Details

Time bar (total: 17.3s)

analyze2.7s (15.7%)

Algorithm
1×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
7.8%92%0.2%9
7.8%92%0.2%10
10.1%89.7%0.2%11
10.1%89.7%0.2%12
13.9%85.9%0.2%13
13.9%85.9%0.2%14
Compiler

Compiled 29 to 18 computations (37.9% saved)

sample226.0ms (1.3%)

Algorithm
1×intervals
Results
167.0ms184×body1024valid
21.0ms37×body512valid
9.0ms20×body128valid
9.0ms5×body2048valid
4.0ms10×body256valid
Compiler

Compiled 61 to 39 computations (36.1% saved)

simplify24.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
83×cancel-sign-sub-inv_binary64
59×distribute-rgt-neg-in_binary64
56×sub-neg_binary64
47×distribute-rgt-in_binary64
42×unsub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01839
13139
25939
310539
412939
519639
624839
730939
842039
943039
1043639
1138539

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
12.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶12.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 84 to 51 computations (39.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.3b
(sin.f64 (-.f64 lambda1 lambda2))
2.4b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite136.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Error
7.8b
Rules
11×add-sqr-sqrt_binary64 pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
9×add-cube-cbrt_binary64 *-un-lft-identity_binary64
6×cancel-sign-sub-inv_binary64 associate-*r*_binary64
4×cos-sum_binary64 add-log-exp_binary64 sin-sum_binary64 pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64 associate-*l*_binary64
3×cos-diff_binary64
Counts
4 → 63
Calls

4 calls:

7.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
Compiler

Compiled 1912 to 347 computations (81.9% saved)

series217.0ms (1.3%)

Error
10.9b
Counts
4 → 51
Calls

4 calls:

89.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
29.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
24.0ms
(cos.f64 (-.f64 lambda1 lambda2))
22.0ms
(sin.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 3739 to 1868 computations (50% saved)

simplify117.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
546×distribute-rgt-neg-in_binary64
486×sub-neg_binary64
471×distribute-lft-neg-in_binary64
368×cancel-sign-sub-inv_binary64
318×neg-mul-1_binary64
Counts
114 → 76
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02442009
16141804
217811721
330801681
446661681
550281681

prune122.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New631376
Fresh000
Picked101
Done000
Total641377
Error
7.8b
Counts
77 → 13
Alt Table
StatusErrorProgram
12.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
27.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) lambda1) (sin.f64 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
23.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))))))
13.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
25.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (/.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (+.f64 (sin.f64 (-.f64 phi1 phi2)) (sin.f64 (+.f64 phi2 phi1)))) 2)))
26.6b
(atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (+.f64 (*.f64 (*.f64 lambda2 lambda2) -1/2) 1)) (*.f64 lambda2 (cos.f64 lambda1))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
28.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (cos.f64 phi1)) (*.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
12.9b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
21.6b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda2))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
16.1b
(atan2.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.5b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
▶8.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
Compiler

Compiled 2453 to 884 computations (64% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.4b
(cos.f64 (-.f64 lambda1 lambda2))

rewrite158.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Error
0.1b
Rules
14×add-sqr-sqrt_binary64
13×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
10×add-cube-cbrt_binary64 *-un-lft-identity_binary64
9×associate-*r*_binary64
7×associate-*l*_binary64
Counts
4 → 71
Calls

4 calls:

8.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 2666 to 363 computations (86.4% saved)

series328.0ms (1.9%)

Error
7.6b
Counts
4 → 57
Calls

4 calls:

97.0ms
(*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
83.0ms
(*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
34.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
25.0ms
(cos.f64 (-.f64 lambda1 lambda2))
Compiler

Compiled 5040 to 2520 computations (50% saved)

simplify122.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
606×cancel-sign-sub-inv_binary64
419×associate-*r*_binary64
406×associate-*l*_binary64
349×distribute-rgt-neg-in_binary64
326×neg-mul-1_binary64
Counts
128 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02902890
17812576
224772459
344522459
449922459

prune166.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91596
Fresh9312
Picked101
Done000
Total1018109
Error
0.1b
Counts
109 → 8
Alt Table
StatusErrorProgram
8.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
36.2b
(atan2.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi2) (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
28.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (cos.f64 phi1)) (*.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
8.6b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (log.f64 (pow.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2))) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
Compiler

Compiled 3263 to 803 computations (75.4% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b
(*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

rewrite220.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
29×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
16×pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
13×add-sqr-sqrt_binary64
10×associate-*l*_binary64
9×add-cube-cbrt_binary64 *-un-lft-identity_binary64
Counts
4 → 81
Calls

4 calls:

9.0ms
(*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
8.0ms
(*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
5.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
Compiler

Compiled 3617 to 432 computations (88.1% saved)

series401.0ms (2.3%)

Error
0.1b
Counts
4 → 61
Calls

4 calls:

127.0ms
(*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1))))
110.0ms
(*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
35.0ms
(*.f64 (cos.f64 phi1) (sin.f64 phi2))
32.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
Compiler

Compiled 7427 to 3193 computations (57% saved)

simplify109.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
808×associate-*r*_binary64
783×cancel-sign-sub-inv_binary64
629×associate-*l*_binary64
501×distribute-rgt-neg-in_binary64
339×*-commutative_binary64
Counts
142 → 107
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
03333338
18782861
233592861
353462861

prune200.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1007107
Fresh257
Picked101
Done000
Total10312115
Error
0.0b
Counts
115 → 12
Alt Table
StatusErrorProgram
14.4b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (sqrt.f64 (cos.f64 lambda2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (sqrt.f64 (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
36.2b
(atan2.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi2) (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
28.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (cos.f64 phi1)) (*.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
▶0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))))))
0.3b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cos.f64 lambda2))) (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cos.f64 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))) (cbrt.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
0.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (log.f64 (exp.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
Compiler

Compiled 5038 to 1218 computations (75.8% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))
0.2b
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)
23.8b
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3))

rewrite378.0ms (2.2%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
28×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
15×pow-prod-down_binary64 prod-exp_binary64 cbrt-unprod_binary64
8×add-cube-cbrt_binary64 cbrt-prod_binary64 add-sqr-sqrt_binary64 *-un-lft-identity_binary64
7×associate-*r/_binary64
6×associate-*l*_binary64
Counts
4 → 88
Calls

4 calls:

10.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)
9.0ms
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))
6.0ms
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3))
Compiler

Compiled 4127 to 674 computations (83.7% saved)

series654.0ms (3.8%)

Error
0.0b
Counts
4 → 68
Calls

4 calls:

204.0ms
(pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3)
116.0ms
(*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))
112.0ms
(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))) 3))
70.0ms
(*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
Compiler

Compiled 9003 to 4449 computations (50.6% saved)

simplify125.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
802×associate-*r*_binary64
800×unswap-sqr_binary64
563×associate-*l*_binary64
258×*-commutative_binary64
201×log-prod_binary64
Counts
156 → 123
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02883999
17113663
233433608
357673608

prune319.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1203123
Fresh2911
Picked101
Done000
Total12312135
Error
0.0b
Counts
135 → 12
Alt Table
StatusErrorProgram
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 lambda1)) (cos.f64 phi2))) 3)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 lambda1)) (cbrt.f64 (sin.f64 lambda1))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cbrt.f64 (sin.f64 lambda1))))) 3)))))
0.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 phi1) (*.f64 (sin.f64 lambda1) (cos.f64 phi2)))) 3)))))))
14.4b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (sqrt.f64 (cos.f64 lambda2)) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (sqrt.f64 (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 lambda2)) (cbrt.f64 (cos.f64 lambda2))) (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cbrt.f64 (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
8.0b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)) 3)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
36.2b
(atan2.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi2) (sqrt.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
13.1b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (cbrt.f64 (*.f64 (sin.f64 phi2) (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
28.8b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (sqrt.f64 (cos.f64 phi1)) (*.f64 (sin.f64 phi2) (sqrt.f64 (cos.f64 phi1)))) (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
0.2b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (*.f64 (cos.f64 lambda2) (*.f64 (cos.f64 lambda1) (*.f64 (cos.f64 phi2) (sin.f64 phi1)))) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (*.f64 (sin.f64 lambda1) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))))))
0.8b
(atan2.f64 (*.f64 (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (+.f64 (log.f64 (exp.f64 (*.f64 (*.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)) (cos.f64 lambda2)))) (*.f64 (*.f64 (cos.f64 phi2) (sin.f64 phi1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
13.3b
(atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (-.f64 (*.f64 (cos.f64 phi1) (sin.f64 phi2)) (cbrt.f64 (pow.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (*.f64 (cos.f64 phi2) (sin.f64 phi1))) 3))))
Compiler

Compiled 4830 to 1154 computations (76.1% saved)

regimes3.1s (17.9%)

Accuracy

Total 0.1b remaining (47.7%)

Threshold costs 0.1b (47.7%)

Compiler

Compiled 66703 to 38819 computations (41.8% saved)

simplify8.0ms (0%)

Algorithm
1×egg-herbie
Rules
20×*-commutative_binary64
14×+-commutative_binary64
13×sub-neg_binary64
11×neg-mul-1_binary64 neg-sub0_binary64
8×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03078
14678
26378
38378
410178
511678
612478
712978
813178
913178

end1.0ms (0%)

Compiler

Compiled 51 to 28 computations (45.1% saved)

sample7.3s (42.3%)

Algorithm
1×intervals
Results
5.0s5340×body1024valid
721.0ms1253×body512valid
382.0ms196×body2048valid
148.0ms414×body256valid
144.0ms797×body128valid
Compiler

Compiled 652 to 365 computations (44% saved)

Profiling

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