Details

Time bar (total: 16.3s)

analyze3.5s (21.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
1.2%98.6%0.2%11
1.4%98.4%0.2%12
10.8%88.9%0.2%13
10.8%88.9%0.2%14
Compiler

Compiled 34 to 24 computations (29.4% saved)

sample208.0ms (1.3%)

Algorithm
intervals
Results
136.0ms117×body1024valid
33.0ms49×body512valid
14.0ms75×body128valid
7.0ms15×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify145.0ms (0.9%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
046355
146355

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.2b
Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite22.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1805
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 pow1_binary64_1844
associate-*l*_binary64_1724 add-log-exp_binary64_1822 associate-*r*_binary64_1723
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sin-mult_binary64_1938 *-commutative_binary64_1714 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
flip3--_binary64_1787 cancel-sign-sub-inv_binary64_1749 asin-acos_binary64_1963 diff-log_binary64_1875 flip--_binary64_1758 sub-neg_binary64_1776
Counts
4 → 58
Calls

4 calls:

5.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
5.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series391.0ms (2.4%)

Counts
4 → 12
Calls

4 calls:

191.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
135.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
43.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
22.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify109.0ms (0.7%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (85.0ms)

IterNodesCost
048682133
148682133

prune127.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New591170
Fresh000
Picked101
Done000
Total601171
Error
0.1b
Counts
71 → 11
Compiler

Compiled 3409 to 653 computations (80.8% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.7b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_1805
add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
pow1_binary64_1844
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-log-exp_binary64_1822
log-prod_binary64_1869
log-pow_binary64_1872
associate-*l*_binary64_1724 exp-prod_binary64_1835 associate-*r*_binary64_1723
exp-sum_binary64_1829 cancel-sign-sub-inv_binary64_1749 sub-neg_binary64_1776
flip3--_binary64_1787 exp-diff_binary64_1831 cbrt-unprod_binary64_1816 prod-exp_binary64_1832 asin-acos_binary64_1963 diff-log_binary64_1875 sin-mult_binary64_1938 *-commutative_binary64_1714 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751 flip--_binary64_1758 rem-log-exp_binary64_1824 log-div_binary64_1870
Counts
4 → 57
Calls

4 calls:

6.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
4.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
4.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series680.0ms (4.2%)

Counts
4 → 12
Calls

4 calls:

337.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
179.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
141.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
22.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify120.0ms (0.7%)

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
050602817

prune118.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New67269
Fresh01010
Picked101
Done000
Total681280
Error
0.1b
Counts
80 → 12
Compiler

Compiled 3689 to 704 computations (80.9% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
0.7b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
3.8b
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite32.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64_1805
11×cancel-sign-sub-inv_binary64_1749 *-un-lft-identity_binary64_1783
10×sin-sum_binary64_1916 associate--r+_binary64_1719
add-cube-cbrt_binary64_1818
add-log-exp_binary64_1822
log-prod_binary64_1869 distribute-lft-in_binary64_1732 distribute-rgt-in_binary64_1733 sub-neg_binary64_1776 pow1_binary64_1844
add-cbrt-cube_binary64_1819 log-pow_binary64_1872 add-exp-log_binary64_1821 acos-asin_binary64_1964
associate--r-_binary64_1722 exp-prod_binary64_1835
flip3--_binary64_1787 difference-of-squares_binary64_1752 exp-sum_binary64_1829 diff-log_binary64_1875 flip--_binary64_1758
exp-diff_binary64_1831 distribute-lft-out--_binary64_1735 times-frac_binary64_1789 rem-log-exp_binary64_1824 log-div_binary64_1870
Counts
4 → 66
Calls

4 calls:

9.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
6.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
4.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
1.0ms
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series735.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

421.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
238.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
48.0ms
(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
27.0ms
(acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify116.0ms (0.7%)

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (81.0ms)

IterNodesCost
049063230
149063230

prune144.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New77178
Fresh2911
Picked011
Done000
Total791190
Error
0.1b
Counts
90 → 11
Compiler

Compiled 4452 to 1068 computations (76% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.6b
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
16.6b
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod_binary64_1814
10×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
unpow-prod-down_binary64_1862 add-log-exp_binary64_1822 cube-prod_binary64_1811
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 pow1_binary64_1844
cube-div_binary64_1812
flip3--_binary64_1787 pow-unpow_binary64_1860 acos-asin_binary64_1964 cos-diff_binary64_1920 flip--_binary64_1758
sqr-pow_binary64_1755 cube-mult_binary64_1813 unpow3_binary64_1849 cbrt-div_binary64_1815 associate--r+_binary64_1719
rem-cbrt-cube_binary64_1807 rem-cube-cbrt_binary64_1806 distribute-lft-in_binary64_1732 cancel-sign-sub-inv_binary64_1749 diff-log_binary64_1875 cos-acos_binary64_1949 distribute-rgt-in_binary64_1733 pow-pow_binary64_1855 pow1/3_binary64_1865 pow-to-exp_binary64_1852 sub-neg_binary64_1776 pow-exp_binary64_1851
Counts
4 → 71
Calls

4 calls:

5.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
4.0ms
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
4.0ms
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
2.0ms
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series840.0ms (5.1%)

Counts
4 → 12
Calls

4 calls:

378.0ms
(pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3)
184.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
170.0ms
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))) 3))
107.0ms
(cos.f64 (acos.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

simplify103.0ms (0.6%)

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
049923993
149923993

prune125.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New81283
Fresh189
Picked101
Done011
Total831194
Error
0.1b
Counts
94 → 11
Compiler

Compiled 3981 to 572 computations (85.6% saved)

regimes654.0ms (4%)

Accuracy

Total 0.1b remaining (62.1%)

Threshold costs 0.1b (62.1%)

Compiler

Compiled 10064 to 5873 computations (41.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05755
15755

end0.0ms (0%)

sample8.0s (48.7%)

Algorithm
intervals
Results
4.6s3992×body1024valid
978.0ms1351×body512valid
678.0ms2097×body128valid
246.0ms552×body256valid
21.0msbody2048valid
Compiler

Compiled 1485 to 871 computations (41.3% saved)

Profiling

Loading profile data...