Details

Time bar (total: 23.1s)

analyze5.0s (21.5%)

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
0%99.8%0.2%9
0%99.8%0.2%10
0.8%99%0.2%11
1.2%98.6%0.2%12
9.9%89.8%0.2%13
9.9%89.8%0.2%14
Compiler

Compiled 39 to 24 computations (38.5% saved)

sample10.7s (46.1%)

Results
7.8s4031×body1024valid
1.5s1399×body512valid
803.0ms2255×body128valid
404.0ms553×body256valid
83.0ms18×body2048valid
Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify43.0ms (0.2%)

Algorithm
egg-herbie
Rules
571×fma-def_binary64
244×fma-neg_binary64
103×unsub-neg_binary64
88×distribute-rgt-in_binary64
84×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02353
14153
27053
39453
411453
515253
622353
729453
842353
955953
1063353
1176253
1289753
13109153
14133253
15165053
16181753
17199153
18199353
19199953
20200453
Stop Event
saturated
Counts
1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (sin.f64 theta))) (fma.f64 (sin.f64 (asin.f64 (fma.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))))) (neg.f64 (sin.f64 phi1)) (cos.f64 delta))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
Compiler

Compiled 220 to 124 computations (43.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

series120.0ms (0.5%)

Counts
4 → 132
Calls

4 calls:

57.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
45.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
11.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
7.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

rewrite51.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
216×add-sqr-sqrt_binary64
204×log1p-expm1-u_binary64
204×expm1-log1p-u_binary64
202×add-cbrt-cube_binary64
199×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01988
140788
Stop Event
node limit
Counts
4 → 100
Calls

4 calls:

47.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
47.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
47.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
47.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

simplify65.0ms (0.3%)

Algorithm
egg-herbie
Rules
849×cancel-sign-sub-inv_binary64
737×associate-*l*_binary64
345×fma-neg_binary64
278×distribute-rgt-neg-in_binary64
253×distribute-lft-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01433588
14823470
216853370
Stop Event
node limit
Counts
232 → 169

prune295.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1618169
Fresh101
Picked101
Done000
Total1638171
Error
0.0b
Counts
171 → 8
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (+.f64 1 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))))))
3.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 delta) (sin.f64 theta)) 3)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (pow.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))) 3)))
10.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 delta (*.f64 (sin.f64 phi1) (cos.f64 theta)))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2)) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (cbrt.f64 (pow.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3)))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2) (*.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))) (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))))))
Compiler

Compiled 8036 to 1977 computations (75.4% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))))
0.3b
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))
0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))
0.5b
(expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))

series234.0ms (1%)

Counts
4 → 144
Calls

4 calls:

87.0ms
(expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))
52.0ms
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))))
52.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))
43.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))

rewrite85.0ms (0.4%)

Algorithm
batch-egg-rewrite
Rules
300×expm1-udef_binary64
300×log1p-udef_binary64
166×add-sqr-sqrt_binary64
157×expm1-log1p-u_binary64
156×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
016121
1319121
24256121
Stop Event
node limit
Counts
4 → 114
Calls

4 calls:

81.0ms
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))))
81.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))
81.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))))
81.0ms
(expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))

simplify100.0ms (0.4%)

Algorithm
egg-herbie
Rules
522×associate-*r*_binary64
521×fma-neg_binary64
349×associate-*l*_binary64
301×sub-neg_binary64
238×*-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02426042
18585637
235755633
Stop Event
node limit
Counts
258 → 151

prune340.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1474151
Fresh527
Picked101
Done000
Total1536159
Error
0.0b
Counts
159 → 6
Alt Table
StatusErrorProgram
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3) 1) (+.f64 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) (+.f64 1 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)))))
10.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 delta (*.f64 (sin.f64 phi1) (cos.f64 theta)))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2) (*.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))) (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))))))
Compiler

Compiled 8495 to 2414 computations (71.6% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
0.3b
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
0.4b
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2)
0.5b
(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))

series1.2s (5.2%)

Counts
4 → 144
Calls

4 calls:

708.0ms
(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))
387.0ms
(/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
70.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2)
42.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

rewrite70.0ms (0.3%)

Algorithm
batch-egg-rewrite
Rules
225×add-sqr-sqrt_binary64
217×log1p-expm1-u_binary64
217×expm1-log1p-u_binary64
214×add-cbrt-cube_binary64
210×add-cube-cbrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
020187
1445183
Stop Event
node limit
Counts
4 → 89
Calls

4 calls:

65.0ms
(/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
65.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
65.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2)
65.0ms
(-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))

simplify220.0ms (1%)

Algorithm
egg-herbie
Rules
657×fma-def_binary64
555×times-frac_binary64
259×*-commutative_binary64
213×+-commutative_binary64
165×associate-+r+_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067320813
1261420584
Stop Event
node limit
Counts
233 → 188

prune937.0ms (4.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2660266
Fresh055
Picked011
Done000
Total2666272
Error
0.0b
Counts
272 → 6
Alt Table
StatusErrorProgram
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3) 1) (+.f64 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) (+.f64 1 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)))))
10.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 delta (*.f64 (sin.f64 phi1) (cos.f64 theta)))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2) (*.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))) (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))))))
Compiler

Compiled 36045 to 11446 computations (68.2% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))
0.3b
(pow.f64 (cos.f64 delta) 3)
0.4b
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2)
0.5b
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3)

series390.0ms (1.7%)

Counts
4 → 112
Calls

4 calls:

198.0ms
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))
109.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3)
78.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2)
5.0ms
(pow.f64 (cos.f64 delta) 3)

rewrite57.0ms (0.2%)

Algorithm
batch-egg-rewrite
Rules
199×add-sqr-sqrt_binary64
195×log1p-expm1-u_binary64
195×expm1-log1p-u_binary64
190×add-cbrt-cube_binary64
184×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
019101
1416101
Stop Event
node limit
Counts
4 → 116
Calls

4 calls:

53.0ms
(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))
53.0ms
(pow.f64 (cos.f64 delta) 3)
53.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2)
53.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3)

simplify140.0ms (0.6%)

Algorithm
egg-herbie
Rules
616×associate-*l*_binary64
514×fma-def_binary64
450×fma-neg_binary64
348×*-commutative_binary64
227×+-commutative_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03588440
112808426
248298425
Stop Event
node limit
Counts
228 → 197

prune659.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1970197
Fresh044
Picked011
Done011
Total1976203
Error
0.0b
Counts
203 → 6
Alt Table
StatusErrorProgram
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (pow.f64 (cbrt.f64 (expm1.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) 3))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (/.f64 (-.f64 (pow.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3) 1) (+.f64 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))) (+.f64 1 (*.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 1)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) 3)))))
10.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 delta (*.f64 (sin.f64 phi1) (cos.f64 theta)))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (/.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))) (/.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))) 2) (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 2) (*.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta)))))))) (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (cos.f64 theta))))) 3))))))
Compiler

Compiled 22032 to 6709 computations (69.5% saved)

regimes2.1s (9.3%)

Accuracy

Total 0.1b remaining (61.3%)

Threshold costs 0.1b (61.3%)

Counts
191 → 1
Compiler

Compiled 70607 to 35714 computations (49.4% saved)

simplify5.0ms (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
033125
145125
252125
356125
459125
560125
Stop Event
saturated

end216.0ms (0.9%)

Compiler

Compiled 543 to 230 computations (57.6% saved)

Profiling

Loading profile data...