Details

Time bar (total: 14.5s)

analyze2.7s (18.9%)

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
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)

sample8.0s (55.3%)

Results
5.7s4597×body1024valid
1.3s1815×body512valid
336.0ms722×body256valid
314.0ms116×body2048valid
280.0ms1006×body128valid
Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify32.0ms (0.2%)

Algorithm
1×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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.9b
(+.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))))
0.9b
(+.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)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
✓0.6b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓3.1b
(cos.f64 (-.f64 lambda1 lambda2))
✓3.1b
(sin.f64 (-.f64 lambda1 lambda2))

series46.0ms (0.3%)

Counts
4 → 64
Calls

4 calls:

29.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
8.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite13.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
18×*-un-lft-identity_binary64
18×add-sqr-sqrt_binary64
18×prod-diff_binary64
18×add-cube-cbrt_binary64
13×cos-sum_binary64
Counts
4 → 65
Calls

4 calls:

4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))
0.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))

simplify123.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
633×cancel-sign-sub-inv_binary64
596×fma-def_binary64
520×sub-neg_binary64
381×*-commutative_binary64
340×unsub-neg_binary64
Counts
129 → 149
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02823217
15222562
215342368
338552292
445912292
549282292

prune230.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New13613149
Fresh101
Picked101
Done000
Total13813151
Error
0.7b
Counts
151 → 13
Alt Table
StatusErrorProgram
6.0b
(+.f64 lambda1 (cbrt.f64 (*.f64 (*.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.9b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
▶0.9b
(+.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))))
13.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (*.f64 (cos.f64 (fma.f64 (*.f64 (cbrt.f64 lambda1) (cbrt.f64 lambda1)) (cbrt.f64 lambda1) (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 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) (fma.f64 lambda1 (sin.f64 lambda2) (cos.f64 lambda2)) (cos.f64 phi1))))
5.7b
(+.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))))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
1.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (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))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (*.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))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
Compiler

Compiled 5903 to 1627 computations (72.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓0.2b
(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)))
✓0.6b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
3.1b
(sin.f64 (-.f64 lambda1 lambda2))

series82.0ms (0.6%)

Counts
3 → 104
Calls

3 calls:

60.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
12.0ms
(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)))
9.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite6.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
7×add-sqr-sqrt_binary64
5×*-un-lft-identity_binary64
5×add-cube-cbrt_binary64
5×add-cbrt-cube_binary64
5×add-exp-log_binary64
Counts
3 → 40
Calls

3 calls:

3.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms
(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)))
0.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

simplify123.0ms (0.8%)

Algorithm
1×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
144 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02064756
15684324
218574244
345874244
452654244

prune377.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1483151
Fresh4812
Picked101
Done000
Total15311164
Error
0.2b
Counts
164 → 11
Alt Table
StatusErrorProgram
6.0b
(+.f64 lambda1 (cbrt.f64 (*.f64 (*.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.9b
(+.f64 lambda1 (log1p.f64 (expm1.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.7b
(+.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 (*.f64 (cos.f64 phi2) (cbrt.f64 (*.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (sin.f64 (-.f64 lambda1 lambda2))) (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))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.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))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (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))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (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)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
Compiler

Compiled 6523 to 1664 computations (74.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓0.2b
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
✓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)))
0.6b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

series26.0ms (0.2%)

Counts
2 → 72
Calls

2 calls:

16.0ms
(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)))
11.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

rewrite5.0ms (0%)

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

2 calls:

3.0ms
(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.0ms
(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)))

simplify168.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
551×fma-neg_binary64
508×distribute-rgt-neg-in_binary64
445×distribute-lft-neg-in_binary64
367×*-commutative_binary64
285×associate-*l*_binary64
Counts
101 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01123532
12373383
26483361
316783352
431863350
548183350
649593350
748893350

prune364.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1515156
Fresh4610
Picked101
Done000
Total15611167
Error
0.1b
Counts
167 → 11
Alt Table
StatusErrorProgram
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.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))))
5.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (*.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))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.4b
(+.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))))))
1.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda1)) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (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))))
5.7b
(+.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))))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
14.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
▶0.4b
(+.f64 lambda1 (log1p.f64 (expm1.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))))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
Compiler

Compiled 7557 to 1704 computations (77.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(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)))
✓0.3b
(expm1.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))))
✓0.3b
(log1p.f64 (expm1.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)))))
✓0.6b
(fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))

series135.0ms (0.9%)

Counts
4 → 176
Calls

4 calls:

65.0ms
(fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))
39.0ms
(expm1.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))))
15.0ms
(log1p.f64 (expm1.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)))))
14.0ms
(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)))

rewrite4.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
5×log1p-expm1-u_binary64
4×*-un-lft-identity_binary64
4×add-sqr-sqrt_binary64
4×add-cube-cbrt_binary64
4×add-cbrt-cube_binary64
Counts
4 → 41
Calls

4 calls:

0.0ms
(fma.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (sin.f64 lambda2) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (cos.f64 phi1))
0.0ms
(expm1.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))))
0.0ms
(log1p.f64 (expm1.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)))))
0.0ms
(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)))

simplify221.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
919×fma-neg_binary64
782×fma-def_binary64
582×cancel-sign-sub-inv_binary64
546×associate-*r*_binary64
514×associate-*l*_binary64
Counts
217 → 101
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
016210384
14259768
213609689
347089689
454879689

prune245.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New992101
Fresh3710
Picked101
Done000
Total1039112
Error
0.1b
Counts
112 → 9
Alt Table
StatusErrorProgram
5.4b
(+.f64 lambda1 (log1p.f64 (cbrt.f64 (pow.f64 (expm1.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) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))) 3))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.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))))
5.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (log.f64 (exp.f64 (*.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))))
1.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda1)) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda2)) (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))))
1.0b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
32.8b
(+.f64 lambda1 (log1p.f64 (exp.f64 (log.f64 (expm1.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))))))))
14.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (*.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (sqrt.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
1.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
Compiler

Compiled 5129 to 938 computations (81.7% saved)

regimes1.2s (8.5%)

Accuracy

Total 0.1b remaining (49.1%)

Threshold costs 0.1b (49.1%)

Counts
139 → 1
Compiler

Compiled 38164 to 19141 computations (49.8% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
9×*-commutative_binary64
6×+-commutative_binary64
4×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02470
13770
24770
35370
45770
55870
65870

end215.0ms (1.5%)

Compiler

Compiled 466 to 230 computations (50.6% saved)

Profiling

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