Details

Time bar (total: 4.6min)

analyze3.4s (1.2%)

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)

sample188.0ms (0.1%)

Algorithm
1×intervals
Results
82.0ms256×body128valid
58.0ms165×body128invalid
Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify322.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
0499937
1499937

prune16.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 7.1b

Counts
2 → 2
Compiler

Compiled 79 to 64 computations (19% saved)

localize35.0ms (0%)

Local error

Found 4 expressions with local error:

1.1b
(/.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)))))
5.7b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
9.6b
(*.f64 r (*.f64 w w))

rewrite236.0ms (0.1%)

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:

71.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
43.0ms
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))
23.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
14.0ms
(*.f64 r (*.f64 w w))

series657.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

216.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))))
215.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w))))
146.0ms
(*.f64 r (*.f64 w w))
74.0ms
(/.f64 (-.f64 1 v) (*.f64 r (*.f64 w w)))

simplify275.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
052504089

prune2.8s (1%)

Pruning

89 alts after pruning (89 fresh and 0 done)

PrunedKeptTotal
New10188189
Fresh011
Picked101
Done000
Total10289191

Merged error: 2.2b

Counts
191 → 89
Compiler

Compiled 9283 to 5820 computations (37.3% saved)

localize63.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2 (*.f64 r r))
1.1b
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
5.6b
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
5.7b
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))

rewrite272.0ms (0.1%)

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:

79.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
50.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
44.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
18.0ms
(/.f64 2 (*.f64 r r))

series539.0ms (0.2%)

Counts
4 → 12
Calls

4 calls:

202.0ms
(*.f64 (+.f64 3/8 (*.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))))
146.0ms
(/.f64 r (/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w)))
123.0ms
(/.f64 (-.f64 1 v) (*.f64 (*.f64 r w) w))
67.0ms
(/.f64 2 (*.f64 r r))

simplify303.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (170.0ms)

IterNodesCost
049504154
149504154

prune3.4s (1.3%)

Pruning

146 alts after pruning (146 fresh and 0 done)

PrunedKeptTotal
New9992191
Fresh345488
Picked101
Done000
Total134146280

Merged error: 0.0b

Counts
280 → 146
Compiler

Compiled 11400 to 7466 computations (34.5% saved)

localize41.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
0.4b
(/.f64 2 (*.f64 r r))
0.7b
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
2.5b
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))

rewrite502.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
379×times-frac_binary64
249×add-sqr-sqrt_binary64
247×*-un-lft-identity_binary64
184×add-cube-cbrt_binary64
126×cbrt-prod_binary64
125×add-exp-log_binary64
102×add-cbrt-cube_binary64
101×associate-*r*_binary64
55×cbrt-unprod_binary64 prod-exp_binary64
42×difference-of-squares_binary64
39×cbrt-undiv_binary64 div-exp_binary64
32×associate-/r*_binary64
21×distribute-lft-out--_binary64
15×frac-times_binary64
14×associate-*l*_binary64
12×cbrt-div_binary64
11×pow1_binary64 div-inv_binary64
10×associate-/r/_binary64 associate-*l/_binary64
9×associate-*r/_binary64
6×flip3-+_binary64 flip3--_binary64 associate-/l*_binary64 flip--_binary64 flip-+_binary64
4×pow-prod-down_binary64 add-log-exp_binary64
2×clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64
Counts
4 → 362
Calls

4 calls:

162.0ms
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
58.0ms
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
41.0ms
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))
13.0ms
(/.f64 2 (*.f64 r r))

series1.3s (0.5%)

Counts
4 → 12
Calls

4 calls:

671.0ms
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))
307.0ms
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
253.0ms
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
92.0ms
(/.f64 2 (*.f64 r r))

simplify501.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
374 → 374
Iterations

Useful iterations: 0 (127.0ms)

IterNodesCost
0582013058

prune15.0s (5.5%)

Pruning

296 alts after pruning (296 fresh and 0 done)

PrunedKeptTotal
New199175374
Fresh24121145
Picked101
Done000
Total224296520

Merged error: 0.0b

Counts
520 → 296
Compiler

Compiled 30175 to 20960 computations (30.5% saved)

localize41.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
0.3b
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
0.7b
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
2.5b
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))

rewrite411.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
376×times-frac_binary64
275×add-sqr-sqrt_binary64
271×*-un-lft-identity_binary64
190×add-cube-cbrt_binary64
158×cbrt-prod_binary64
122×add-exp-log_binary64
110×associate-*r*_binary64
97×add-cbrt-cube_binary64
55×cbrt-unprod_binary64 prod-exp_binary64
50×difference-of-squares_binary64
37×cbrt-undiv_binary64 div-exp_binary64
31×associate-/r*_binary64
27×distribute-lft-out--_binary64
24×cbrt-div_binary64
23×associate-*l*_binary64
19×frac-times_binary64
18×pow1_binary64
12×flip3--_binary64 flip--_binary64 associate-*l/_binary64
11×swap-sqr_binary64 associate-*r/_binary64
10×associate-/r/_binary64 div-inv_binary64
6×pow-prod-down_binary64 flip3-+_binary64 pow1/3_binary64 flip-+_binary64
5×unswap-sqr_binary64
4×add-log-exp_binary64
3×associate-/l*_binary64 *-commutative_binary64
2×pow-prod-up_binary64 pow-sqr_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64 pow-plus_binary64 clear-num_binary64 frac-2neg_binary64 pow2_binary64
Counts
4 → 400
Calls

4 calls:

89.0ms
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
40.0ms
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))
27.0ms
(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
23.0ms
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))

series1.5s (0.6%)

Counts
4 → 12
Calls

4 calls:

812.0ms
(*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4)))
336.0ms
(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
292.0ms
(*.f64 (*.f64 (/.f64 (*.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (*.f64 v -1/4))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
99.0ms
(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))

simplify627.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
412 → 412
Iterations

Useful iterations: 0 (203.0ms)

IterNodesCost
0498713506
1498713506

prune22.3s (8.1%)

Pruning

309 alts after pruning (309 fresh and 0 done)

PrunedKeptTotal
New258154412
Fresh140155295
Picked101
Done000
Total399309708

Merged error: 0.0b

Counts
708 → 309
Compiler

Compiled 18698 to 12480 computations (33.3% saved)

regimes43.1s (15.7%)

Compiler

Compiled 223109 to 171593 computations (23.1% saved)

bsearch1.4min (31.3%)

simplify58.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
013055
113055

end0.0ms (0%)

sample1.5min (32.9%)

Algorithm
1×intervals
Results
2.1s8000×body128valid
1.3s4843×body128invalid
Compiler

Compiled 36857 to 28372 computations (23% saved)

Pareto

0.03657268706851425

Profiling

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