Details

Time bar (total: 17.0s)

analyze3.9s (22.8%)

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)

sample211.0ms (1.2%)

Algorithm
intervals
Results
136.0ms118×body1024valid
35.0ms51×body512valid
14.0ms72×body128valid
7.0ms15×body256valid
Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify48.0ms (0.3%)

Algorithm
egg-herbie
Rules
103×unsub-neg_binary64
90×associate-*l*_binary64
88×distribute-rgt-in_binary64
82×cancel-sign-sub-inv_binary64
80×associate-*r*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02355
13955
26155
37255
48355
510755
613455
716455
821755
921655
1024055
1127555
1231755
1343155
1448655
1553455
1656755
1752155
1852355
1952555
2052655
2146355

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
Alt Table
StatusErrorProgram
0.2b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
Compiler

Compiled 114 to 69 computations (39.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.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))))))
0.3b
(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)))))))

rewrite159.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
11×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 associate-*r*_binary64
pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
Counts
4 → 57
Calls

4 calls:

7.0ms
(*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
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))))))
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 2499 to 410 computations (83.6% saved)

series259.0ms (1.5%)

Error
0.2b
Counts
4 → 42
Calls

4 calls:

85.0ms
(-.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)))))))
71.0ms
(*.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))))))
55.0ms
(*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))
29.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
Compiler

Compiled 3651 to 2007 computations (45% saved)

simplify168.0ms (1%)

Algorithm
egg-herbie
Rules
475×distribute-rgt-in_binary64
347×distribute-lft-in_binary64
338×*-commutative_binary64
306×cancel-sign-sub-inv_binary64
295×distribute-rgt-neg-in_binary64
Counts
99 → 70
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01523297
13433090
29693017
316663017
428643008
545383008
649163008

prune120.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New64670
Fresh000
Picked101
Done000
Total65671
Error
0.1b
Counts
71 → 6
Alt Table
StatusErrorProgram
13.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (sqrt.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))))))))) (sqrt.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))))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.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))))))) (*.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))))))))) (+.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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.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)))))))) 3))))
0.2b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
33.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sqrt.f64 (sin.f64 phi1)) (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (sqrt.f64 (sin.f64 phi1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
Compiler

Compiled 2734 to 681 computations (75.1% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(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)))))
0.4b
(*.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))))))) (*.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
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.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))))))) (*.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)))))))))

rewrite282.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
43×pow1_binary64
17×pow-prod-down_binary64
16×add-exp-log_binary64 add-cbrt-cube_binary64
10×sin-mult_binary64
prod-exp_binary64 cbrt-unprod_binary64
Counts
4 → 72
Calls

4 calls:

11.0ms
(*.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))))))) (*.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))))))))
9.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.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))))))) (*.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)))))
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 6171 to 464 computations (92.5% saved)

series326.0ms (1.9%)

Error
0.1b
Counts
4 → 40
Calls

4 calls:

131.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.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))))))) (*.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)))))))))
104.0ms
(*.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))))))) (*.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))))))))
30.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
29.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 6513 to 2414 computations (62.9% saved)

simplify222.0ms (1.3%)

Algorithm
egg-herbie
Rules
500×distribute-rgt-neg-in_binary64
480×distribute-lft-neg-in_binary64
464×cancel-sign-sub-inv_binary64
322×*-commutative_binary64
171×exp-prod_binary64
Counts
112 → 71
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01354868
13274565
210124460
325164460
446104343
549514343
649194343

prune154.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New67471
Fresh055
Picked101
Done000
Total68977
Error
0.1b
Counts
77 → 9
Alt Table
StatusErrorProgram
13.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (sqrt.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))))))))) (sqrt.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))))))))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (log.f64 (exp.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (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))))))) 2)))) (+.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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.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)))))))) 3))))
0.2b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
33.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sqrt.f64 (sin.f64 phi1)) (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (sqrt.f64 (sin.f64 phi1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (cbrt.f64 (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))))))) 2)) (cbrt.f64 (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))))))) 2))) (cbrt.f64 (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))))))) 2)))) (+.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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (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))))))) 2)) 3)) (+.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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
Compiler

Compiled 3755 to 888 computations (76.4% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(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)))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))

rewrite224.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
add-log-exp_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
asin-acos_binary64
diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64 sqr-cos-a_binary64 associate--l+_binary64
Counts
4 → 37
Calls

4 calls:

8.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (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)))))
1.0ms
(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 3661 to 472 computations (87.1% saved)

series244.0ms (1.4%)

Error
0.1b
Counts
4 → 39
Calls

4 calls:

132.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
34.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
34.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
33.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 6394 to 2417 computations (62.2% saved)

simplify197.0ms (1.2%)

Algorithm
egg-herbie
Rules
688×unswap-sqr_binary64
469×associate-*l*_binary64
428×cancel-sign-sub-inv_binary64
405×associate-*r*_binary64
311×distribute-rgt-neg-in_binary64
Counts
76 → 17
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0793565
11962806
24882763
320322728
445492722
549412722
650002722
749142722

prune100.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New16117
Fresh358
Picked011
Done000
Total19726
Error
0.1b
Counts
26 → 7
Alt Table
StatusErrorProgram
13.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (sqrt.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))))))))) (sqrt.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))))))))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (log.f64 (exp.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (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))))))) 2)))) (+.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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (+.f64 1/2 (-.f64 (*.f64 1/2 (cos.f64 (*.f64 delta 2))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2)))) (+.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)))))))))))
0.2b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
33.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sqrt.f64 (sin.f64 phi1)) (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (sqrt.f64 (sin.f64 phi1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
Compiler

Compiled 1984 to 636 computations (67.9% saved)

localize47.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b
(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)))))
0.4b
(pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)
0.5b
(+.f64 1/2 (-.f64 (*.f64 1/2 (cos.f64 (*.f64 delta 2))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2))))

rewrite256.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
add-log-exp_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64
pow1_binary64 add-exp-log_binary64
add-cbrt-cube_binary64
Counts
4 → 50
Calls

4 calls:

7.0ms
(+.f64 1/2 (-.f64 (*.f64 1/2 (cos.f64 (*.f64 delta 2))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2))))
4.0ms
(pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)
1.0ms
(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 3954 to 1076 computations (72.8% saved)

series316.0ms (1.9%)

Error
0.1b
Counts
4 → 39
Calls

4 calls:

139.0ms
(+.f64 1/2 (-.f64 (*.f64 1/2 (cos.f64 (*.f64 delta 2))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2))))
78.0ms
(pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)
38.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
38.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 5888 to 2928 computations (50.3% saved)

simplify123.0ms (0.7%)

Algorithm
egg-herbie
Rules
748×associate-+l+_binary64
455×cancel-sign-sub-inv_binary64
223×associate-*l*_binary64
217×distribute-rgt-in_binary64
216×associate-*r*_binary64
Counts
89 → 34
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01103657
12303383
25483351
321003348
449923348

prune107.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New33134
Fresh145
Picked011
Done011
Total34741
Error
0.1b
Counts
41 → 7
Alt Table
StatusErrorProgram
13.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (sqrt.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))))))))) (sqrt.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))))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (+.f64 1/2 (-.f64 (*.f64 1/2 (cos.f64 (*.f64 delta 2))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2)))) (+.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)))))))))))
0.2b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (log.f64 (exp.f64 (-.f64 (+.f64 1/2 (*.f64 1/2 (cos.f64 (*.f64 delta 2)))) (*.f64 (pow.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2) (pow.f64 (sin.f64 phi1) 2))))) (+.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)))))))))))
33.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sqrt.f64 (sin.f64 phi1)) (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (sqrt.f64 (sin.f64 phi1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (pow.f64 (sin.f64 phi1) 2)) (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)))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (*.f64 (sin.f64 phi1) (*.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
Compiler

Compiled 2108 to 692 computations (67.2% saved)

regimes2.4s (14.2%)

Accuracy

Total 0.1b remaining (49.3%)

Threshold costs 0.1b (49.3%)

Compiler

Compiled 73554 to 31598 computations (57% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
030271
142271
247271
349271
450271
550271

end1.0ms (0%)

Compiler

Compiled 165 to 30 computations (81.8% saved)

sample7.0s (41.3%)

Algorithm
intervals
Results
4.5s3884×body1024valid
986.0ms1397×body512valid
452.0ms2195×body128valid
237.0ms515×body256valid
25.0msbody2048valid
Compiler

Compiled 657 to 272 computations (58.6% saved)

Profiling

Loading profile data...