Details

Time bar (total: 28.4s)

analyze5.0s (17.6%)

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
9.4%90.4%0.2%9
9.4%90.4%0.2%10
10.9%88.9%0.2%11
10.9%88.9%0.2%12
10.9%88.9%0.2%13
10.9%88.9%0.2%14
Compiler

Compiled 25 to 15 computations (40% saved)

sample384.0ms (1.4%)

Algorithm
intervals
Results
286.0ms158×body1024valid
46.0ms51×body512valid
12.0msbody2048valid
11.0ms18×body256valid
8.0ms26×body128valid
Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify56.0ms (0.2%)

Algorithm
egg-herbie
Rules
284×fma-def_binary64
141×fma-neg_binary64
44×distribute-rgt-in_binary64
38×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01532
12130
22830
33530
44230
56830
69830
713230
817630
922030
1028830
1131030
1234630
1339330
1440330
1542130
1644230
1744930
1847030
1947830
2048030
2145330

prune8.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
1.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
Compiler

Compiled 137 to 71 computations (48.2% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.4b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
2.6b
(sin.f64 (-.f64 lambda1 lambda2))
2.7b
(cos.f64 (-.f64 lambda1 lambda2))

series104.0ms (0.4%)

Counts
4 → 76
Calls

4 calls:

58.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
30.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
8.0ms
(cos.f64 (-.f64 lambda1 lambda2))
8.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite50.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
39×sin-sum_binary64
36×add-sqr-sqrt_binary64
36×prod-diff_binary64
34×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
Counts
4 → 102
Calls

4 calls:

13.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
11.0ms
(cos.f64 (-.f64 lambda1 lambda2))
7.0ms
(sin.f64 (-.f64 lambda1 lambda2))
1.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))

simplify260.0ms (0.9%)

Algorithm
egg-herbie
Rules
394×fma-neg_binary64
343×distribute-rgt-neg-in_binary64
318×associate-*r*_binary64
302×distribute-lft-neg-in_binary64
294×associate-*l*_binary64
Counts
178 → 207
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03844373
17473586
222483335
346143218
449503210
550313210

prune797.0ms (2.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New19116207
Fresh101
Picked101
Done000
Total19316209
Error
1.0b
Counts
209 → 16
Alt Table
StatusErrorProgram
15.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2))) (*.f64 (cbrt.f64 (cos.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (-.f64 (cos.f64 lambda2) (*.f64 lambda1 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) 1/2) lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))))
14.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
15.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (+.f64 (cos.f64 lambda2) (*.f64 lambda1 (sin.f64 lambda2))) (cos.f64 phi1))))
1.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
13.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2)))) (*.f64 (sin.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2))) (cbrt.f64 lambda2))))) (cos.f64 phi1))))
39.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (cos.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (*.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))) (sin.f64 (fma.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2) (*.f64 (sqrt.f64 lambda2) (sqrt.f64 lambda2))))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
13.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1))))
4.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.9b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)) (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
Compiler

Compiled 8534 to 2337 computations (72.6% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
2.6b
(sin.f64 (-.f64 lambda1 lambda2))

series140.0ms (0.5%)

Counts
2 → 56
Calls

2 calls:

119.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
20.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite10.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 31
Calls

2 calls:

7.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

simplify142.0ms (0.5%)

Algorithm
egg-herbie
Rules
754×cancel-sign-sub-inv_binary64
595×sub-neg_binary64
440×associate-+l+_binary64
421×associate--l+_binary64
218×distribute-rgt-neg-in_binary64
Counts
87 → 92
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01882512
15522155
218422075
345702075
452482075

prune933.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2042206
Fresh6915
Picked101
Done000
Total21111222
Error
0.1b
Counts
222 → 11
Alt Table
StatusErrorProgram
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2))) (*.f64 (cbrt.f64 (cos.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
14.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
1.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
13.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))) (cos.f64 phi1))))
4.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.9b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)) (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
Compiler

Compiled 9233 to 2216 computations (76% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
0.2b
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

series49.0ms (0.2%)

Counts
2 → 72
Calls

2 calls:

30.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
18.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 29
Calls

2 calls:

6.0ms
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))

simplify290.0ms (1%)

Algorithm
egg-herbie
Rules
540×fma-neg_binary64
514×distribute-rgt-neg-in_binary64
423×distribute-lft-neg-in_binary64
364×*-commutative_binary64
280×associate-*l*_binary64
Counts
101 → 65
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01123536
12403395
26313375
316763354
429813352
547713352
649873352
748983352

prune810.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1498157
Fresh5510
Picked101
Done000
Total15513168
Error
0.1b
Counts
168 → 13
Alt Table
StatusErrorProgram
4.9b
(+.f64 lambda1 (cbrt.f64 (*.f64 (*.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))) (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (cos.f64 phi2)) (cbrt.f64 (cos.f64 phi2))) (*.f64 (cbrt.f64 (cos.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))))
29.9b
(+.f64 lambda1 (exp.f64 (log.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
1.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (expm1.f64 (log1p.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
14.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (exp.f64 (log.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
13.3b
(+.f64 lambda1 (expm1.f64 (log1p.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
5.9b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)) (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
2.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
Compiler

Compiled 7920 to 1810 computations (77.1% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b
(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b
(+.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))

series206.0ms (0.7%)

Counts
2 → 84
Calls

2 calls:

124.0ms
(+.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))
81.0ms
(*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite19.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
fma-udef_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 38
Calls

2 calls:

7.0ms
(+.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1))
7.0ms
(*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify222.0ms (0.8%)

Algorithm
egg-herbie
Rules
576×associate--l+_binary64
348×distribute-rgt-in_binary64
325×distribute-lft-in_binary64
268×fma-neg_binary64
230×fma-def_binary64
Counts
122 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01863724
15753451
220783331
349793331
449813331

prune1.1s (3.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2063209
Fresh4812
Picked101
Done000
Total21111222
Error
0.0b
Counts
222 → 11
Alt Table
StatusErrorProgram
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (cos.f64 phi1))))
2.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) 3)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
2.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (*.f64 (cos.f64 phi1) (cos.f64 phi1))) (-.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1)))))
29.9b
(+.f64 lambda1 (exp.f64 (log.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) 3) (pow.f64 (cos.f64 phi1) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (*.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))) (cos.f64 phi1)))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (*.f64 (*.f64 (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
13.3b
(+.f64 lambda1 (expm1.f64 (log1p.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
5.9b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 phi2) (cos.f64 phi2)) (cos.f64 phi2)) (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))))))
Compiler

Compiled 9489 to 2015 computations (78.8% saved)

regimes5.7s (20%)

Accuracy

Total 0.1b remaining (52.2%)

Threshold costs 0.1b (52.2%)

Counts
310 → 1
Compiler

Compiled 86765 to 45727 computations (47.3% saved)

simplify6.0ms (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
02052
13052
24052
34652
45052
55152
65152

end1.0ms (0%)

Compiler

Compiled 36 to 19 computations (47.2% saved)

sample12.0s (42.2%)

Algorithm
intervals
Results
8.0s4443×body1024valid
1.7s1770×body512valid
517.0ms119×body2048valid
406.0ms701×body256valid
276.0ms967×body128valid
Compiler

Compiled 682 to 281 computations (58.8% saved)

Profiling

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