Details

Time bar (total: 3.7s)

analyze500.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%50%0%4
50%50%0%5
50%50%0%6
50%50%0%7
50%50%0%8
50%50%0%9
50%50%0%10
50%50%0%11
50%50%0%12
50%50%0%13
50%49.9%0%14

sample38.0ms

Algorithm
intervals
Results
13.0ms48×body1280valid
7.0ms40×body640valid
5.0ms132×body80valid
3.0ms21×body320valid
1.0ms15×body160valid

simplify538.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (126.0ms)

IterNodesCost
0528415

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b
(/.f64 (-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
0.3b
(*.f64 (tan.f64 x) (tan.f64 x))
0.3b
(*.f64 (tan.f64 x) (tan.f64 x))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt_binary64
21×*-un-lft-identity_binary64 add-cube-cbrt_binary64
18×pow1_binary64
12×times-frac_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
8×tan-quot_binary64
6×add-log-exp_binary64 swap-sqr_binary64 associate-*r*_binary64 associate-*l*_binary64
5×difference-of-squares_binary64
4×associate-/l*_binary64
3×associate-/r*_binary64
2×pow-prod-down_binary64 associate-/l/_binary64 flip3--_binary64 cbrt-unprod_binary64 pow-prod-up_binary64 associate-*r/_binary64 associate-/r/_binary64 pow-plus_binary64 unswap-sqr_binary64 prod-exp_binary64 pow-sqr_binary64 flip--_binary64 frac-times_binary64 pow2_binary64 associate-*l/_binary64 *-commutative_binary64
1×flip3-+_binary64 sub-neg_binary64 diff-log_binary64 cbrt-undiv_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 flip-+_binary64
Counts
4 → 104
Calls
4 calls:
3.0ms
(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
7.0ms
(/.f64 (-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
5.0ms
(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms
(*.f64 (tan.f64 x) (tan.f64 x))

series94.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
49.0ms
(/.f64 (-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
11.0ms
(*.f64 (tan.f64 x) (tan.f64 x))
22.0ms
(*.f64 (tan.f64 x) (tan.f64 x))

simplify57.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049511205
149511205

prune170.0ms

Filtered
82 candidates to 116 candidates (-41.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10313116
Fresh000
Picked101
Done000
Total10413117

Merged error: 0.0b

Counts
117 → 13

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
0.2b
(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
0.3b
(pow.f64 (tan.f64 x) 2)
0.3b
(pow.f64 (tan.f64 x) 2)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
274×times-frac_binary64
239×add-sqr-sqrt_binary64
237×*-un-lft-identity_binary64
113×add-cube-cbrt_binary64
84×difference-of-squares_binary64
46×associate-/r*_binary64
41×distribute-lft-out_binary64
27×unpow-prod-down_binary64
23×unpow2_binary64 sqr-pow_binary64
21×distribute-lft-out--_binary64
19×add-exp-log_binary64
11×add-cbrt-cube_binary64 associate-/r/_binary64
8×div-exp_binary64
7×pow1_binary64 associate-/l*_binary64
6×pow-unpow_binary64 div-inv_binary64
5×flip3--_binary64 flip--_binary64
4×add-log-exp_binary64 cbrt-undiv_binary64
2×pow-to-exp_binary64 associate-/l/_binary64 1-exp_binary64 pow-pow_binary64 clear-num_binary64 frac-2neg_binary64 rec-exp_binary64 pow-exp_binary64
1×flip3-+_binary64 inv-pow_binary64 pow-flip_binary64 flip-+_binary64
Counts
4 → 272
Calls
4 calls:
13.0ms
(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
17.0ms
(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
3.0ms
(pow.f64 (tan.f64 x) 2)
3.0ms
(pow.f64 (tan.f64 x) 2)

series115.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2)))
43.0ms
(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0) (-.f64 1.0 (pow.f64 (tan.f64 x) 2))))
11.0ms
(pow.f64 (tan.f64 x) 2)
14.0ms
(pow.f64 (tan.f64 x) 2)

simplify76.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
051705486

prune259.0ms

Filtered
135 candidates to 284 candidates (-110.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2795284
Fresh3912
Picked101
Done000
Total28314297

Merged error: 0.0b

Counts
297 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
0.3b
(pow.f64 (tan.f64 x) 2)
0.3b
(pow.f64 (tan.f64 x) 2)
0.3b
(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt_binary64
88×*-un-lft-identity_binary64
64×times-frac_binary64
39×log-pow_binary64
38×exp-prod_binary64
36×add-cube-cbrt_binary64 difference-of-squares_binary64
17×distribute-lft-out_binary64
15×unpow-prod-down_binary64
11×unpow2_binary64 sqr-pow_binary64
9×distribute-lft-out--_binary64
8×add-exp-log_binary64 associate-/l*_binary64
7×pow1_binary64
6×pow-unpow_binary64 add-cbrt-cube_binary64
4×associate-/r*_binary64 add-log-exp_binary64 associate-/r/_binary64
3×log-prod_binary64
2×pow-to-exp_binary64 flip3-+_binary64 associate-/l/_binary64 pow-pow_binary64 div-sub_binary64 div-inv_binary64 flip-+_binary64 pow-exp_binary64
1×flip3--_binary64 cbrt-undiv_binary64 rem-log-exp_binary64 exp-diff_binary64 clear-num_binary64 frac-2neg_binary64 div-exp_binary64 log-div_binary64 flip--_binary64
Counts
4 → 148
Calls
4 calls:
13.0ms
(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
3.0ms
(pow.f64 (tan.f64 x) 2)
3.0ms
(pow.f64 (tan.f64 x) 2)
18.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))

series111.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))
10.0ms
(pow.f64 (tan.f64 x) 2)
13.0ms
(pow.f64 (tan.f64 x) 2)
44.0ms
(log.f64 (exp.f64 (/.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
050182243

prune181.0ms

Filtered
107 candidates to 160 candidates (-49.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1591160
Fresh11213
Picked011
Done000
Total16014174

Merged error: 0.0b

Counts
174 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b
(*.f64 (tan.f64 x) (sin.f64 x))
0.2b
(/.f64 (-.f64 1.0 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
0.3b
(*.f64 (tan.f64 x) (tan.f64 x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
18×times-frac_binary64
15×add-exp-log_binary64 add-cbrt-cube_binary64
13×pow1_binary64
6×associate-/r*_binary64 associate-*r*_binary64 associate-*l*_binary64 associate-/l*_binary64 tan-quot_binary64
4×add-log-exp_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64
3×associate-/l/_binary64 swap-sqr_binary64 cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64 associate-*l/_binary64
2×pow-prod-down_binary64 associate-/r/_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 *-commutative_binary64
1×flip3-+_binary64 flip3--_binary64 pow-prod-up_binary64 associate-*r/_binary64 pow-plus_binary64 div-sub_binary64 pow-sqr_binary64 flip--_binary64 flip-+_binary64 frac-times_binary64 pow2_binary64
Counts
4 → 109
Calls
4 calls:
6.0ms
(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms
(*.f64 (tan.f64 x) (sin.f64 x))
9.0ms
(/.f64 (-.f64 1.0 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
6.0ms
(*.f64 (tan.f64 x) (tan.f64 x))

series93.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
12.0ms
(*.f64 (tan.f64 x) (sin.f64 x))
53.0ms
(/.f64 (-.f64 1.0 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x))))
11.0ms
(*.f64 (tan.f64 x) (tan.f64 x))

simplify47.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050541679

prune95.0ms

Filtered
84 candidates to 121 candidates (-44.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1192121
Fresh21012
Picked101
Done011
Total12213135

Merged error: 0.0b

Counts
135 → 13

regimes159.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04521
14521

end0.0ms

sample960.0ms

Algorithm
intervals
Results
379.0ms1508×body1280valid
193.0ms1171×body640valid
163.0ms4377×body80valid
77.0ms640×body320valid
27.0ms304×body160valid

Profiling

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