Details

Time bar (total: 17.1s)

analyze4.0s (23.2%)

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 39 to 24 computations (38.5% saved)

sample217.0ms (1.3%)

Algorithm
intervals
Results
138.0ms128×body1024valid
39.0ms47×body512valid
12.0ms63×body128valid
8.0ms18×body256valid
Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify46.0ms (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

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
0.1b
Counts
2 → 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 (+.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)

localize33.0ms (0.2%)

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))))))
0.4b
(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)))))))

rewrite150.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
12×add-sqr-sqrt_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64 associate-*l*_binary64 associate-*r*_binary64
sin-mult_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 unswap-sqr_binary64 *-commutative_binary64
diff-log_binary64 flip3--_binary64 sub-neg_binary64 flip--_binary64 cancel-sign-sub-inv_binary64 asin-acos_binary64
Counts
4 → 58
Calls

4 calls:

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))))))
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 2518 to 351 computations (86.1% saved)

series264.0ms (1.5%)

Error
0.1b
Counts
4 → 43
Calls

4 calls:

97.0ms
(-.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)))))))
79.0ms
(*.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))))))
34.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
28.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
Compiler

Compiled 3708 to 1981 computations (46.6% saved)

simplify170.0ms (1%)

Algorithm
egg-herbie
Rules
571×sub-neg_binary64
430×cancel-sign-sub-inv_binary64
352×unsub-neg_binary64
301×distribute-rgt-neg-in_binary64
278×neg-mul-1_binary64
Counts
101 → 77
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01743297
13923132
210313054
319323044
438693044
544693044
648733044

prune113.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New72577
Fresh000
Picked101
Done000
Total73578
Error
0.0b
Counts
78 → 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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.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)))))))))) (cbrt.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 (*.f64 (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (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)))))))))
0.1b
(+.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)))))))))))
0.1b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
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 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
Compiler

Compiled 2962 to 645 computations (78.2% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite231.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
add-log-exp_binary64 sin-mult_binary64
cos-mult_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
frac-sub_binary64 asin-acos_binary64
associate-*l/_binary64 associate-*r/_binary64 sub-div_binary64
Counts
4 → 43
Calls

4 calls:

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)))))
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 4342 to 355 computations (91.8% saved)

series255.0ms (1.5%)

Error
0.0b
Counts
4 → 40
Calls

4 calls:

140.0ms
(-.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)))))))))
31.0ms
(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)))))
30.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 6471 to 2270 computations (64.9% saved)

simplify152.0ms (0.9%)

Algorithm
egg-herbie
Rules
464×cancel-sign-sub-inv_binary64
409×unswap-sqr_binary64
364×neg-mul-1_binary64
315×distribute-rgt-neg-in_binary64
294×distribute-lft-neg-in_binary64
Counts
83 → 31
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01133777
12813481
28713444
322923444
445353369
550753369

prune101.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New30131
Fresh044
Picked011
Done000
Total30636
Error
0.0b
Counts
36 → 6
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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.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)))))))))) (cbrt.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 (*.f64 (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)))))))))))
0.1b
(+.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)))))))))))
0.1b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
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 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
Compiler

Compiled 2508 to 599 computations (76.1% saved)

localize32.0ms (0.2%)

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)))))))
0.4b
(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))))))))))

rewrite220.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
10×add-sqr-sqrt_binary64
add-cube-cbrt_binary64 *-un-lft-identity_binary64
pow1_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
log-prod_binary64
Counts
4 → 57
Calls

4 calls:

5.0ms
(*.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 2786 to 396 computations (85.8% saved)

series453.0ms (2.7%)

Error
0.0b
Counts
4 → 47
Calls

4 calls:

188.0ms
(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))))))))))
103.0ms
(-.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))))))))
77.0ms
(*.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)))))))
32.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
Compiler

Compiled 4101 to 2304 computations (43.8% saved)

simplify172.0ms (1%)

Algorithm
egg-herbie
Rules
482×cancel-sign-sub-inv_binary64
470×sub-neg_binary64
382×unsub-neg_binary64
305×*-commutative_binary64
262×distribute-rgt-in_binary64
Counts
104 → 62
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01524362
12944121
27004034
318084034
440324034
550494034

prune114.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New62062
Fresh044
Picked011
Done011
Total62668
Error
0.0b
Counts
68 → 6
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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.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)))))))))) (cbrt.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 (*.f64 (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)))))))))))
0.1b
(+.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)))))))))))
0.1b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
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 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
Compiler

Compiled 2292 to 569 computations (75.2% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
0.6b
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
0.6b
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
0.6b
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))

rewrite211.0ms (1.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
cbrt-prod_binary64
add-cube-cbrt_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
add-log-exp_binary64
pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
pow1/3_binary64
Counts
4 → 45
Calls

4 calls:

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

Compiled 4142 to 349 computations (91.6% saved)

series454.0ms (2.7%)

Error
0.0b
Counts
4 → 41
Calls

4 calls:

112.0ms
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
111.0ms
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
110.0ms
(cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))
96.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
Compiler

Compiled 5419 to 2172 computations (59.9% saved)

simplify163.0ms (1%)

Algorithm
egg-herbie
Rules
420×neg-mul-1_binary64
389×neg-sub0_binary64
354×cancel-sign-sub-inv_binary64
324×sub-neg_binary64
294×unsub-neg_binary64
Counts
86 → 65
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0873236
11993077
24923048
312893048
428263036
542033036
649223036

prune70.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New65065
Fresh033
Picked011
Done022
Total65671
Error
0.0b
Counts
71 → 6
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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))) (cbrt.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)))))))))) (cbrt.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 (*.f64 (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (cbrt.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)))) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (*.f64 (*.f64 (cbrt.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))) (cbrt.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)))) (cbrt.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)))))))))))
0.1b
(+.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)))))))))))
0.1b
(+.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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
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 (*.f64 (*.f64 (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))) (cbrt.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))))))
Compiler

Compiled 1979 to 397 computations (79.9% saved)

regimes2.3s (13.3%)

Accuracy

Total 0.1b remaining (39.9%)

Threshold costs 0.1b (39.9%)

Compiler

Compiled 58385 to 29211 computations (50% saved)

simplify7.0ms (0%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-mul-1_binary64 neg-sub0_binary64
distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027133
141133
254133
362133
468133
570133
670133

end1.0ms (0%)

Compiler

Compiled 84 to 27 computations (67.9% saved)

sample7.1s (41.7%)

Algorithm
intervals
Results
4.6s3917×body1024valid
976.0ms1341×body512valid
438.0ms2204×body128valid
243.0ms529×body256valid
25.0msbody2048valid
Compiler

Compiled 587 to 230 computations (60.8% saved)

Profiling

Loading profile data...