Details

Time bar (total: 12.4min)

analyze2.6s (0.3%)

Algorithm
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%99.9%0.1%9
0%99.9%0.1%10
0%99.5%0.5%11
0%99.1%0.9%12
0.4%97.3%2.3%13
0.7%95.8%3.5%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample411.0ms (0.1%)

Algorithm
intervals
Results
146.0ms47×body4096invalid
73.0ms127×body1024valid
67.0ms33×body2048invalid
31.0msbody4096valid
30.0ms29×body2048valid
18.0ms46×body512valid
8.0ms14×body1024invalid
5.0ms20×body256valid
4.0ms11×body512invalid
4.0ms27×body128valid
3.0ms24×body128invalid
2.0msbody256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify115.0ms (0%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
0518532

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
41.5b
Counts
2 → 2
Compiler

Compiled 21 to 17 computations (19% saved)

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.3b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.2b
(pow.f64 (/.f64 k t) 2)
1.3b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
1.5b
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
17.2b
(/.f64 (pow.f64 t 3) (*.f64 l l))
30.6b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite78.0ms (0%)

Algorithm
rewrite-expression-head
Rules
78×add-exp-log_binary64_116
40×prod-exp_binary64_127
38×add-cbrt-cube_binary64_114
36×add-sqr-sqrt_binary64_100
31×*-un-lft-identity_binary64_78
28×times-frac_binary64_84
19×add-cube-cbrt_binary64_113
18×cbrt-unprod_binary64_111 div-exp_binary64_129
17×associate-*l*_binary64_19
15×pow1_binary64_139
13×associate-*l/_binary64_21
12×associate-/l*_binary64_23
11×associate-*r*_binary64_18
10×unpow-prod-down_binary64_157 cube-prod_binary64_106
add-log-exp_binary64_117 frac-times_binary64_88 cancel-sign-sub-inv_binary64_44
pow-prod-down_binary64_149
tan-quot_binary64_237 pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-undiv_binary64_112
distribute-lft-in_binary64_27 flip3--_binary64_82 distribute-rgt-in_binary64_28 flip--_binary64_53 unswap-sqr_binary64_46 associate-*r/_binary64_20
distribute-lft-out--_binary64_30 sqr-pow_binary64_50 difference-of-squares_binary64_47
cube-mult_binary64_108 associate--l+_binary64_15 unpow3_binary64_144 sub-neg_binary64_71
*-commutative_binary64_9 diff-log_binary64_170 div-inv_binary64_75 distribute-lft-out_binary64_29 difference-of-sqr-1_binary64_48
frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77 sum-log_binary64_169
Counts
4 → 163
Calls

8 calls:

29.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
12.0ms
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(pow.f64 (/.f64 k t) 2)

series1.0s (0.1%)

Counts
4 → 33
Calls

4 calls:

553.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
257.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
107.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
96.0ms
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
Compiler

Compiled 1529 to 1326 computations (13.3% saved)

simplify82.0ms (0%)

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
051124163

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

1.3b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
0.6b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
0.2b
(pow.f64 (/.f64 k t) 2)
0.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
1.3b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
17.2b
(/.f64 (pow.f64 t 3) (*.f64 l l))
27.4b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite80.0ms (0%)

Algorithm
rewrite-expression-head
Rules
228×add-exp-log_binary64_116
139×prod-exp_binary64_127
52×add-cbrt-cube_binary64_114
51×div-exp_binary64_129
37×times-frac_binary64_84
33×add-sqr-sqrt_binary64_100
32×pow-exp_binary64_146
26×cbrt-unprod_binary64_111
24×add-cube-cbrt_binary64_113 associate-*r*_binary64_18 *-un-lft-identity_binary64_78
23×pow-to-exp_binary64_147 unpow-prod-down_binary64_157
18×associate-*l*_binary64_19
12×associate-/l*_binary64_23
11×pow1_binary64_139
10×associate-*l/_binary64_21 cube-prod_binary64_106
cbrt-undiv_binary64_112
sqr-pow_binary64_50 unswap-sqr_binary64_46
tan-quot_binary64_237 add-log-exp_binary64_117 pow-prod-down_binary64_149
cube-mult_binary64_108 *-commutative_binary64_9 div-inv_binary64_75 unpow3_binary64_144
frac-times_binary64_88 associate-*r/_binary64_20
unpow2_binary64_143 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77
Counts
4 → 187
Calls

8 calls:

20.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
17.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(pow.f64 (/.f64 k t) 2)

series1.4s (0.2%)

Counts
4 → 38
Calls

4 calls:

537.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
501.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
263.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
99.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 1653 to 1424 computations (13.9% saved)

simplify103.0ms (0%)

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
050674824

prune2.6s (0.3%)

Pruning

121 alts after pruning (121 fresh and 0 done)

PrunedKeptTotal
New300121421
Fresh000
Picked000
Done202
Total302121423
Error
17.8b
Counts
423 → 121
Compiler

Compiled 9525 to 5894 computations (38.1% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
0.6b
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
0.4b
(pow.f64 (sin.f64 k) 2)
0.1b
(*.f64 (*.f64 l l) (cos.f64 k))
0.6b
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
1.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
6.9b
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
22.3b
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))

rewrite74.0ms (0%)

Algorithm
rewrite-expression-head
Rules
320×add-exp-log_binary64_116
183×prod-exp_binary64_127
173×add-cbrt-cube_binary64_114
87×cbrt-unprod_binary64_111
82×div-exp_binary64_129
46×cbrt-undiv_binary64_112
23×add-sqr-sqrt_binary64_100
20×times-frac_binary64_84
17×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
15×pow-exp_binary64_146 pow-to-exp_binary64_147
associate-*r*_binary64_18 pow1_binary64_139
div-inv_binary64_75 associate-/r*_binary64_22
associate-*l*_binary64_19 add-log-exp_binary64_117 unpow-prod-down_binary64_157 associate-/l*_binary64_23 unswap-sqr_binary64_46
pow-prod-down_binary64_149
*-commutative_binary64_9 unpow2_binary64_143 frac-2neg_binary64_89 sqr-pow_binary64_50 clear-num_binary64_77
associate-/r/_binary64_24
Counts
4 → 184
Calls

8 calls:

18.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
14.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))
9.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
6.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
0.0ms
(*.f64 (*.f64 l l) (cos.f64 k))

series1.4s (0.2%)

Counts
4 → 34
Calls

4 calls:

607.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k))))
490.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (*.f64 l l) (cos.f64 k)))
158.0ms
(*.f64 (*.f64 k k) (*.f64 t (pow.f64 (sin.f64 k) 2)))
103.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
Compiler

Compiled 1266 to 1085 computations (14.3% saved)

simplify126.0ms (0%)

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
050005645

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

20.3b
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
0.3b
(/.f64 2 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))))
0.1b
(/.f64 l (/.f64 t l))
0.1b
(/.f64 l (/.f64 t l))
0.3b
(/.f64 2 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))))
20.3b
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))

rewrite464.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
4930×times-frac_binary64_84
2065×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
663×unpow-prod-down_binary64_157
370×associate-/r*_binary64_22
221×sqr-pow_binary64_50
155×div-inv_binary64_75
67×add-exp-log_binary64_116
49×div-exp_binary64_129
43×associate-/r/_binary64_24
31×add-cbrt-cube_binary64_114
19×cbrt-undiv_binary64_112
13×associate-/l*_binary64_23
pow-exp_binary64_146 pow-to-exp_binary64_147
add-log-exp_binary64_117 frac-2neg_binary64_89 clear-num_binary64_77 pow1_binary64_139
Counts
3 → 1000
Calls

6 calls:

77.0ms
(/.f64 2 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))))
18.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
6.0ms
(/.f64 l (/.f64 t l))
0.0ms
(/.f64 l (/.f64 t l))
0.0ms
(/.f64 2 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))))

series503.0ms (0.1%)

Counts
3 → 24
Calls

3 calls:

237.0ms
(/.f64 2 (/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l))))
195.0ms
(/.f64 (pow.f64 k 4) (/.f64 l (/.f64 t l)))
71.0ms
(/.f64 l (/.f64 t l))
Compiler

Compiled 528 to 528 computations (0% saved)

simplify394.0ms (0.1%)

Algorithm
egg-herbie
Counts
1024 → 1024
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0513941575

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.8b
(*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))))
0.3b
(/.f64 2 (*.f64 (*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))))) (pow.f64 (/.f64 (sqrt.f64 k) t) 2)))
0.2b
(pow.f64 (/.f64 (sqrt.f64 k) t) 2)
0.1b
(/.f64 (sqrt.f64 k) t)
1.3b
(*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))
4.8b
(*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))))
11.8b
(*.f64 (*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))))) (pow.f64 (/.f64 (sqrt.f64 k) t) 2))
17.2b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite96.0ms (0%)

Algorithm
rewrite-expression-head
Rules
282×add-exp-log_binary64_116
188×prod-exp_binary64_127
65×add-cbrt-cube_binary64_114
52×div-exp_binary64_129
46×times-frac_binary64_84
44×associate-*r*_binary64_18
39×add-sqr-sqrt_binary64_100
37×cbrt-unprod_binary64_111
34×pow-exp_binary64_146
32×unpow-prod-down_binary64_157
30×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
24×pow-to-exp_binary64_147
15×pow1_binary64_139
13×associate-*r/_binary64_20
12×associate-/l*_binary64_23
10×cube-prod_binary64_106
sqrt-prod_binary64_94
cbrt-undiv_binary64_112
associate-*l*_binary64_19 pow-prod-down_binary64_149
sqr-pow_binary64_50 associate-*l/_binary64_21 unswap-sqr_binary64_46
tan-quot_binary64_237 add-log-exp_binary64_117
cube-mult_binary64_108 *-commutative_binary64_9 div-inv_binary64_75 unpow3_binary64_144
frac-times_binary64_88
unpow2_binary64_143 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77
Counts
4 → 204
Calls

8 calls:

26.0ms
(*.f64 (*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))))) (pow.f64 (/.f64 (sqrt.f64 k) t) 2))
15.0ms
(*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))))
13.0ms
(*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))
13.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
0.0ms
(/.f64 (sqrt.f64 k) t)

series1.5s (0.2%)

Counts
4 → 36
Calls

4 calls:

572.0ms
(*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))))
513.0ms
(*.f64 (*.f64 k (*.f64 (tan.f64 k) (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l))))) (pow.f64 (/.f64 (sqrt.f64 k) t) 2))
253.0ms
(*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) (*.f64 l l)))
123.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 1698 to 1438 computations (15.3% saved)

simplify111.0ms (0%)

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
052295739

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(pow.f64 (/.f64 k t) 2)
0.2b
(pow.f64 (sqrt.f64 t) 3)
0.2b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
0.1b
(*.f64 (/.f64 t l) (sqrt.f64 t))
1.0b
(*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k))
1.4b
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t))))
1.5b
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
15.1b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

rewrite210.0ms (0%)

Algorithm
rewrite-expression-head
Rules
405×times-frac_binary64_84
196×add-sqr-sqrt_binary64_100
181×*-un-lft-identity_binary64_78
177×add-exp-log_binary64_116
169×add-cube-cbrt_binary64_113
150×associate-*l*_binary64_19
104×sqrt-prod_binary64_94 unpow-prod-down_binary64_157 cube-prod_binary64_106
73×add-cbrt-cube_binary64_114 prod-exp_binary64_127
72×div-exp_binary64_129
50×associate-*l/_binary64_21
39×div-inv_binary64_75 associate-/r/_binary64_24
29×cbrt-unprod_binary64_111
24×cbrt-undiv_binary64_112
18×sqr-pow_binary64_50 associate-/l*_binary64_23
17×cube-mult_binary64_108 unpow3_binary64_144
15×pow1_binary64_139
12×pow-exp_binary64_146 pow-to-exp_binary64_147
11×associate-*r*_binary64_18
add-log-exp_binary64_117 frac-times_binary64_88 cancel-sign-sub-inv_binary64_44
associate-/r*_binary64_22
pow-prod-down_binary64_149 unswap-sqr_binary64_46
tan-quot_binary64_237
distribute-lft-in_binary64_27 flip3--_binary64_82 distribute-rgt-in_binary64_28 flip--_binary64_53 associate-*r/_binary64_20
distribute-lft-out--_binary64_30 difference-of-squares_binary64_47
associate--l+_binary64_15 sub-neg_binary64_71
*-commutative_binary64_9 diff-log_binary64_170 distribute-lft-out_binary64_29 difference-of-sqr-1_binary64_48
frac-2neg_binary64_89 clear-num_binary64_77 sum-log_binary64_169
Counts
4 → 468
Calls

8 calls:

44.0ms
(*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k))
43.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
17.0ms
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t))))
12.0ms
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
0.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))

series962.0ms (0.1%)

Counts
4 → 33
Calls

4 calls:

511.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k)) (tan.f64 k)) (-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))
257.0ms
(*.f64 (/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t)))) (sin.f64 k))
103.0ms
(/.f64 (pow.f64 (sqrt.f64 t) 3) (/.f64 l (*.f64 (/.f64 t l) (sqrt.f64 t))))
89.0ms
(-.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)
Compiler

Compiled 1666 to 1413 computations (15.2% saved)

simplify170.0ms (0%)

Algorithm
egg-herbie
Counts
501 → 501
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0497012309
1497012309

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (sin.f64 k))
0.1b
(sqrt.f64 (sin.f64 k))
0.1b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))))
0.0b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))) (tan.f64 k))
0.3b
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))
3.0b
(/.f64 (pow.f64 t 3/2) l)
3.0b
(/.f64 (pow.f64 t 3/2) l)
6.0b
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

rewrite117.0ms (0%)

Algorithm
rewrite-expression-head
Rules
684×add-exp-log_binary64_116
476×prod-exp_binary64_127
156×div-exp_binary64_129
97×pow-exp_binary64_146
80×add-sqr-sqrt_binary64_100
78×times-frac_binary64_84
72×add-cbrt-cube_binary64_114
70×pow-to-exp_binary64_147
60×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
48×unpow-prod-down_binary64_157
44×cbrt-unprod_binary64_111
26×associate-*l*_binary64_19
24×associate-*r*_binary64_18
21×associate-*l/_binary64_21
14×sqr-pow_binary64_50 associate-/l*_binary64_23
cbrt-undiv_binary64_112
unswap-sqr_binary64_46
sqrt-prod_binary64_94
associate-/r*_binary64_22 pow1_binary64_139
frac-times_binary64_88
tan-quot_binary64_237 add-log-exp_binary64_117 div-inv_binary64_75
associate-*r/_binary64_20
*-commutative_binary64_9 frac-2neg_binary64_89 clear-num_binary64_77
unpow2_binary64_143 pow-prod-down_binary64_149
Counts
4 → 298
Calls

8 calls:

34.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
12.0ms
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))
5.0ms
(/.f64 (pow.f64 t 3/2) l)
5.0ms
(/.f64 (pow.f64 t 3/2) l)
0.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))) (tan.f64 k))

series908.0ms (0.1%)

Counts
4 → 31
Calls

4 calls:

509.0ms
(*.f64 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
222.0ms
(*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k)))
90.0ms
(/.f64 (pow.f64 t 3/2) l)
87.0ms
(/.f64 (pow.f64 t 3/2) l)
Compiler

Compiled 1825 to 1428 computations (21.8% saved)

simplify143.0ms (0%)

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
049617506
149617506

prune1.4min (11%)

Pruning

1030 alts after pruning (1026 fresh and 4 done)

PrunedKeptTotal
New13849282312
Fresh1898116
Picked000
Done145
Total140310302433
Error
8.2b
Counts
2433 → 1030
Compiler

Compiled 75993 to 42689 computations (43.8% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(pow.f64 (sin.f64 k) 2)
0.2b
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
0.1b
(*.f64 (*.f64 l l) (cos.f64 k))
0.1b
(*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))
0.4b
(pow.f64 (sin.f64 k) 2)
0.6b
(/.f64 2 (/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
1.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
22.3b
(/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))

rewrite65.0ms (0%)

Algorithm
rewrite-expression-head
Rules
204×add-exp-log_binary64_116
128×add-cbrt-cube_binary64_114
111×prod-exp_binary64_127
61×cbrt-unprod_binary64_111
55×div-exp_binary64_129
37×cbrt-undiv_binary64_112
25×add-sqr-sqrt_binary64_100
20×times-frac_binary64_84
19×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
pow-exp_binary64_146 pow-to-exp_binary64_147 associate-*r*_binary64_18
unpow-prod-down_binary64_157
div-inv_binary64_75 associate-/r*_binary64_22
pow1_binary64_139
add-log-exp_binary64_117 associate-/l*_binary64_23 unswap-sqr_binary64_46
associate-*l*_binary64_19 unpow2_binary64_143 sqr-pow_binary64_50 pow-unpow_binary64_155
frac-2neg_binary64_89 clear-num_binary64_77
*-commutative_binary64_9 pow-pow_binary64_150 associate-/r/_binary64_24
Counts
4 → 154
Calls

8 calls:

16.0ms
(/.f64 2 (/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
15.0ms
(/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))
6.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
3.0ms
(pow.f64 (sin.f64 k) 2)
0.0ms
(*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))))

series1.2s (0.2%)

Counts
4 → 31
Calls

4 calls:

605.0ms
(/.f64 2 (/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
494.0ms
(/.f64 (*.f64 k (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))
99.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
25.0ms
(pow.f64 (sin.f64 k) 2)
Compiler

Compiled 1158 to 988 computations (14.7% saved)

simplify143.0ms (0%)

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
049684631
149684631

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

8.5b
(*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))
7.9b
(/.f64 (*.f64 k k) l)
5.8b
(*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l)))
0.3b
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))))
0.3b
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))))
5.8b
(*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l)))
7.9b
(/.f64 (*.f64 k k) l)
8.5b
(*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))

rewrite72.0ms (0%)

Algorithm
rewrite-expression-head
Rules
176×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
83×cbrt-unprod_binary64_111 prod-exp_binary64_127
52×cbrt-undiv_binary64_112 div-exp_binary64_129
27×add-sqr-sqrt_binary64_100
22×times-frac_binary64_84
18×pow1_binary64_139
17×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
14×associate-*r*_binary64_18
pow-prod-down_binary64_149 associate-*r/_binary64_20
associate-*l*_binary64_19
add-log-exp_binary64_117 div-inv_binary64_75 associate-/l*_binary64_23 associate-/r*_binary64_22 unswap-sqr_binary64_46
frac-times_binary64_88 associate-*l/_binary64_21 associate-/r/_binary64_24
*-commutative_binary64_9 frac-2neg_binary64_89 clear-num_binary64_77
Counts
4 → 164
Calls

8 calls:

15.0ms
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))))
14.0ms
(*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l)))
12.0ms
(*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))
5.0ms
(/.f64 (*.f64 k k) l)
0.0ms
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))))

series685.0ms (0.1%)

Counts
4 → 33
Calls

4 calls:

249.0ms
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))))
203.0ms
(*.f64 (*.f64 k k) (*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l)))
169.0ms
(*.f64 (/.f64 (*.f64 k k) l) (/.f64 t l))
64.0ms
(/.f64 (*.f64 k k) l)
Compiler

Compiled 846 to 774 computations (8.5% saved)

simplify129.0ms (0%)

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 0 (91.0ms)

IterNodesCost
049552972
149552972

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(pow.f64 (sin.f64 k) 2)
0.3b
(*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))
0.2b
(*.f64 t (fabs.f64 (sin.f64 k)))
0.1b
(*.f64 (*.f64 l l) (cos.f64 k))
0.6b
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
1.1b
(sqrt.f64 (pow.f64 (sin.f64 k) 2))
6.9b
(*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2))))
22.3b
(/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))

rewrite89.0ms (0%)

Algorithm
rewrite-expression-head
Rules
264×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
147×cbrt-unprod_binary64_111 prod-exp_binary64_127
64×cbrt-undiv_binary64_112 div-exp_binary64_129
25×pow1_binary64_139
20×times-frac_binary64_84
18×add-sqr-sqrt_binary64_100
16×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
15×pow-prod-down_binary64_149
sqrt-prod_binary64_94
div-inv_binary64_75 associate-/r*_binary64_22
add-log-exp_binary64_117 unpow-prod-down_binary64_157 rem-sqrt-square_binary64_91 associate-/l*_binary64_23
unpow2_binary64_143 frac-2neg_binary64_89 sqr-pow_binary64_50 clear-num_binary64_77
*-commutative_binary64_9 associate-*l*_binary64_19 sqrt-pow1_binary64_96 associate-*r*_binary64_18 associate-/r/_binary64_24 pow1/2_binary64_158
Counts
4 → 182
Calls

8 calls:

23.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))
19.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
13.0ms
(*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2))))
3.0ms
(sqrt.f64 (pow.f64 (sin.f64 k) 2))
0.0ms
(*.f64 (*.f64 l l) (cos.f64 k))

series1.3s (0.2%)

Counts
4 → 32
Calls

4 calls:

573.0ms
(/.f64 2 (/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k))))
505.0ms
(/.f64 (*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2)))) (*.f64 (*.f64 l l) (cos.f64 k)))
176.0ms
(*.f64 (*.f64 k k) (*.f64 (*.f64 t (fabs.f64 (sin.f64 k))) (sqrt.f64 (pow.f64 (sin.f64 k) 2))))
15.0ms
(sqrt.f64 (pow.f64 (sin.f64 k) 2))
Compiler

Compiled 1377 to 1060 computations (23% saved)

simplify142.0ms (0%)

Algorithm
egg-herbie
Counts
214 → 214
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
050155739

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) (/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))))))
0.1b
(/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l)))
0.1b
(/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))))
0.1b
(*.f64 (/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) (/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))) (/.f64 (cbrt.f64 2) (/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l))))))
6.9b
(/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
12.0b
(cbrt.f64 (/.f64 t l))
12.0b
(cbrt.f64 (/.f64 t l))
12.0b
(cbrt.f64 (/.f64 t l))

rewrite40.0ms (0%)

Algorithm
rewrite-expression-head
Rules
52×times-frac_binary64_84
39×cbrt-prod_binary64_109
31×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
25×add-exp-log_binary64_116
21×add-cbrt-cube_binary64_114
13×associate-/r*_binary64_22
11×cbrt-div_binary64_110
10×cbrt-undiv_binary64_112 div-exp_binary64_129
associate-/r/_binary64_24
sqrt-prod_binary64_94 div-inv_binary64_75
cbrt-unprod_binary64_111 prod-exp_binary64_127
add-log-exp_binary64_117 pow1_binary64_139
pow1/3_binary64_160
frac-times_binary64_88 associate-*l/_binary64_21 associate-*r/_binary64_20
frac-2neg_binary64_89 associate-/l*_binary64_23 clear-num_binary64_77
Counts
4 → 116
Calls

8 calls:

15.0ms
(/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
3.0ms
(cbrt.f64 (/.f64 t l))
3.0ms
(cbrt.f64 (/.f64 t l))
3.0ms
(cbrt.f64 (/.f64 t l))
0.0ms
(*.f64 (/.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 2)) (/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))) (/.f64 (cbrt.f64 2) (/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l))))))

series1.5s (0.2%)

Counts
4 → 27
Calls

4 calls:

786.0ms
(/.f64 (*.f64 k k) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
224.0ms
(cbrt.f64 (/.f64 t l))
222.0ms
(cbrt.f64 (/.f64 t l))
218.0ms
(cbrt.f64 (/.f64 t l))
Compiler

Compiled 2334 to 1771 computations (24.1% saved)

simplify112.0ms (0%)

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
049652636
149652636

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b
(/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))))))
0.1b
(/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l)))
0.1b
(/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l))))
0.0b
(*.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l))))))
4.1b
(/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
12.0b
(cbrt.f64 (/.f64 t l))
12.0b
(cbrt.f64 (/.f64 t l))
12.0b
(cbrt.f64 (/.f64 t l))

rewrite71.0ms (0%)

Algorithm
rewrite-expression-head
Rules
223×times-frac_binary64_84
100×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
84×unpow-prod-down_binary64_157
75×sqrt-prod_binary64_94
47×cbrt-div_binary64_110
39×cbrt-prod_binary64_109
34×associate-/r/_binary64_24
28×add-exp-log_binary64_116
15×div-exp_binary64_129 div-inv_binary64_75
14×sqr-pow_binary64_50
13×associate-/r*_binary64_22
11×add-cbrt-cube_binary64_114 frac-times_binary64_88 associate-*l/_binary64_21 associate-*r/_binary64_20
10×associate-/l*_binary64_23
cbrt-undiv_binary64_112
add-log-exp_binary64_117 pow1_binary64_139
pow-exp_binary64_146 pow-to-exp_binary64_147 prod-exp_binary64_127 pow1/3_binary64_160
cbrt-unprod_binary64_111 frac-2neg_binary64_89 clear-num_binary64_77
Counts
4 → 242
Calls

8 calls:

19.0ms
(/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
3.0ms
(cbrt.f64 (/.f64 t l))
3.0ms
(cbrt.f64 (/.f64 t l))
3.0ms
(cbrt.f64 (/.f64 t l))
0.0ms
(*.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (cbrt.f64 (/.f64 t l))))))

series1.4s (0.2%)

Counts
4 → 27
Calls

4 calls:

711.0ms
(/.f64 (pow.f64 (sqrt.f64 k) 4) (/.f64 (sqrt.f64 l) (*.f64 (cbrt.f64 (/.f64 t l)) (cbrt.f64 (/.f64 t l)))))
232.0ms
(cbrt.f64 (/.f64 t l))
226.0ms
(cbrt.f64 (/.f64 t l))
222.0ms
(cbrt.f64 (/.f64 t l))
Compiler

Compiled 2284 to 1809 computations (20.8% saved)

simplify152.0ms (0%)

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
050067205

prune1.1min (8.9%)

Pruning

1261 alts after pruning (1255 fresh and 6 done)

PrunedKeptTotal
New7182901008
Fresh569651021
Picked000
Done369
Total77712612038
Error
6.9b
Counts
2038 → 1261
Compiler

Compiled 59337 to 35028 computations (41% saved)

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b
(pow.f64 (sin.f64 k) 2)
0.3b
(/.f64 2 (/.f64 k (*.f64 l l)))
0.2b
(/.f64 (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k))
0.2b
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))
0.4b
(pow.f64 (sin.f64 k) 2)
1.0b
(*.f64 t (pow.f64 (sin.f64 k) 2))
8.3b
(/.f64 k (*.f64 l l))
13.6b
(/.f64 (/.f64 2 (/.f64 k (*.f64 l l))) (/.f64 (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))

rewrite86.0ms (0%)

Algorithm
rewrite-expression-head
Rules
506×times-frac_binary64_84
183×add-sqr-sqrt_binary64_100
177×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
143×add-exp-log_binary64_116
91×add-cbrt-cube_binary64_114
76×div-exp_binary64_129
61×div-inv_binary64_75
50×cbrt-undiv_binary64_112
38×prod-exp_binary64_127
29×associate-/l*_binary64_23
18×cbrt-unprod_binary64_111
associate-/r/_binary64_24
associate-*r*_binary64_18 associate-/r*_binary64_22
unpow-prod-down_binary64_157
pow-exp_binary64_146 pow-to-exp_binary64_147
pow1_binary64_139
add-log-exp_binary64_117 unswap-sqr_binary64_46
associate-*l*_binary64_19 unpow2_binary64_143 sqr-pow_binary64_50 pow-unpow_binary64_155
frac-2neg_binary64_89 clear-num_binary64_77
*-commutative_binary64_9 pow-pow_binary64_150 associate-/l/_binary64_25
Counts
4 → 333
Calls

8 calls:

20.0ms
(/.f64 (/.f64 2 (/.f64 k (*.f64 l l))) (/.f64 (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
7.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
4.0ms
(/.f64 k (*.f64 l l))
3.0ms
(pow.f64 (sin.f64 k) 2)
0.0ms
(*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2)))

series782.0ms (0.1%)

Counts
4 → 27
Calls

4 calls:

586.0ms
(/.f64 (/.f64 2 (/.f64 k (*.f64 l l))) (/.f64 (*.f64 k (*.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)))
99.0ms
(*.f64 t (pow.f64 (sin.f64 k) 2))
73.0ms
(/.f64 k (*.f64 l l))
23.0ms
(pow.f64 (sin.f64 k) 2)
Compiler

Compiled 1013 to 848 computations (16.3% saved)

simplify148.0ms (0%)

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0537113577

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

8.5b
(*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))
5.8b
(*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l)))
0.3b
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))))
0.1b
(*.f64 k (/.f64 k l))
0.1b
(*.f64 k (/.f64 k l))
0.3b
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))))
5.8b
(*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l)))
8.5b
(*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))

rewrite75.0ms (0%)

Algorithm
rewrite-expression-head
Rules
176×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
94×cbrt-unprod_binary64_111 prod-exp_binary64_127
41×cbrt-undiv_binary64_112 div-exp_binary64_129
32×pow1_binary64_139
27×associate-*r*_binary64_18
26×add-sqr-sqrt_binary64_100
22×times-frac_binary64_84
21×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
19×pow-prod-down_binary64_149
16×associate-*r/_binary64_20
associate-*l*_binary64_19
add-log-exp_binary64_117
*-commutative_binary64_9 div-inv_binary64_75 frac-times_binary64_88 associate-/l*_binary64_23 associate-*l/_binary64_21 associate-/r/_binary64_24
unswap-sqr_binary64_46
frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77
Counts
4 → 168
Calls

8 calls:

16.0ms
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))))
15.0ms
(*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l)))
10.0ms
(*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))
7.0ms
(*.f64 k (/.f64 k l))
0.0ms
(*.f64 k (/.f64 k l))

series665.0ms (0.1%)

Counts
4 → 33
Calls

4 calls:

236.0ms
(/.f64 2 (*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))))
195.0ms
(*.f64 (*.f64 k k) (*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l)))
169.0ms
(*.f64 (*.f64 k (/.f64 k l)) (/.f64 t l))
64.0ms
(*.f64 k (/.f64 k l))
Compiler

Compiled 846 to 774 computations (8.5% saved)

simplify116.0ms (0%)

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
050062912

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b
(/.f64 1 (*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (sqrt.f64 l)))
0.1b
(*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (sqrt.f64 l))
0.1b
(/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l)))
0.1b
(/.f64 t (sqrt.f64 l))
0.6b
(cbrt.f64 l)
0.6b
(cbrt.f64 l)
4.7b
(*.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (sqrt.f64 l))) (/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l)))))
6.2b
(/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l))))

rewrite942.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
5572×times-frac_binary64_84
2492×add-sqr-sqrt_binary64_100
2404×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
1005×cbrt-prod_binary64_109
964×associate-*r*_binary64_18
832×unpow-prod-down_binary64_157
816×sqrt-prod_binary64_94
498×add-exp-log_binary64_116
282×sqr-pow_binary64_50
258×div-exp_binary64_129
190×prod-exp_binary64_127
137×associate-/r*_binary64_22
108×div-inv_binary64_75
75×add-cbrt-cube_binary64_114
42×cbrt-undiv_binary64_112
33×pow-exp_binary64_146 pow-to-exp_binary64_147
30×1-exp_binary64_122 rec-exp_binary64_128
28×cbrt-unprod_binary64_111
22×unswap-sqr_binary64_46
17×associate-/r/_binary64_24
associate-*l*_binary64_19 associate-/l*_binary64_23
pow1_binary64_139
add-log-exp_binary64_117
pow1/3_binary64_160
*-commutative_binary64_9 frac-2neg_binary64_89 frac-times_binary64_88 associate-*l/_binary64_21 pow-prod-down_binary64_149 associate-*r/_binary64_20 clear-num_binary64_77
Counts
4 → 1000
Calls

8 calls:

323.0ms
(*.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (sqrt.f64 l))) (/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l)))))
48.0ms
(/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l))))
1.0ms
(cbrt.f64 l)
1.0ms
(cbrt.f64 l)
0.0ms
(/.f64 t (sqrt.f64 l))

series853.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

485.0ms
(/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l))))
209.0ms
(*.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (sqrt.f64 l))) (/.f64 (pow.f64 k 4) (/.f64 (cbrt.f64 l) (/.f64 t (sqrt.f64 l)))))
82.0ms
(cbrt.f64 l)
77.0ms
(cbrt.f64 l)
Compiler

Compiled 1045 to 894 computations (14.4% saved)

simplify420.0ms (0.1%)

Algorithm
egg-herbie
Counts
1024 → 1024
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
0526143603

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b
(/.f64 (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l)))
0.3b
(pow.f64 (sqrt.f64 k) 4)
0.3b
(pow.f64 (sqrt.f64 k) 4)
0.2b
(/.f64 (cbrt.f64 t) l)
2.6b
(*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))
3.3b
(*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
3.9b
(*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))))
4.1b
(/.f64 (pow.f64 (sqrt.f64 k) 4) l)

rewrite136.0ms (0%)

Algorithm
rewrite-expression-head
Rules
546×add-exp-log_binary64_116
251×prod-exp_binary64_127
235×div-exp_binary64_129
135×add-cbrt-cube_binary64_114
123×add-sqr-sqrt_binary64_100
112×times-frac_binary64_84
69×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
65×cbrt-unprod_binary64_111
59×cbrt-undiv_binary64_112
56×unpow-prod-down_binary64_157
54×associate-*l*_binary64_19
41×pow-exp_binary64_146 pow-to-exp_binary64_147
36×associate-*r*_binary64_18
34×sqrt-prod_binary64_94
20×unswap-sqr_binary64_46
14×cbrt-prod_binary64_109
12×sqr-pow_binary64_50
10×associate-/l*_binary64_23
pow1_binary64_139
div-inv_binary64_75
add-log-exp_binary64_117
*-commutative_binary64_9 frac-times_binary64_88 associate-*l/_binary64_21 associate-/r*_binary64_22 associate-/r/_binary64_24 associate-*r/_binary64_20
pow-prod-down_binary64_149
frac-2neg_binary64_89 clear-num_binary64_77
Counts
4 → 323
Calls

8 calls:

33.0ms
(*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))
31.0ms
(*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))))
11.0ms
(*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
6.0ms
(/.f64 (pow.f64 (sqrt.f64 k) 4) l)
0.0ms
(/.f64 (cbrt.f64 t) l)

series975.0ms (0.1%)

Counts
4 → 30
Calls

4 calls:

363.0ms
(*.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))) (/.f64 (sqrt.f64 2) (*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))))
325.0ms
(*.f64 (/.f64 (pow.f64 (sqrt.f64 k) 4) l) (/.f64 (cbrt.f64 t) l))
212.0ms
(*.f64 (pow.f64 (sqrt.f64 k) 4) (*.f64 (cbrt.f64 t) (cbrt.f64 t)))
75.0ms
(/.f64 (pow.f64 (sqrt.f64 k) 4) l)
Compiler

Compiled 1497 to 1311 computations (12.4% saved)

simplify153.0ms (0%)

Algorithm
egg-herbie
Counts
353 → 353
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049627186
149627186

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))
0.1b
(/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))
0.1b
(/.f64 2 (*.f64 (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))))
0.1b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))))
3.7b
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
6.7b
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
15.9b
(sqrt.f64 (pow.f64 k 4))
15.9b
(sqrt.f64 (pow.f64 k 4))

rewrite999.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
7792×times-frac_binary64_84
3383×add-sqr-sqrt_binary64_100
3379×add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
3069×sqrt-prod_binary64_94
2508×cbrt-prod_binary64_109
794×unpow-prod-down_binary64_157
266×sqr-pow_binary64_50
260×associate-/r*_binary64_22
101×div-inv_binary64_75
42×add-exp-log_binary64_116
29×add-cbrt-cube_binary64_114
24×associate-/r/_binary64_24
23×cbrt-undiv_binary64_112 div-exp_binary64_129
20×associate-/l*_binary64_23
rem-sqrt-square_binary64_91
cbrt-unprod_binary64_111 prod-exp_binary64_127
add-log-exp_binary64_117 pow1_binary64_139
sqrt-pow1_binary64_96 frac-2neg_binary64_89 clear-num_binary64_77 pow1/2_binary64_158
Counts
4 → 1000
Calls

8 calls:

104.0ms
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
19.0ms
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
2.0ms
(sqrt.f64 (pow.f64 k 4))
2.0ms
(sqrt.f64 (pow.f64 k 4))
0.0ms
(*.f64 (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))) (/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l)))))

series884.0ms (0.1%)

Counts
4 → 24
Calls

4 calls:

432.0ms
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) (/.f64 (sqrt.f64 t) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))))
405.0ms
(/.f64 (sqrt.f64 (pow.f64 k 4)) (/.f64 (cbrt.f64 l) (/.f64 (sqrt.f64 t) (cbrt.f64 l))))
24.0ms
(sqrt.f64 (pow.f64 k 4))
23.0ms
(sqrt.f64 (pow.f64 k 4))
Compiler

Compiled 1724 to 1246 computations (27.7% saved)

simplify534.0ms (0.1%)

Algorithm
egg-herbie
Counts
1024 → 1024
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0498853742
1498853742

prune7.6min (61.3%)

Pruning

2163 alts after pruning (2158 fresh and 5 done)

PrunedKeptTotal
New194610162962
Fresh10811421250
Picked000
Done6511
Total206021634223
Error
0.7b
Counts
4223 → 2163
Compiler

Compiled 77504 to 28020 computations (63.8% saved)

simplify5.1s (0.7%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
015281227452

regimes1.4min (11.4%)

Compiler

Compiled 854236 to 562086 computations (34.2% saved)

bsearch656.0ms (0.1%)

Steps
ItersRangePoint
8
1.8573869520408583e-119
1.0596424367138579e-116
1.0482771448169259e-116
5
-4.511473464098064e-19
-2.2214859579877656e-19
-2.806566223980714e-19
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.6s (0.2%)

Compiler

Compiled 11741 to 9029 computations (23.1% saved)

bsearch201.0ms (0%)

Steps
ItersRangePoint
10
5.719607497666477e-22
4.744796720233424e-11
1.4179595266281353e-18
5
-4.511473464098064e-19
-2.2214859579877656e-19
-4.252058645845645e-19
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.7s (0.2%)

Compiler

Compiled 11209 to 8609 computations (23.2% saved)

bsearch232.0ms (0%)

Steps
ItersRangePoint
10
5.719607497666477e-22
4.744796720233424e-11
9.786874362112557e-12
8
-1.0912635177783057e-35
-1.7294003558782798e-40
-1.0725378665625126e-35
Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.1s (0.2%)

Compiler

Compiled 11114 to 8534 computations (23.2% saved)

bsearch0.0ms (0%)

regimes34.0ms (0%)

Compiler

Compiled 105 to 114 computations (-8.6% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch9.0ms (0%)

Compiler

Compiled 215 to 133 computations (38.1% saved)

simplify5.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074241
174241

end0.0ms (0%)

sample14.7s (2%)

Algorithm
intervals
Results
3.4s1103×body4096invalid
2.2s1075×body2048invalid
2.2s3888×body1024valid
1.0s465×body4096valid
973.0ms982×body2048valid
552.0ms1379×body512valid
371.0ms683×body1024invalid
188.0ms477×body512invalid
148.0ms1073×body128invalid
119.0ms833×body128valid
118.0ms453×body256valid
82.0ms308×body256invalid
Compiler

Compiled 139663 to 91686 computations (34.4% saved)

Profiling

Loading profile data...