Details

Time bar (total: 15.1s)

analyze3.2s (21.4%)

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)

sample7.9s (52.4%)

Results
5.5s4552×body1024valid
1.3s1829×body512valid
360.0ms766×body256valid
319.0ms125×body2048valid
250.0ms984×body128valid
Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify33.0ms (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

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.9b
Counts
3 → 1
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))))
Compiler

Compiled 89 to 43 computations (51.7% saved)

localize15.0ms (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)))
✓0.5b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓4.0b
(cos.f64 (-.f64 lambda1 lambda2))
✓4.2b
(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))
9.0ms
(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))

rewrite14.0ms (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:

5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.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)))

simplify121.0ms (0.8%)

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

prune276.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New13514149
Fresh000
Picked101
Done000
Total13614150
Error
0.7b
Counts
150 → 14
Alt Table
StatusErrorProgram
35.3b
(+.f64 lambda1 (*.f64 (sqrt.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)))) (sqrt.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) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
1.3b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
1.0b
(+.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))))
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))))))
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) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
13.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (*.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
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))))))
12.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 (*.f64 lambda2 (*.f64 lambda2 (cos.f64 lambda1))) -1/2 (fma.f64 lambda2 (sin.f64 lambda1) (cos.f64 lambda1))) (cos.f64 phi1))))
5.4b
(+.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))))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
▶0.8b
(+.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))))
1.0b
(+.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))))
37.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
Compiler

Compiled 5889 to 1669 computations (71.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
✓0.3b
(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)))
✓0.5b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
4.2b
(sin.f64 (-.f64 lambda1 lambda2))

series83.0ms (0.5%)

Counts
3 → 104
Calls

3 calls:

61.0ms
(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:

4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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))
0.0ms
(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)))

simplify133.0ms (0.9%)

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

prune339.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1492151
Fresh5813
Picked101
Done000
Total15510165
Error
0.1b
Counts
165 → 10
Alt Table
StatusErrorProgram
35.3b
(+.f64 lambda1 (*.f64 (sqrt.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)))) (sqrt.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) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
13.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (*.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
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))))))
5.4b
(+.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))))))
9.1b
(+.f64 lambda1 (expm1.f64 (log1p.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
1.3b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
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))))))
37.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 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)))) (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 6461 to 1638 computations (74.6% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series55.0ms (0.4%)

Counts
2 → 84
Calls

2 calls:

39.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
15.0ms
(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)))

rewrite11.0ms (0.1%)

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 → 37
Calls

2 calls:

9.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.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)))

simplify169.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
703×fma-def_binary64
444×sub-neg_binary64
428×*-commutative_binary64
382×cancel-sign-sub-inv_binary64
216×fma-neg_binary64
Counts
121 → 89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01754928
14424715
215314652
342284652
449484652
549424652

prune394.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1774181
Fresh279
Picked101
Done000
Total18011191
Error
0.0b
Counts
191 → 11
Alt Table
StatusErrorProgram
35.3b
(+.f64 lambda1 (*.f64 (sqrt.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)))) (sqrt.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) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (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)))) (log.f64 (exp.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 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (*.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
13.4b
(+.f64 lambda1 (atan2.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 phi2)) (*.f64 lambda2 (*.f64 (cos.f64 phi2) (cos.f64 lambda1)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
5.4b
(+.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))))))
9.1b
(+.f64 lambda1 (expm1.f64 (log1p.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
1.3b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
0.2b
(+.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 (pow.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)) 3))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.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))))
37.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
Compiler

Compiled 8836 to 1851 computations (79.1% saved)

localize26.0ms (0.2%)

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) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))
✓0.5b
(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
✓0.6b
(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))

series134.0ms (0.9%)

Counts
3 → 144
Calls

3 calls:

60.0ms
(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
59.0ms
(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
15.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))

rewrite4.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
5×*-un-lft-identity_binary64
5×add-sqr-sqrt_binary64
5×add-cube-cbrt_binary64
4×log-prod_binary64
4×log-pow_binary64
Counts
3 → 37
Calls

3 calls:

2.0ms
(log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.0ms
(fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))

simplify172.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
936×fma-neg_binary64
787×fma-def_binary64
582×cancel-sign-sub-inv_binary64
545×associate-*r*_binary64
512×associate-*l*_binary64
Counts
181 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01737353
14386583
213586449
346716445
454666445

prune333.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh3710
Picked101
Done000
Total13511146
Error
0.0b
Counts
146 → 11
Alt Table
StatusErrorProgram
5.4b
(+.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))))))
10.2b
(+.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 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))
35.3b
(+.f64 lambda1 (*.f64 (sqrt.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)))) (sqrt.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) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
37.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (sin.f64 lambda1) (cos.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))) (*.f64 (cos.f64 lambda1) (sin.f64 (*.f64 (neg.f64 (sqrt.f64 lambda2)) (sqrt.f64 lambda2)))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.5b
(+.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 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))) (cbrt.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 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (*.f64 1/2 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (pow.f64 phi2 2))))))
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)))) (cbrt.f64 (*.f64 (*.f64 (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))
1.3b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.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)))) (cbrt.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))))) (cbrt.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))))))
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))) (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (cbrt.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))))) (cbrt.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))))
Compiler

Compiled 6542 to 1330 computations (79.7% saved)

regimes1.3s (8.5%)

Accuracy

Total 0.1b remaining (48.2%)

Threshold costs 0.1b (48.2%)

Counts
147 → 1
Compiler

Compiled 38934 to 20268 computations (47.9% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02356
13556
23756
33856
43856

end253.0ms (1.7%)

Compiler

Compiled 638 to 266 computations (58.3% saved)

Profiling

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