Details

Time bar (total: 21.8s)

analyze3.5s (16.1%)

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)

sample9.0s (41.1%)

Results
6.4s4621×body1024valid
1.4s1777×body512valid
422.0ms769×body256valid
329.0ms110×body2048valid
266.0ms979×body128valid
Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify55.0ms (0.3%)

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

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.8b
(+.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))))
0.8b
(+.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)

localize26.0ms (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))
✓3.0b
(sin.f64 (-.f64 lambda1 lambda2))
✓3.1b
(cos.f64 (-.f64 lambda1 lambda2))

series78.0ms (0.4%)

Counts
4 → 64
Calls

4 calls:

47.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
16.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
8.0ms
(sin.f64 (-.f64 lambda1 lambda2))
7.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms (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×sin-sum_binary64
Counts
4 → 65
Calls

4 calls:

8.0ms
(sin.f64 (-.f64 lambda1 lambda2))
7.0ms
(cos.f64 (-.f64 lambda1 lambda2))
1.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
1.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))

simplify239.0ms (1.1%)

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
445872292
549282292

prune510.0ms (2.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New13316149
Fresh101
Picked101
Done000
Total13516151
Error
0.6b
Counts
151 → 16
Alt Table
StatusErrorProgram
1.1b
(+.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))))
0.9b
(+.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))))
15.2b
(+.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))))))
32.2b
(+.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))))))
31.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (exp.f64 (log.f64 (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) (fma.f64 (cos.f64 lambda2) lambda1 (sin.f64 (neg.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
32.6b
(+.f64 lambda1 (exp.f64 (log.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))))))
0.8b
(+.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))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
11.5b
(+.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))))))
16.6b
(+.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))))
▶0.7b
(+.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))))
3.4b
(+.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))))))
31.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
8.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.2b
(+.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))))))
Compiler

Compiled 6091 to 1733 computations (71.5% saved)

localize46.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series108.0ms (0.5%)

Counts
2 → 84
Calls

2 calls:

79.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
29.0ms
(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)))

rewrite23.0ms (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:

18.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
1.0ms
(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)))

simplify290.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
696×fma-def_binary64
448×sub-neg_binary64
421×*-commutative_binary64
383×cancel-sign-sub-inv_binary64
224×unsub-neg_binary64
Counts
121 → 87
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01674328
14354135
215204072
341934062
447774062
549514062

prune922.0ms (4.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1773180
Fresh41115
Picked101
Done000
Total18214196
Error
0.1b
Counts
196 → 14
Alt Table
StatusErrorProgram
▶0.2b
(+.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) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
31.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (log1p.f64 (expm1.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 (expm1.f64 (log1p.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))))
0.9b
(+.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))))
15.2b
(+.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))))))
11.5b
(+.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))))))
16.6b
(+.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))))
3.4b
(+.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))))))
8.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
32.2b
(+.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))))))
1.2b
(+.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))))))
32.6b
(+.f64 lambda1 (exp.f64 (log.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))))))
Compiler

Compiled 8023 to 1865 computations (76.8% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series144.0ms (0.7%)

Counts
3 → 104
Calls

3 calls:

98.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
26.0ms
(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) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
20.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite12.0ms (0.1%)

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:

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

simplify291.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
756×cancel-sign-sub-inv_binary64
603×sub-neg_binary64
440×associate-+l+_binary64
421×associate--l+_binary64
220×distribute-rgt-neg-in_binary64
Counts
144 → 112
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02105476
15815020
218904940
346314940
453164940

prune927.0ms (4.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1774181
Fresh4913
Picked101
Done000
Total18213195
Error
0.1b
Counts
195 → 13
Alt Table
StatusErrorProgram
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
31.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.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))))
15.2b
(+.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 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi1))))
32.6b
(+.f64 lambda1 (exp.f64 (log.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))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
11.5b
(+.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))))))
0.2b
(+.f64 lambda1 (atan2.f64 (log1p.f64 (expm1.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) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
16.6b
(+.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))))
8.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
3.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
32.2b
(+.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))))))
Compiler

Compiled 9007 to 1929 computations (78.6% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))
✓0.5b
(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
✓0.6b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi1))
✓0.7b
(cbrt.f64 (sin.f64 lambda2))

series824.0ms (3.8%)

Counts
4 → 96
Calls

4 calls:

347.0ms
(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
326.0ms
(cbrt.f64 (sin.f64 lambda2))
133.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi1))
19.0ms
(*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))

rewrite34.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
22×cbrt-prod_binary64
20×pow1_binary64
15×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
Counts
4 → 91
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))
6.0ms
(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
2.0ms
(cbrt.f64 (sin.f64 lambda2))
1.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2)))) (cos.f64 phi1))

simplify257.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
824×cancel-sign-sub-inv_binary64
350×unswap-sqr_binary64
340×fma-neg_binary64
336×associate-*r*_binary64
312×associate-*l*_binary64
Counts
187 → 191
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02743673
17733164
226433122
344303080
446092948
552072948

prune780.0ms (3.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2381239
Fresh01212
Picked101
Done000
Total23913252
Error
0.1b
Counts
252 → 13
Alt Table
StatusErrorProgram
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (cos.f64 phi2) (*.f64 (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda2) (cos.f64 lambda1)))))) (cbrt.f64 (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
31.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (sqrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (expm1.f64 (log1p.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))))
15.2b
(+.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))))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
11.5b
(+.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))))))
0.2b
(+.f64 lambda1 (atan2.f64 (log1p.f64 (expm1.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) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
16.6b
(+.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))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (*.f64 (sin.f64 lambda1) (*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))) (cbrt.f64 (sin.f64 lambda2))))) (cos.f64 phi1))))
8.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (sin.f64 (-.f64 lambda1 lambda2)) 3))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
3.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 phi2) (fma.f64 (cos.f64 lambda2) (cos.f64 lambda1) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))))
32.2b
(+.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))))))
32.6b
(+.f64 lambda1 (exp.f64 (log.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))))))
Compiler

Compiled 11785 to 2548 computations (78.4% saved)

regimes3.0s (13.7%)

Accuracy

Total 0.1b remaining (40.7%)

Threshold costs 0.1b (40.7%)

Counts
170 → 1
Compiler

Compiled 43967 to 23978 computations (45.5% saved)

simplify9.0ms (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
02480
13780
24780
35380
45780
55880
65880

end637.0ms (2.9%)

Compiler

Compiled 634 to 298 computations (53% saved)

Profiling

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