Details

Time bar (total: 28.3s)

analyze16.7s

Algorithm
search
Search
TrueOtherFalseIter
0%0.2%99.8%0
0%0.2%99.8%1
0%0.2%99.8%2
0%0.2%99.8%3
0%0.2%99.8%4
0%0.2%99.8%5
0%0.2%99.8%6
0%0.2%99.8%7
0%0.2%99.8%8
0%0.2%99.8%9
0%0.2%99.8%10
0%0.2%99.8%11
0%0.2%99.8%12
0%0.2%99.8%13
0%0.2%99.8%14

sample126.0ms

Algorithm
intervals
Results
62.0ms129×body1280valid
28.0ms256×pre80true
14.0ms57×body640valid
4.0ms21×body320valid
2.0ms41×body80valid
1.0msbody160valid

simplify412.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (8.0ms)

IterNodesCost
01859
11859

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 11.9b

Counts
2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.1b
(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
3.1b
(tan.f64 (+.f64 y z))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64 add-log-exp_binary64
add-sqr-sqrt_binary64
tan-quot_binary64
pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
tan-sum_binary64 sub-neg_binary64 diff-log_binary64 distribute-lft-out_binary64 distribute-lft-out--_binary64 frac-sub_binary64 sum-log_binary64
flip3-+_binary64 associate-+r-_binary64 flip3--_binary64 difference-of-squares_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 associate-+r+_binary64
Counts
3 → 40
Calls
3 calls:
7.0ms
(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
6.0ms
(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
16.0ms
(tan.f64 (+.f64 y z))

series126.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
54.0ms
(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
31.0ms
(tan.f64 (+.f64 y z))

simplify65.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
04910561
14910561

prune83.0ms

Filtered
39 candidates to 49 candidates (-25.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New41849
Fresh000
Picked101
Done000
Total42850

Merged error: 0.1b

Counts
50 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+.f64 (tan.f64 y) (tan.f64 z))
0.1b
(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.1b
(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.2b
(*.f64 (tan.f64 y) (tan.f64 z))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity_binary64
13×add-log-exp_binary64 add-sqr-sqrt_binary64
tan-quot_binary64
pow1_binary64 add-cube-cbrt_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
distribute-lft-out_binary64 associate-*r*_binary64 associate-*l*_binary64 sum-log_binary64
flip3-+_binary64 sub-neg_binary64 diff-log_binary64 difference-of-squares_binary64 distribute-lft-out--_binary64 +-commutative_binary64 flip-+_binary64
pow-prod-down_binary64 associate-+r-_binary64 flip3--_binary64 cbrt-unprod_binary64 associate-*r/_binary64 frac-add_binary64 unswap-sqr_binary64 prod-exp_binary64 times-frac_binary64 flip--_binary64 associate-+r+_binary64 frac-sub_binary64 frac-times_binary64 associate-*l/_binary64 *-commutative_binary64
Counts
4 → 65
Calls
4 calls:
5.0ms
(+.f64 (tan.f64 y) (tan.f64 z))
13.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
13.0ms
(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
6.0ms
(*.f64 (tan.f64 y) (tan.f64 z))

series367.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+.f64 (tan.f64 y) (tan.f64 z))
153.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
162.0ms
(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
27.0ms
(*.f64 (tan.f64 y) (tan.f64 z))

simplify34.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
049511271
149511271

prune105.0ms

Filtered
59 candidates to 77 candidates (-30.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh437
Picked101
Done000
Total78785

Merged error: 0.1b

Counts
85 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (tan.f64 y) (tan.f64 z))
0.2b
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
0.3b
(-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
0.4b
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
61×*-un-lft-identity_binary64
56×add-sqr-sqrt_binary64
28×times-frac_binary64
22×add-cube-cbrt_binary64
21×difference-of-squares_binary64 distribute-lft-out--_binary64
13×pow1_binary64
12×tan-quot_binary64
11×flip3--_binary64 flip--_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64 frac-times_binary64
associate-*r*_binary64 associate-*l*_binary64
swap-sqr_binary64 frac-sub_binary64
associate-/r*_binary64 add-log-exp_binary64
sub-neg_binary64
associate-*r/_binary64 associate-/l*_binary64 associate-*l/_binary64
pow-prod-down_binary64 associate-/l/_binary64 associate--r+_binary64 cbrt-unprod_binary64 distribute-lft-in_binary64 associate-/r/_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 prod-exp_binary64 *-commutative_binary64
diff-log_binary64 pow-prod-up_binary64 cbrt-undiv_binary64 pow-plus_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64 pow-sqr_binary64 pow2_binary64
Counts
4 → 139
Calls
4 calls:
5.0ms
(*.f64 (tan.f64 y) (tan.f64 z))
22.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
10.0ms
(-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
28.0ms
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))

series1.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(*.f64 (tan.f64 y) (tan.f64 z))
856.0ms
(/.f64 (-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
604.0ms
(-.f64 (*.f64 x x) (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
196.0ms
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))

simplify79.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
060545606

prune232.0ms

Filtered
104 candidates to 151 candidates (-45.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1429151
Fresh336
Picked101
Done000
Total14612158

Merged error: 0.0b

Counts
158 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (tan.f64 y) (tan.f64 z))
0.2b
(/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
0.3b
(-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
0.4b
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
52×associate-*l/_binary64
47×*-un-lft-identity_binary64 add-sqr-sqrt_binary64
33×frac-sub_binary64
29×tan-quot_binary64
28×flip3--_binary64 flip--_binary64
25×times-frac_binary64 frac-times_binary64
20×add-cube-cbrt_binary64
16×distribute-lft-out--_binary64
15×difference-of-squares_binary64
10×add-exp-log_binary64 add-cbrt-cube_binary64
associate-*r/_binary64 associate-*l*_binary64
flip3-+_binary64 pow1_binary64 frac-add_binary64 flip-+_binary64
associate-/r*_binary64 add-log-exp_binary64 associate-*r*_binary64
associate-/l*_binary64
sub-neg_binary64
pow-prod-down_binary64 associate-/l/_binary64 cbrt-unprod_binary64 associate-/r/_binary64 unswap-sqr_binary64 prod-exp_binary64 *-commutative_binary64
diff-log_binary64 cbrt-undiv_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 div-exp_binary64
Counts
4 → 142
Calls
4 calls:
6.0ms
(*.f64 (tan.f64 y) (tan.f64 z))
27.0ms
(/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
12.0ms
(-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
29.0ms
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))))

series3.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(*.f64 (tan.f64 y) (tan.f64 z))
2.0s
(/.f64 (-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))) (-.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))))
1.5s
(-.f64 (*.f64 x x) (/.f64 (*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a)))) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
287.0ms
(*.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) (-.f64 (*.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (*.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))))

simplify74.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0553812175

prune318.0ms

Filtered
122 candidates to 154 candidates (-26.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1522154
Fresh11011
Picked101
Done000
Total15412166

Merged error: 0.0b

Counts
166 → 12

regimes581.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
0424108
1424108

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s3918×body1280valid
537.0ms8000×pre80true
488.0ms2018×body640valid
114.0ms677×body320valid
60.0ms1092×body80valid
34.0ms295×body160valid

Profiling

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