Details

Time bar (total: 25.1s)

analyze4.1s (16.1%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04909605
14909605
055
155
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
Symmetry
Compiler

Compiled 34 to 24 computations (29.4% saved)

sample242.0ms (1%)

Algorithm
1×intervals
Results
168.0ms136×body1024valid
31.0ms44×body512valid
12.0ms53×body128valid
10.0ms23×body256valid
Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify43.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
046355
146355

prune4.0ms (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)

localize32.0ms (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)))))))

rewrite123.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
12×add-sqr-sqrt_binary64_2146
8×pow1_binary64_2185 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 add-cube-cbrt_binary64_2159 *-un-lft-identity_binary64_2124
6×add-log-exp_binary64_2163 associate-*l*_binary64_2065 associate-*r*_binary64_2064
2×sin-mult_binary64_2279 pow-prod-down_binary64_2195 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 unswap-sqr_binary64_2092 *-commutative_binary64_2055
1×diff-log_binary64_2216 flip3--_binary64_2128 sub-neg_binary64_2117 flip--_binary64_2099 cancel-sign-sub-inv_binary64_2090 asin-acos_binary64_2304
Counts
4 → 58
Calls

4 calls:

6.0ms
(*.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))))
Compiler

Compiled 2653 to 371 computations (86% saved)

series997.0ms (4%)

Error
0.2b
Counts
4 → 42
Calls

4 calls:

420.0ms
(-.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)))))))
353.0ms
(*.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))))))
107.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
74.0ms
(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)

simplify108.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
048643000
148643000

prune158.0ms (0.6%)

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)

localize41.0ms (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)

rewrite306.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
23×add-sqr-sqrt_binary64_2146
13×*-un-lft-identity_binary64_2124
11×add-cube-cbrt_binary64_2159
10×pow1_binary64_2185 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
9×sqr-pow_binary64_2096
8×difference-of-squares_binary64_2093 cancel-sign-sub-inv_binary64_2090
7×unpow-prod-down_binary64_2203 cube-prod_binary64_2152
6×pow-unpow_binary64_2201 add-log-exp_binary64_2163
3×pow-pow_binary64_2196 pow-exp_binary64_2192 unpow3_binary64_2190 cube-mult_binary64_2154 rem-cube-cbrt_binary64_2147 associate-*l*_binary64_2065 associate-*r*_binary64_2064
2×pow-prod-down_binary64_2195 pow-to-exp_binary64_2193 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 associate-*r/_binary64_2066
1×sin-mult_binary64_2279 cube-div_binary64_2153 diff-log_binary64_2216 flip3--_binary64_2128 difference-cubes_binary64_2126 sub-neg_binary64_2117 flip--_binary64_2099 distribute-lft-out--_binary64_2076 unswap-sqr_binary64_2092 distribute-rgt-in_binary64_2074 distribute-lft-in_binary64_2073 flip3-+_binary64_2127 flip-+_binary64_2098 *-commutative_binary64_2055
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 (10.3%)

Error
0.1b
Counts
4 → 39
Calls

4 calls:

987.0ms
(-.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))
751.0ms
(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)
719.0ms
(*.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)))))))))
52.0ms
(pow.f64 (cos.f64 delta) 3)
Compiler

Compiled 9455 to 2937 computations (68.9% saved)

simplify104.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
050445954

prune336.0ms (1.3%)

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)

localize31.0ms (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 (0.5%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
13×add-sqr-sqrt_binary64_2146
12×*-un-lft-identity_binary64_2124
9×pow1_binary64_2185 add-cube-cbrt_binary64_2159
7×add-log-exp_binary64_2163 log-pow_binary64_2213
6×log-prod_binary64_2210 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160 cancel-sign-sub-inv_binary64_2090
3×associate--r+_binary64_2060 associate-*l*_binary64_2065 associate-*r*_binary64_2064
2×exp-to-pow_binary64_2186 exp-prod_binary64_2176 distribute-lft-out--_binary64_2076
1×rem-log-exp_binary64_2165 diff-log_binary64_2216 flip3--_binary64_2128 sub-neg_binary64_2117 flip--_binary64_2099 difference-of-squares_binary64_2093 asin-acos_binary64_2304 sin-mult_binary64_2279 pow-prod-down_binary64_2195 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 unswap-sqr_binary64_2092 *-commutative_binary64_2055
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)

series2.3s (9.2%)

Error
0.1b
Counts
4 → 42
Calls

4 calls:

934.0ms
(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)))))))))
892.0ms
(-.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))))))))))
374.0ms
(*.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)))))))
75.0ms
(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)

simplify107.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049293874
149293874

prune142.0ms (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))))))))))

rewrite114.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
10×add-sqr-sqrt_binary64_2146
8×add-cube-cbrt_binary64_2159 *-un-lft-identity_binary64_2124
7×pow1_binary64_2185
6×add-log-exp_binary64_2163 add-exp-log_binary64_2162 add-cbrt-cube_binary64_2160
5×log-prod_binary64_2210
4×log-pow_binary64_2213
3×exp-prod_binary64_2176 associate-*l*_binary64_2065 associate-*r*_binary64_2064
2×sub-neg_binary64_2117 exp-sum_binary64_2170 cancel-sign-sub-inv_binary64_2090
1×exp-diff_binary64_2172 log-div_binary64_2211 rem-log-exp_binary64_2165 diff-log_binary64_2216 flip3--_binary64_2128 flip--_binary64_2099 asin-acos_binary64_2304 sin-mult_binary64_2279 pow-prod-down_binary64_2195 prod-exp_binary64_2173 cbrt-unprod_binary64_2157 unswap-sqr_binary64_2092 *-commutative_binary64_2055
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)))))))
5.0ms
(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)

series1.9s (7.6%)

Error
0.1b
Counts
4 → 45
Calls

4 calls:

1.0s
(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))))))))))
416.0ms
(-.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))))))))
355.0ms
(*.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)))))))
83.0ms
(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)

simplify86.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
052113948

prune125.0ms (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)

regimes1.5s (6.1%)

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%)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05959
15959
Removed

()

end0.0ms (0%)

sample9.4s (37.6%)

Algorithm
1×intervals
Results
4.8s3937×body1024valid
1.0s1293×body512valid
483.0ms2201×body128valid
266.0ms557×body256valid
35.0ms12×body2048valid
Compiler

Compiled 3678 to 1939 computations (47.3% saved)

Profiling

Loading profile data...