Details

Time bar (total: 20.8s)

analyze942.0ms (4.5%)

Algorithm
1×search
Search
TrueOtherFalseIter
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 (0.2%)

Algorithm
1×intervals
Results
21.0ms256×body80valid
10.0ms140×body80invalid
Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify503.0ms (2.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
0548837

prune11.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 6.5b

Counts
2 → 2
Compiler

Compiled 79 to 64 computations (19% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
5.3b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
7.3b
(*.f64 r (*.f64 w w))

rewrite68.0ms (0.3%)

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)))))
16.0ms
(/.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))

series70.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

23.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
17.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
17.0ms
(*.f64 r (*.f64 w w))
14.0ms
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))

simplify87.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
049734134
149734134

prune268.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1818189
Fresh101
Picked101
Done000
Total1838191

Merged error: 2.2b

Counts
191 → 8
Compiler

Compiled 6308 to 3645 computations (42.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 2 (*.f64 r r))
1.0b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
5.3b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))

rewrite56.0ms (0.3%)

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:

21.0ms
(*.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))

series60.0ms (0.3%)

Counts
4 → 12
Calls

4 calls:

27.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
16.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
14.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
3.0ms
(/.f64 2 (*.f64 r r))

simplify91.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
055184232

prune278.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1829191
Fresh437
Picked101
Done000
Total18712199

Merged error: 0.0b

Counts
199 → 12
Compiler

Compiled 6505 to 3774 computations (42% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 2 (*.f64 r r))
0.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
2.1b
(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite200.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
759×times-frac_binary64
509×add-sqr-sqrt_binary64
461×*-un-lft-identity_binary64
433×add-exp-log_binary64 cbrt-prod_binary64
344×add-cube-cbrt_binary64
256×add-cbrt-cube_binary64
192×associate-*r*_binary64
179×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
78×difference-of-squares_binary64
39×distribute-lft-out--_binary64
32×associate-/r*_binary64
18×div-inv_binary64
14×unswap-sqr_binary64
13×associate-*l*_binary64
11×pow1_binary64
10×frac-times_binary64
9×associate-/l*_binary64
7×associate-*r/_binary64
6×associate-*l/_binary64
4×pow-prod-down_binary64 flip3-+_binary64 add-log-exp_binary64 flip-+_binary64
3×associate-/r/_binary64
2×clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
Counts
4 → 645
Calls

4 calls:

79.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
45.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
14.0ms
(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms
(/.f64 2 (*.f64 r r))

series100.0ms (0.5%)

Counts
4 → 12
Calls

4 calls:

40.0ms
(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
36.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
20.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
3.0ms
(/.f64 2 (*.f64 r r))

simplify317.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
657 → 657
Iterations

Useful iterations: 0 (96.0ms)

IterNodesCost
0498527305
1498527305

prune4.2s (20.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New6561657
Fresh01111
Picked011
Done000
Total65613669

Merged error: 0.0b

Counts
669 → 13
Compiler

Compiled 35077 to 21631 computations (38.3% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
3.5b
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
3.5b
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
4.3b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))))

rewrite238.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
1176×cbrt-prod_binary64
1044×times-frac_binary64
644×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
482×add-cube-cbrt_binary64
231×add-exp-log_binary64
139×cbrt-unprod_binary64 prod-exp_binary64
133×add-cbrt-cube_binary64
108×difference-of-squares_binary64
81×frac-times_binary64
75×cbrt-div_binary64
54×cbrt-undiv_binary64 associate-*r/_binary64 distribute-lft-out--_binary64 div-exp_binary64
35×associate-*l/_binary64
21×div-inv_binary64
18×pow1_binary64
16×flip3-+_binary64 flip-+_binary64
10×pow-prod-down_binary64
4×add-log-exp_binary64
3×pow1/3_binary64 associate-/r/_binary64 associate-*l*_binary64
1×associate-*r*_binary64 *-commutative_binary64
Counts
4 → 731
Calls

4 calls:

108.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))))
22.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
18.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
18.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))

series206.0ms (1%)

Counts
4 → 12
Calls

4 calls:

57.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
55.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
55.0ms
(cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
40.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (*.f64 (/.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (*.f64 r w))) (*.f64 (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w)))) (cbrt.f64 (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))))

simplify381.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
743 → 743
Iterations

Useful iterations: 0 (102.0ms)

IterNodesCost
0499831890
1499831890

prune10.0s (48.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New7430743
Fresh01111
Picked011
Done011
Total74313756

Merged error: 0.0b

Counts
756 → 13
Compiler

Compiled 56011 to 33936 computations (39.4% saved)

regimes310.0ms (1.5%)

Compiler

Compiled 1859 to 1432 computations (23% saved)

bsearch118.0ms (0.6%)

Steps
ItersRangePoint
7
8.827045077364559e-70
1.9077787655580844e-68
1.8322291642935536e-68
10
-2.1497442754238297e+172
-6.611015863336913e+159
-5.003095036691503e+160
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify10.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0354194
1354194

end0.0ms (0%)

sample2.2s (10.4%)

Algorithm
1×intervals
Results
556.0ms8000×body80valid
331.0ms4756×body80invalid
Compiler

Compiled 597 to 447 computations (25.1% saved)

Profiling

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