Details

Time bar (total: 26.8s)

analyze4.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0.1%14
Compiler

Compiled 9 to 5 computations (44.4% saved)

sample11.0ms (0%)

Algorithm
intervals
Results
6.0ms256×body128valid
Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify98.0ms (0.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0139
1139

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
28.7b
Counts
2 → 2
Compiler

Compiled 6 to 4 computations (33.3% saved)

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

27.5b
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
0.0b
(+.f64 (*.f64 x x) (*.f64 x x))
0.0b
(+.f64 (*.f64 x x) (*.f64 x x))
27.5b
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
sqrt-prod_binary64_94
add-sqr-sqrt_binary64_100 add-log-exp_binary64_117
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78 pow1_binary64_139
add-cbrt-cube_binary64_114 flip-+_binary64_52 distribute-rgt-out_binary64_31 add-exp-log_binary64_116 sqrt-div_binary64_95 count-2_binary64_26 distribute-lft-out_binary64_29 flip3-+_binary64_81
+-commutative_binary64_8 sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 pow1/2_binary64_158 sum-log_binary64_169
Counts
2 → 32
Calls

4 calls:

4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
4.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
0.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
0.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))

series57.0ms (0.2%)

Counts
2 → 6
Calls

2 calls:

30.0ms
(sqrt.f64 (+.f64 (*.f64 x x) (*.f64 x x)))
27.0ms
(+.f64 (*.f64 x x) (*.f64 x x))
Compiler

Compiled 64 to 64 computations (0% saved)

simplify97.0ms (0.4%)

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
04788334
14788334

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite8.0ms (0%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64_139
sqrt-pow1_binary64_96 sqrt-div_binary64_95 associate-*r/_binary64_20
add-cbrt-cube_binary64_114 sqrt-prod_binary64_94 add-sqr-sqrt_binary64_100 add-log-exp_binary64_117 flip-+_binary64_52 add-cube-cbrt_binary64_113 add-exp-log_binary64_116 pow-prod-down_binary64_149 pow1/2_binary64_158 *-un-lft-identity_binary64_78 flip3-+_binary64_81
Counts
1 → 13
Calls

2 calls:

7.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
0.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 28 to 28 computations (0% saved)

simplify72.0ms (0.3%)

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
05009140

prune140.0ms (0.5%)

Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New302454
Fresh000
Picked000
Done112
Total312556
Error
0.1b
Counts
56 → 25
Compiler

Compiled 537 to 258 computations (52% saved)

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.5b
(*.f64 (sqrt.f64 2) (fabs.f64 x))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_100
associate-*l*_binary64_19
sqrt-prod_binary64_94 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-cbrt-cube_binary64_114 associate-*r*_binary64_18 add-exp-log_binary64_116 pow1_binary64_139
unswap-sqr_binary64_46
*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
0.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 (sqrt.f64 2) (fabs.f64 x))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify73.0ms (0.3%)

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04863270
14863270

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_100
associate-*r*_binary64_18
sqrt-prod_binary64_94 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-cbrt-cube_binary64_114 associate-*l*_binary64_19 add-exp-log_binary64_116 pow1_binary64_139
unswap-sqr_binary64_46
*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

30.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 24 to 24 computations (0% saved)

simplify44.0ms (0.2%)

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05010211

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.1b
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×sqrt-prod_binary64_94
17×add-sqr-sqrt_binary64_100
15×associate-*r*_binary64_18
11×*-un-lft-identity_binary64_78
add-cube-cbrt_binary64_113
associate-*l*_binary64_19
pow1_binary64_139
unswap-sqr_binary64_46
add-cbrt-cube_binary64_114 distribute-rgt-out_binary64_31 add-exp-log_binary64_116 pow-prod-down_binary64_149 distribute-lft-out_binary64_29
sqrt-pow1_binary64_96 sqrt-div_binary64_95 associate-*r/_binary64_20 pow1/2_binary64_158
*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 flip-+_binary64_52 sqrt-unprod_binary64_98 distribute-lft1-in_binary64_33 count-2_binary64_26 distribute-rgt1-in_binary64_34 flip3-+_binary64_81
Counts
1 → 41
Calls

2 calls:

11.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

30.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify86.0ms (0.3%)

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 0 (75.0ms)

IterNodesCost
04778527
14778527

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))
5.7b
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
0.0b
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.0b
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.7b
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite21.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×pow1_binary64_139
log-prod_binary64_164 log-pow_binary64_167
exp-prod_binary64_130
add-sqr-sqrt_binary64_100 sqrt-pow1_binary64_96 add-cube-cbrt_binary64_113 sqrt-div_binary64_95 associate-*r/_binary64_20 *-un-lft-identity_binary64_78
exp-sum_binary64_124 add-exp-log_binary64_116 log-div_binary64_165
add-cbrt-cube_binary64_114 sqrt-prod_binary64_94 add-log-exp_binary64_117 flip-+_binary64_52 pow-prod-down_binary64_149 pow1/2_binary64_158 flip3-+_binary64_81
exp-diff_binary64_126
rem-exp-log_binary64_118 rem-log-exp_binary64_119
Counts
3 → 52
Calls

6 calls:

7.0ms
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
0.0ms
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.0ms
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))

series190.0ms (0.7%)

Counts
3 → 9
Calls

3 calls:

89.0ms
(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
72.0ms
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
28.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 140 to 140 computations (0% saved)

simplify104.0ms (0.4%)

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
04819654
14819654

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

2.2b
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
0.0b
(exp.f64 (*.f64 x x))
0.0b
(pow.f64 (exp.f64 (*.f64 x x)) 2)
0.0b
(pow.f64 (exp.f64 (*.f64 x x)) 2)
0.0b
(exp.f64 (*.f64 x x))
2.2b
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log-prod_binary64_164
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-log-exp_binary64_117 unpow-prod-down_binary64_157
add-exp-log_binary64_116 pow1_binary64_139
add-cbrt-cube_binary64_114 pow-pow_binary64_150 rem-log-exp_binary64_119 pow-unpow_binary64_155
pow-exp_binary64_146 pow-to-exp_binary64_147 unpow2_binary64_143 sqr-pow_binary64_50 exp-to-pow_binary64_140 exp-prod_binary64_130
rem-exp-log_binary64_118 log-pow_binary64_167
Counts
3 → 49
Calls

6 calls:

3.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)
2.0ms
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
2.0ms
(exp.f64 (*.f64 x x))
0.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)
0.0ms
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))

series139.0ms (0.5%)

Counts
3 → 15
Calls

3 calls:

94.0ms
(log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))
29.0ms
(pow.f64 (exp.f64 (*.f64 x x)) 2)
16.0ms
(exp.f64 (*.f64 x x))
Compiler

Compiled 206 to 202 computations (1.9% saved)

simplify88.0ms (0.3%)

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
04924580
14924580

prune1.3s (5%)

Pruning

103 alts after pruning (99 fresh and 4 done)

PrunedKeptTotal
New13683219
Fresh31619
Picked000
Done246
Total141103244
Error
0b
Counts
244 → 103
Compiler

Compiled 2820 to 1604 computations (43.1% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
0.2b
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
16×add-exp-log_binary64_116 pow1_binary64_139
12×add-sqr-sqrt_binary64_100
10×associate-*r*_binary64_18
add-cbrt-cube_binary64_114 cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
cbrt-prod_binary64_109
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
sqrt-prod_binary64_94 associate-*l*_binary64_19
unswap-sqr_binary64_46
*-commutative_binary64_9 add-log-exp_binary64_117
Counts
2 → 48
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
6.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
0.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
0.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))

series121.0ms (0.5%)

Counts
2 → 6
Calls

2 calls:

90.0ms
(*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2)))
31.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (fabs.f64 x) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 120 to 120 computations (0% saved)

simplify73.0ms (0.3%)

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
05097624

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_100
associate-*r*_binary64_18
sqrt-prod_binary64_94 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-cbrt-cube_binary64_114 associate-*l*_binary64_19 add-exp-log_binary64_116 pow1_binary64_139
unswap-sqr_binary64_46
*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series30.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

30.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 30 to 30 computations (0% saved)

simplify44.0ms (0.2%)

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
05010211

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

28.5b
(log.f64 (*.f64 x (+.f64 x x)))
6.2b
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x x))))
6.2b
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x x))))
28.5b
(log.f64 (*.f64 x (+.f64 x x)))

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64_139
add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 add-exp-log_binary64_116 pow-unpow_binary64_155 *-un-lft-identity_binary64_78
pow-pow_binary64_150 log-div_binary64_165 associate-*r/_binary64_20 log-pow_binary64_167
unpow-prod-down_binary64_157 exp-prod_binary64_130
add-cbrt-cube_binary64_114 pow-sub_binary64_154 add-log-exp_binary64_117 flip-+_binary64_52 log-prod_binary64_164 rem-log-exp_binary64_119 pow-prod-down_binary64_149 flip3-+_binary64_81
pow-exp_binary64_146 pow-to-exp_binary64_147 prod-exp_binary64_127 sqr-pow_binary64_50 unpow-prod-up_binary64_156
Counts
2 → 39
Calls

4 calls:

7.0ms
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x x))))
5.0ms
(log.f64 (*.f64 x (+.f64 x x)))
0.0ms
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x x))))
0.0ms
(log.f64 (*.f64 x (+.f64 x x)))

series194.0ms (0.7%)

Counts
2 → 6
Calls

2 calls:

133.0ms
(pow.f64 (exp.f64 1/2) (log.f64 (*.f64 x (+.f64 x x))))
60.0ms
(log.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 144 to 144 computations (0% saved)

simplify76.0ms (0.3%)

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
04897515
14897515

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))
0.0b
(+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4))))
0.0b
(*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))
0.0b
(+.f64 (*.f64 x x) (pow.f64 x 4))
0.0b
(*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))
0.1b
(sqrt.f64 (log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))
0.1b
(*.f64 (pow.f64 x 6) 4/3)
29.4b
(log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4))))))

rewrite28.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64_100
13×*-un-lft-identity_binary64_78
12×add-exp-log_binary64_116
11×add-cube-cbrt_binary64_113
10×associate-*l*_binary64_19
pow1_binary64_139
add-cbrt-cube_binary64_114
associate-*r*_binary64_18
sqrt-prod_binary64_94 add-log-exp_binary64_117 prod-exp_binary64_127 unpow-prod-down_binary64_157 log-prod_binary64_164 unswap-sqr_binary64_46
*-commutative_binary64_9 cbrt-unprod_binary64_111 flip-+_binary64_52 sqr-pow_binary64_50 log-div_binary64_165 associate-*r/_binary64_20 log-pow_binary64_167 flip3-+_binary64_81
distribute-lft-in_binary64_27 pow-exp_binary64_146 pow-to-exp_binary64_147 sqrt-pow1_binary64_96 rem-sqrt-square_binary64_91 distribute-rgt-in_binary64_28 rem-log-exp_binary64_119 pow-prod-down_binary64_149 distribute-lft-out_binary64_29 pow1/2_binary64_158
Counts
4 → 76
Calls

8 calls:

8.0ms
(*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))
6.0ms
(log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4))))))
5.0ms
(*.f64 (pow.f64 x 6) 4/3)
2.0ms
(sqrt.f64 (log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))
0.0ms
(+.f64 (*.f64 x x) (pow.f64 x 4))

series326.0ms (1.2%)

Counts
4 → 18
Calls

4 calls:

112.0ms
(sqrt.f64 (log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))))))
88.0ms
(log.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 6) 4/3) (*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4))))))
83.0ms
(*.f64 2 (+.f64 (*.f64 x x) (pow.f64 x 4)))
43.0ms
(*.f64 (pow.f64 x 6) 4/3)
Compiler

Compiled 532 to 485 computations (8.8% saved)

simplify95.0ms (0.4%)

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
049061831
149061831

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

0.3b
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.2b
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))))

rewrite43.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
66×pow1_binary64_139
42×sqrt-prod_binary64_94
41×pow-prod-down_binary64_149
37×add-sqr-sqrt_binary64_100
20×sqrt-pow1_binary64_96 pow1/2_binary64_158
19×add-cbrt-cube_binary64_114 associate-*r*_binary64_18 add-exp-log_binary64_116
13×associate-*l*_binary64_19 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
12×unswap-sqr_binary64_46
10×cbrt-unprod_binary64_111 prod-exp_binary64_127
pow-prod-up_binary64_148
sqrt-unprod_binary64_98
pow-sqr_binary64_51
*-commutative_binary64_9 add-log-exp_binary64_117
pow-plus_binary64_141
pow2_binary64_159 swap-sqr_binary64_45 rem-square-sqrt_binary64_90
Counts
3 → 114
Calls

6 calls:

17.0ms
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))))
9.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
8.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
0.0ms
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))))

series73.0ms (0.3%)

Counts
3 → 9
Calls

3 calls:

27.0ms
(*.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))) (*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2))))
23.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
23.0ms
(*.f64 (sqrt.f64 x) (sqrt.f64 (sqrt.f64 2)))
Compiler

Compiled 251 to 235 computations (6.4% saved)

simplify79.0ms (0.3%)

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049271246
149271246

prune4.4s (16.3%)

Pruning

195 alts after pruning (186 fresh and 9 done)

PrunedKeptTotal
New24398341
Fresh68894
Picked000
Done099
Total249195444
Error
0b
Counts
444 → 195
Compiler

Compiled 6823 to 5127 computations (24.9% saved)

localize14.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.4b
(*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.3b
(*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
0.2b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.2b
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.3b
(*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))

rewrite58.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
49×add-exp-log_binary64_116 pow1_binary64_139
33×cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
24×add-cbrt-cube_binary64_114
15×cbrt-prod_binary64_109
14×associate-*r*_binary64_18
add-sqr-sqrt_binary64_100
add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
associate-*l*_binary64_19
sqrt-prod_binary64_94 *-commutative_binary64_9 add-log-exp_binary64_117
unswap-sqr_binary64_46
Counts
3 → 83
Calls

6 calls:

22.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
15.0ms
(*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
10.0ms
(*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
0.0ms
(*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))

series250.0ms (0.9%)

Counts
3 → 9
Calls

3 calls:

118.0ms
(*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
96.0ms
(*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
36.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (*.f64 (fabs.f64 x) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))))
Compiler

Compiled 252 to 252 computations (0% saved)

simplify90.0ms (0.3%)

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
048951187
148951187

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.5b
(*.f64 x (sqrt.f64 2))
0.5b
(*.f64 x (sqrt.f64 2))

rewrite6.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64_100
associate-*r*_binary64_18
sqrt-prod_binary64_94 add-cube-cbrt_binary64_113 *-un-lft-identity_binary64_78
add-cbrt-cube_binary64_114 associate-*l*_binary64_19 add-exp-log_binary64_116 pow1_binary64_139
unswap-sqr_binary64_46
*-commutative_binary64_9 add-log-exp_binary64_117 cbrt-unprod_binary64_111 prod-exp_binary64_127 pow-prod-down_binary64_149
Counts
1 → 22
Calls

2 calls:

5.0ms
(*.f64 x (sqrt.f64 2))
0.0ms
(*.f64 x (sqrt.f64 2))

series29.0ms (0.1%)

Counts
1 → 3
Calls

1 calls:

29.0ms
(*.f64 x (sqrt.f64 2))
Compiler

Compiled 36 to 36 computations (0% saved)

simplify45.0ms (0.2%)

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05010211

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

2.7b
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x))))
1.0b
(log.f64 (sqrt.f64 2))
0.1b
(+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x)))
0.1b
(+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x)))
1.0b
(log.f64 (sqrt.f64 2))
2.7b
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x))))

rewrite21.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
22×log-prod_binary64_164
19×*-un-lft-identity_binary64_78
13×pow1_binary64_139
11×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 log-pow_binary64_167
10×associate-+r+_binary64_10
distribute-lft-out_binary64_29
exp-prod_binary64_130
sqrt-prod_binary64_94 associate-+l+_binary64_11
add-log-exp_binary64_117 add-exp-log_binary64_116
add-cbrt-cube_binary64_114 distribute-lft-neg-in_binary64_35 distribute-rgt-neg-in_binary64_36
rem-exp-log_binary64_118 sum-log_binary64_169
+-commutative_binary64_8 sqrt-pow1_binary64_96 exp-sum_binary64_124 flip-+_binary64_52 neg-mul-1_binary64_74 rem-log-exp_binary64_119 pow1/2_binary64_158 flip3-+_binary64_81
Counts
3 → 65
Calls

6 calls:

8.0ms
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x))))
6.0ms
(+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x)))
2.0ms
(log.f64 (sqrt.f64 2))
0.0ms
(+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x)))
0.0ms
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x))))

series244.0ms (0.9%)

Counts
3 → 6
Calls

3 calls:

124.0ms
(+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x)))
120.0ms
(exp.f64 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 (neg.f64 x))))
0.0ms
(log.f64 (sqrt.f64 2))
Compiler

Compiled 124 to 124 computations (0% saved)

simplify70.0ms (0.3%)

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04988755
14988755

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

17.7b
(sqrt.f64 (*.f64 2 (pow.f64 x 4)))
5.7b
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x))))
0.6b
(-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x)))
0.0b
(*.f64 2 (pow.f64 x 4))
0.6b
(-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x)))
5.7b
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x))))
17.7b
(sqrt.f64 (*.f64 2 (pow.f64 x 4)))
28.5b
(log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))))

rewrite33.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity_binary64_78
17×pow1_binary64_139
15×add-sqr-sqrt_binary64_100 log-prod_binary64_164
13×log-pow_binary64_167
11×add-cube-cbrt_binary64_113
exp-sum_binary64_124
distribute-lft-out--_binary64_30 associate--l+_binary64_15 exp-prod_binary64_130 cancel-sign-sub-inv_binary64_44
add-log-exp_binary64_117 add-exp-log_binary64_116
add-cbrt-cube_binary64_114 sqrt-prod_binary64_94
associate--r+_binary64_14
sqrt-pow1_binary64_96 diff-log_binary64_170 rem-exp-log_binary64_118 difference-of-squares_binary64_47 pow1/2_binary64_158 sub-neg_binary64_71
flip3--_binary64_82 flip--_binary64_53 exp-diff_binary64_126 rem-log-exp_binary64_119
Counts
4 → 79
Calls

8 calls:

12.0ms
(-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x)))
8.0ms
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x))))
4.0ms
(log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))))
3.0ms
(sqrt.f64 (*.f64 2 (pow.f64 x 4)))
0.0ms
(*.f64 2 (pow.f64 x 4))

series395.0ms (1.5%)

Counts
4 → 12
Calls

4 calls:

150.0ms
(exp.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x))))
137.0ms
(-.f64 (log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4)))) (log.f64 (fabs.f64 x)))
73.0ms
(log.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 4))))
34.0ms
(sqrt.f64 (*.f64 2 (pow.f64 x 4)))
Compiler

Compiled 330 to 306 computations (7.3% saved)

simplify97.0ms (0.4%)

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
048951422
148951422

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b
(sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
0.1b
(sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
0.0b
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.0b
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
1.2b
(exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
3.1b
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))
27.5b
(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite38.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
23×sqrt-prod_binary64_94 pow1_binary64_139
20×exp-prod_binary64_130
12×log-pow_binary64_167
11×add-sqr-sqrt_binary64_100 add-cube-cbrt_binary64_113 pow-pow_binary64_150 *-un-lft-identity_binary64_78
10×sqrt-pow1_binary64_96 pow-unpow_binary64_155
add-log-exp_binary64_117 pow-prod-down_binary64_149 pow1/2_binary64_158
add-cbrt-cube_binary64_114 add-exp-log_binary64_116 sqrt-div_binary64_95 associate-*r/_binary64_20
unpow-prod-down_binary64_157
flip-+_binary64_52 flip3-+_binary64_81
pow-exp_binary64_146 pow-to-exp_binary64_147 rem-exp-log_binary64_118 sqr-pow_binary64_50
Counts
4 → 78
Calls

8 calls:

15.0ms
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
6.0ms
(exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
5.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
0.0ms
(log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))

series475.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

312.0ms
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
104.0ms
(exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))))
29.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
29.0ms
(sqrt.f64 (*.f64 x (+.f64 x x)))
Compiler

Compiled 422 to 360 computations (14.7% saved)

simplify101.0ms (0.4%)

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
048901654
148901654

prune6.7s (24.9%)

Pruning

308 alts after pruning (294 fresh and 14 done)

PrunedKeptTotal
New245124369
Fresh11170181
Picked000
Done01414
Total256308564
Error
0b
Counts
564 → 308
Compiler

Compiled 4390 to 2559 computations (41.7% saved)

simplify234.0ms (0.9%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0238514592
1238514592

regimes2.6s (9.9%)

Compiler

Compiled 28020 to 21175 computations (24.4% saved)

bsearch0.0ms (0%)

regimes1.6s (5.9%)

Compiler

Compiled 14111 to 11336 computations (19.7% saved)

bsearch0.0ms (0%)

regimes1.5s (5.7%)

Compiler

Compiled 11337 to 9162 computations (19.2% saved)

bsearch0.0ms (0%)

regimes1.1s (4.1%)

Compiler

Compiled 9064 to 7478 computations (17.5% saved)

bsearch0.0ms (0%)

regimes639.0ms (2.4%)

Compiler

Compiled 4484 to 3715 computations (17.1% saved)

bsearch0.0ms (0%)

regimes630.0ms (2.4%)

Compiler

Compiled 4444 to 3675 computations (17.3% saved)

bsearch0.0ms (0%)

regimes153.0ms (0.6%)

Compiler

Compiled 424 to 342 computations (19.3% saved)

bsearch19.0ms (0.1%)

Steps
ItersRangePoint
11
-2.545738461740407e-290
1.9658603115733064e-305
-1.43388241055396e-310
Compiler

Compiled 1 to 1 computations (0% saved)

regimes14.0ms (0.1%)

Compiler

Compiled 13 to 17 computations (-30.8% saved)

bsearch13.0ms (0%)

Steps
ItersRangePoint
10
-2.1355396828630583e-202
-6.130160872703383e-218
-3.489520080313717e-206
Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch10.0ms (0%)

Compiler

Compiled 96 to 94 computations (2.1% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
073157
173157

end0.0ms (0%)

sample1.1s (4.2%)

Algorithm
intervals
Results
193.0ms8000×body128valid
Compiler

Compiled 7070 to 5379 computations (23.9% saved)

Profiling

Loading profile data...