Details

Time bar (total: 2.9min)

analyze8.6s (5%)

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)

sample646.0ms (0.4%)

Algorithm
intervals
Results
322.0ms104×body1024valid
166.0ms61×body512valid
50.0ms72×body128valid
22.0ms19×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify402.0ms (0.2%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (151.0ms)

IterNodesCost
046355
146355

prune21.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 0.1b

Counts
2 → 1
Compiler

Compiled 66 to 46 computations (30.3% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b
(-.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)))))))

rewrite59.0ms (0%)

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:

15.0ms
(-.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)))))))
12.0ms
(*.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))))))
10.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.1s (0.7%)

Counts
4 → 12
Calls

4 calls:

697.0ms
(-.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)))))))
230.0ms
(*.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))))))
137.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
60.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify346.0ms (0.2%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (265.0ms)

IterNodesCost
048682133
148682133

prune1.4s (0.8%)

Pruning

33 alts after pruning (32 fresh and 1 done)

PrunedKeptTotal
New383270
Fresh000
Picked011
Done000
Total383371

Merged error: 0.0b

Counts
71 → 33
Compiler

Compiled 4398 to 1193 computations (72.9% saved)

localize70.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))))
0.3b
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b
(+.f64 (cos.f64 delta) (neg.f64 (*.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))))))))

rewrite119.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64_1805
10×*-un-lft-identity_binary64_1783
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-cube-cbrt_binary64_1818 add-log-exp_binary64_1822 pow1_binary64_1844
associate-*l*_binary64_1724 associate-*r*_binary64_1723
cbrt-unprod_binary64_1816 prod-exp_binary64_1832 sin-mult_binary64_1938 *-commutative_binary64_1714 sum-log_binary64_1874 pow-prod-down_binary64_1854 unswap-sqr_binary64_1751
unsub-neg_binary64_1777 +-commutative_binary64_1713 distribute-lft-out_binary64_1734 flip-+_binary64_1757 asin-acos_binary64_1963 neg-sub0_binary64_1778 flip3-+_binary64_1786 neg-log_binary64_1876 associate-+r-_binary64_1717
Counts
4 → 61
Calls

4 calls:

36.0ms
(+.f64 (cos.f64 delta) (neg.f64 (*.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))))))))
30.0ms
(*.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))))))
19.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
3.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.2s (0.7%)

Counts
4 → 12
Calls

4 calls:

491.0ms
(+.f64 (cos.f64 delta) (neg.f64 (*.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))))))))
415.0ms
(*.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))))))
149.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
93.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify375.0ms (0.2%)

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (255.0ms)

IterNodesCost
049962144
149962144

prune1.5s (0.9%)

Pruning

52 alts after pruning (50 fresh and 2 done)

PrunedKeptTotal
New502373
Fresh42731
Picked011
Done011
Total5452106

Merged error: 0.0b

Counts
106 → 52
Compiler

Compiled 5460 to 1702 computations (68.8% saved)

localize58.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))))
0.3b
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b
(-.f64 (cos.f64 delta) (pow.f64 (*.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))

rewrite57.0ms (0%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64_1805
11×*-un-lft-identity_binary64_1783
add-cube-cbrt_binary64_1818
add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 pow1_binary64_1844
associate-*l*_binary64_1724 add-log-exp_binary64_1822 associate-*r*_binary64_1723
cancel-sign-sub-inv_binary64_1749
difference-of-squares_binary64_1752 sqr-pow_binary64_1755 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 unpow-prod-down_binary64_1862 distribute-lft-out--_binary64_1735 asin-acos_binary64_1963 diff-log_binary64_1875 flip--_binary64_1758 sub-neg_binary64_1776
Counts
4 → 65
Calls

4 calls:

11.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
11.0ms
(*.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))))))
10.0ms
(-.f64 (cos.f64 delta) (pow.f64 (*.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))
2.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.5s (0.9%)

Counts
4 → 12
Calls

4 calls:

711.0ms
(-.f64 (cos.f64 delta) (pow.f64 (*.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))
509.0ms
(*.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))))))
176.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
125.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify221.0ms (0.1%)

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (131.0ms)

IterNodesCost
050002437

prune1.7s (1%)

Pruning

72 alts after pruning (69 fresh and 3 done)

PrunedKeptTotal
New522577
Fresh54449
Picked011
Done022
Total5772129

Merged error: 0.0b

Counts
129 → 72
Compiler

Compiled 6741 to 2390 computations (64.5% saved)

localize64.0ms (0%)

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
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b
(*.f64 (*.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)))))) (*.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)))))))
0.4b
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.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)))))) (*.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)))))))) (+.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))))))))

rewrite93.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
43×pow1_binary64_1844
18×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821
17×pow-prod-down_binary64_1854
13×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
12×times-frac_binary64_1789
10×sin-mult_binary64_1938
cbrt-unprod_binary64_1816 prod-exp_binary64_1832
associate-/l/_binary64_1730
cos-mult_binary64_1937
difference-of-squares_binary64_1752 associate-/l*_binary64_1728 pow-prod-up_binary64_1853 pow-sqr_binary64_1756 add-log-exp_binary64_1822
associate-*r/_binary64_1725 associate-/r*_binary64_1727 associate-*l/_binary64_1726 frac-sub_binary64_1792
associate-/r/_binary64_1729 sub-div_binary64_1790 pow-plus_binary64_1846 asin-acos_binary64_1963 frac-times_binary64_1793
flip3--_binary64_1787 div-sub_binary64_1788 swap-sqr_binary64_1750 flip-+_binary64_1757 div-inv_binary64_1780 associate-*l*_binary64_1724 cbrt-undiv_binary64_1817 *-commutative_binary64_1714 frac-2neg_binary64_1794 div-exp_binary64_1834 flip3-+_binary64_1786 clear-num_binary64_1782 flip--_binary64_1758 pow2_binary64_1864 associate-*r*_binary64_1723
Counts
4 → 94
Calls

4 calls:

23.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.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)))))) (*.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)))))))) (+.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))))))))
19.0ms
(*.f64 (*.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)))))) (*.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)))))))
2.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
2.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series3.2s (1.8%)

Counts
4 → 12
Calls

4 calls:

2.2s
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.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)))))) (*.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)))))))) (+.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))))))))
869.0ms
(*.f64 (*.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)))))) (*.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)))))))
43.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
39.0ms
(asin.f64 (+.f64 (*.f64 (cos.f64 delta) (sin.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify177.0ms (0.1%)

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
050885707

prune4.9s (2.8%)

Pruning

112 alts after pruning (108 fresh and 4 done)

PrunedKeptTotal
New6640106
Fresh06868
Picked011
Done033
Total66112178

Merged error: 0.0b

Counts
178 → 112
Compiler

Compiled 8416 to 841 computations (90% saved)

regimes15.4s (8.9%)

Compiler

Compiled 83823 to 40880 computations (51.2% saved)

bsearch1.4min (50.1%)

simplify74.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
061133
161133

end0.0ms (0%)

sample43.2s (24.9%)

Algorithm
intervals
Results
14.7s3981×body1024valid
2.9s1362×body512valid
1.2s2115×body128valid
727.0ms527×body256valid
126.0ms15×body2048valid
Compiler

Compiled 12683 to 6165 computations (51.4% saved)

Pareto

0.02320676276652417

Profiling

Loading profile data...