Details

Time bar (total: 31.6s)

analyze4.9s (15.5%)

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 39 to 24 computations (38.5% saved)

sample448.0ms (1.4%)

Algorithm
intervals
Results
217.0ms127×body1024valid
38.0ms40×body512valid
26.0ms69×body128valid
11.0ms20×body256valid
Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify54.0ms (0.2%)

Algorithm
egg-herbie
Rules
571×fma-def_binary64
244×fma-neg_binary64
103×unsub-neg_binary64
90×associate-*l*_binary64
88×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02353
14053
26653
38553
49953
513353
617353
721753
828153
930553
1036253
1140753
1246853
1360453
1472853
1583653
1694353
1789153
1889353
1989953
2090453
2184153

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
Compiler

Compiled 144 to 76 computations (47.2% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series140.0ms (0.4%)

Counts
4 → 132
Calls

4 calls:

68.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
53.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
9.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
8.0ms
(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite18.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 72
Calls

4 calls:

4.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
4.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
3.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
0.0ms
(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

simplify185.0ms (0.6%)

Algorithm
egg-herbie
Rules
447×fma-neg_binary64
376×distribute-rgt-neg-in_binary64
325×distribute-lft-neg-in_binary64
257×associate-*r*_binary64
241×neg-mul-1_binary64
Counts
204 → 185
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02626113
16965704
222275493
347965493
449895493
549245493

prune339.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1805185
Fresh000
Picked101
Done000
Total1815186
Error
0.0b
Counts
186 → 5
Alt Table
StatusErrorProgram
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
11.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
Compiler

Compiled 8334 to 1722 computations (79.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))
0.8b
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))

series178.0ms (0.6%)

Counts
4 → 144
Calls

4 calls:

61.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))
59.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))
51.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
6.0ms
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

rewrite23.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
log-prod_binary64
pow1_binary64
Counts
4 → 74
Calls

4 calls:

11.0ms
(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))
4.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
3.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))
0.0ms
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

simplify385.0ms (1.2%)

Algorithm
egg-herbie
Rules
804×cancel-sign-sub-inv_binary64
573×sub-neg_binary64
378×fma-neg_binary64
298×distribute-rgt-neg-in_binary64
253×distribute-lft-neg-in_binary64
Counts
218 → 134
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02318078
15497440
217227088
340957088
448667088
549197088

prune296.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh044
Picked011
Done000
Total1345139
Error
0.0b
Counts
139 → 5
Alt Table
StatusErrorProgram
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
11.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
Compiler

Compiled 6699 to 1430 computations (78.7% saved)

localize37.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
0.4b
(*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.4b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))

series219.0ms (0.7%)

Counts
2 → 72
Calls

2 calls:

143.0ms
(*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
76.0ms
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))

rewrite46.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
33×flip--_binary64
33×flip3--_binary64
32×frac-times_binary64
26×cbrt-div_binary64
16×associate-*l/_binary64
Counts
2 → 83
Calls

2 calls:

9.0ms
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
7.0ms
(*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

simplify399.0ms (1.3%)

Algorithm
egg-herbie
Rules
596×associate-*r*_binary64
490×associate-*l*_binary64
354×fma-neg_binary64
321×fma-def_binary64
310×*-commutative_binary64
Counts
155 → 167
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
040016901
1109914210
2443513004
3497613004
4499413004
5496813004

prune1.2s (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New5171518
Fresh123
Picked011
Done011
Total5185523
Error
0.0b
Counts
523 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cbrt.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
11.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
Compiler

Compiled 50015 to 5824 computations (88.4% saved)

localize357.0ms (1.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.4b
(cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.5b
(cbrt.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))

series7.0s (22%)

Counts
2 → 72
Calls

2 calls:

4.0s
(cbrt.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
2.9s
(cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

rewrite12.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×cbrt-div_binary64
flip--_binary64
flip3--_binary64
cbrt-prod_binary64
frac-times_binary64
Counts
2 → 34
Calls

2 calls:

5.0ms
(cbrt.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
2.0ms
(cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))

simplify210.0ms (0.7%)

Algorithm
egg-herbie
Rules
595×fma-def_binary64
379×associate-+r+_binary64
292×*-commutative_binary64
279×+-commutative_binary64
233×associate-+l+_binary64
Counts
106 → 111
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
060811805
1203611050
2478611050
3502911050

prune983.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New3730373
Fresh022
Picked011
Done022
Total3735378
Error
0.0b
Counts
378 → 5
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cbrt.f64 (*.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.f64 (sin.f64 theta)) (sin.f64 delta))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
11.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
Compiler

Compiled 43267 to 8611 computations (80.1% saved)

regimes3.4s (10.7%)

Accuracy

Total 0.1b remaining (60.3%)

Threshold costs 0.1b (60.3%)

Counts
259 → 1
Compiler

Compiled 101519 to 49707 computations (51% saved)

simplify4.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02253
13353
24353
34953
45353
55453
65453

end1.0ms (0%)

Compiler

Compiled 37 to 22 computations (40.5% saved)

sample10.8s (34.3%)

Algorithm
intervals
Results
7.6s3966×body1024valid
1.3s1336×body512valid
655.0ms524×body256valid
601.0ms2165×body128valid
40.0msbody2048valid
Compiler

Compiled 360 to 169 computations (53.1% saved)

Profiling

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