Details

Time bar (total: 24.5s)

analyze3.7s (15.2%)

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)

sample236.0ms (1%)

Algorithm
intervals
Results
164.0ms136×body1024valid
30.0ms44×body512valid
10.0ms53×body128valid
10.0ms23×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify130.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (38.0ms)

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 (0.1%)

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))))
0.6b
(-.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)))))))

rewrite124.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
12×add-sqr-sqrt_binary64_3851
pow1_binary64_3890 add-exp-log_binary64_3867 add-cbrt-cube_binary64_3865 add-cube-cbrt_binary64_3864 *-un-lft-identity_binary64_3829
add-log-exp_binary64_3868 associate-*l*_binary64_3770 associate-*r*_binary64_3769
sin-mult_binary64_3984 pow-prod-down_binary64_3900 prod-exp_binary64_3878 cbrt-unprod_binary64_3862 unswap-sqr_binary64_3797 *-commutative_binary64_3760
diff-log_binary64_3921 flip3--_binary64_3833 sub-neg_binary64_3822 flip--_binary64_3804 cancel-sign-sub-inv_binary64_3795 asin-acos_binary64_4009
Counts
4 → 58
Calls

4 calls:

9.0ms
(*.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))
5.0ms
(-.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))))
Compiler

Compiled 2653 to 371 computations (86% saved)

series1.0s (4.1%)

Error
0.2b
Counts
4 → 42
Calls

4 calls:

422.0ms
(-.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)))))))
346.0ms
(*.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))))))
112.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
76.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
Compiler

Compiled 4057 to 1937 computations (52.3% saved)

simplify106.0ms (0.4%)

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
048643000
148643000

prune159.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New937100
Fresh000
Picked101
Done000
Total947101
Error
0.1b
Counts
101 → 7
Compiler

Compiled 4282 to 652 computations (84.8% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
0.4b
(pow.f64 (cos.f64 delta) 3)
0.4b
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
0.5b
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)

rewrite310.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
23×add-sqr-sqrt_binary64_3851
13×*-un-lft-identity_binary64_3829
11×add-cube-cbrt_binary64_3864
10×pow1_binary64_3890 add-exp-log_binary64_3867 add-cbrt-cube_binary64_3865
sqr-pow_binary64_3801
difference-of-squares_binary64_3798 cancel-sign-sub-inv_binary64_3795
unpow-prod-down_binary64_3908 cube-prod_binary64_3857
pow-unpow_binary64_3906 add-log-exp_binary64_3868
pow-pow_binary64_3901 pow-exp_binary64_3897 unpow3_binary64_3895 cube-mult_binary64_3859 rem-cube-cbrt_binary64_3852 associate-*l*_binary64_3770 associate-*r*_binary64_3769
pow-prod-down_binary64_3900 pow-to-exp_binary64_3898 prod-exp_binary64_3878 cbrt-unprod_binary64_3862 associate-*r/_binary64_3771
sin-mult_binary64_3984 cube-div_binary64_3858 diff-log_binary64_3921 flip3--_binary64_3833 difference-cubes_binary64_3831 sub-neg_binary64_3822 flip--_binary64_3804 distribute-lft-out--_binary64_3781 unswap-sqr_binary64_3797 distribute-rgt-in_binary64_3779 distribute-lft-in_binary64_3778 flip3-+_binary64_3832 flip-+_binary64_3803 *-commutative_binary64_3760
Counts
4 → 97
Calls

4 calls:

11.0ms
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
7.0ms
(*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
6.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
3.0ms
(pow.f64 (cos.f64 delta) 3)
Compiler

Compiled 10254 to 1261 computations (87.7% saved)

series2.6s (10.4%)

Error
0.1b
Counts
4 → 39
Calls

4 calls:

957.0ms
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3))
763.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
695.0ms
(*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
59.0ms
(pow.f64 (cos.f64 delta) 3)
Compiler

Compiled 9455 to 2937 computations (68.9% saved)

simplify102.0ms (0.4%)

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050445954

prune344.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1342136
Fresh156
Picked011
Done000
Total1358143
Error
0.1b
Counts
143 → 8
Compiler

Compiled 13365 to 1730 computations (87.1% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.6b
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
4.0b
(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))

rewrite136.0ms (0.6%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
13×add-sqr-sqrt_binary64_3851
12×*-un-lft-identity_binary64_3829
pow1_binary64_3890 add-cube-cbrt_binary64_3864
add-log-exp_binary64_3868 log-pow_binary64_3918
log-prod_binary64_3915 add-exp-log_binary64_3867 add-cbrt-cube_binary64_3865 cancel-sign-sub-inv_binary64_3795
associate--r+_binary64_3765 associate-*l*_binary64_3770 associate-*r*_binary64_3769
exp-to-pow_binary64_3891 exp-prod_binary64_3881 distribute-lft-out--_binary64_3781
rem-log-exp_binary64_3870 diff-log_binary64_3921 flip3--_binary64_3833 sub-neg_binary64_3822 flip--_binary64_3804 difference-of-squares_binary64_3798 asin-acos_binary64_4009 sin-mult_binary64_3984 pow-prod-down_binary64_3900 prod-exp_binary64_3878 cbrt-unprod_binary64_3862 unswap-sqr_binary64_3797 *-commutative_binary64_3760
Counts
4 → 64
Calls

4 calls:

7.0ms
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
6.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
3.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 3270 to 427 computations (86.9% saved)

series2.2s (9.1%)

Error
0.1b
Counts
4 → 42
Calls

4 calls:

890.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
878.0ms
(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
333.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
85.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 4363 to 2087 computations (52.2% saved)

simplify108.0ms (0.4%)

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049293874
149293874

prune145.0ms (0.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1060106
Fresh066
Picked011
Done011
Total1068114
Error
0.1b
Counts
114 → 8
Compiler

Compiled 4702 to 642 computations (86.3% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.6b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
0.9b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))

rewrite113.0ms (0.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
10×add-sqr-sqrt_binary64_3851
add-cube-cbrt_binary64_3864 *-un-lft-identity_binary64_3829
pow1_binary64_3890
add-log-exp_binary64_3868 add-exp-log_binary64_3867 add-cbrt-cube_binary64_3865
log-prod_binary64_3915
log-pow_binary64_3918
exp-prod_binary64_3881 associate-*l*_binary64_3770 associate-*r*_binary64_3769
sub-neg_binary64_3822 exp-sum_binary64_3875 cancel-sign-sub-inv_binary64_3795
exp-diff_binary64_3877 log-div_binary64_3916 rem-log-exp_binary64_3870 diff-log_binary64_3921 flip3--_binary64_3833 flip--_binary64_3804 asin-acos_binary64_4009 sin-mult_binary64_3984 pow-prod-down_binary64_3900 prod-exp_binary64_3878 cbrt-unprod_binary64_3862 unswap-sqr_binary64_3797 *-commutative_binary64_3760
Counts
4 → 57
Calls

4 calls:

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

Compiled 2929 to 414 computations (85.9% saved)

series1.8s (7.5%)

Error
0.1b
Counts
4 → 45
Calls

4 calls:

947.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
411.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
360.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))))
81.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 4515 to 2216 computations (50.9% saved)

simplify85.0ms (0.3%)

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
052113948

prune129.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1002102
Fresh055
Picked101
Done022
Total1019110
Error
0.1b
Counts
110 → 9
Compiler

Compiled 4221 to 469 computations (88.9% saved)

regimes1.6s (6.4%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Compiler

Compiled 25401 to 13335 computations (47.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05959
15959

end0.0ms (0%)

sample9.2s (37.6%)

Algorithm
intervals
Results
4.6s3937×body1024valid
975.0ms1293×body512valid
473.0ms2201×body128valid
258.0ms557×body256valid
35.0ms12×body2048valid
Compiler

Compiled 3678 to 1939 computations (47.3% saved)

Profiling

Loading profile data...