.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))
12.0ms	(*.f64 w (/.f64 r (-.f64 1 v)))
4.0ms	(sqrt.f64 (/.f64 2 (*.f64 r r)))
4.0ms	(sqrt.f64 (/.f64 2 (*.f64 r r)))

Compiler

Compiled 4935 to 3054 computations (38.1% saved)

series566.0ms (4%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

272.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 w r) (*.f64 w (/.f64 r (-.f64 1 v)))))
169.0ms	(*.f64 w (/.f64 r (-.f64 1 v)))
37.0ms	(sqrt.f64 (/.f64 2 (*.f64 r r)))
32.0ms	(sqrt.f64 (/.f64 2 (*.f64 r r)))

Compiler

Compiled 3312 to 2324 computations (29.8% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4956	2569
1	4956	2569

prune266.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	151	13	164

Error

0.0b

Counts

164 → 13

Compiler

Compiled 5737 to 3392 computations (40.9% saved)

regimes2.1s (15.1%)

Accuracy

Total 0.6b remaining (97.7%)

Threshold costs 0.6b (97.7%)

Compiler

Compiled 34195 to 26208 computations (23.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	37
1	131	37

Removed

()

end0.0ms (0%)

sample5.1s (36.1%)

Algorithm

1×

intervals

Results

585.0ms	8000×	body	128	valid
357.0ms	4863×	body	128	invalid

Compiler

Compiled 5311 to 4075 computations (23.3% saved)

Details

analyze1.3s (8.9%)

sample52.0ms (0.4%)

simplify50.0ms (0.4%)

prune8.0ms (0.1%)

localize23.0ms (0.2%)

rewrite369.0ms (2.6%)

series580.0ms (4.1%)

simplify109.0ms (0.8%)

prune342.0ms (2.4%)

localize16.0ms (0.1%)

rewrite395.0ms (2.8%)

series734.0ms (5.2%)

simplify117.0ms (0.8%)

prune371.0ms (2.6%)

localize16.0ms (0.1%)

rewrite257.0ms (1.8%)

series684.0ms (4.9%)

simplify63.0ms (0.4%)

prune249.0ms (1.8%)

localize19.0ms (0.1%)

rewrite285.0ms (2%)

series566.0ms (4%)

simplify58.0ms (0.4%)

prune266.0ms (1.9%)

regimes2.1s (15.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.1s (36.1%)

Profiling