Details

Time bar (total: 25.2s)

analyze5.4s (21.5%)

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
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)

sample11.8s (46.6%)

Results
8.6s4148×body1024valid
1.8s1337×body512valid
766.0ms2219×body128valid
387.0ms540×body256valid
52.0ms12×body2048valid
Compiler

Compiled 116 to 71 computations (38.8% saved)

simplify50.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
571×fma-def_binary64
244×fma-neg_binary64
103×unsub-neg_binary64
90×associate-*l*_binary64
88×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02353
14053
26653
38553
49953
513353
617353
721753
828153
930553
1036253
1140753
1246853
1360453
1472853
1583653
1694353
1789153
1889353
1989953
2090453
2184153

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.2b
(+.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 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
Compiler

Compiled 144 to 76 computations (47.2% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series169.0ms (0.7%)

Counts
4 → 144
Calls

4 calls:

62.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
53.0ms
(*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
48.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
6.0ms
(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite92.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
383×log1p-udef_binary64
211×add-sqr-sqrt_binary64
197×log1p-expm1-u_binary64
197×expm1-log1p-u_binary64
194×add-log-exp_binary64
Counts
4 → 104
Calls

4 calls:

88.0ms
(*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
88.0ms
(*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))
88.0ms
(asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
88.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01993
139393
2498693
3561593

simplify138.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
531×*-commutative_binary64
427×fma-neg_binary64
342×distribute-rgt-neg-in_binary64
314×distribute-lft-neg-in_binary64
237×associate-*r*_binary64
Counts
248 → 179
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01764012
15593890
218803747
347863747
450233747

prune535.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1709179
Fresh000
Picked101
Done000
Total1719180
Error
0.0b
Counts
180 → 9
Alt Table
StatusErrorProgram
▶0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
10.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 phi1) delta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (+.f64 (pow.f64 (cos.f64 delta) 2) (*.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 delta)) 2) (cbrt.f64 (cos.f64 delta)) (neg.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)))))
0.3b
(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
26.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (*.f64 1/2 (*.f64 (cos.f64 phi1) (*.f64 theta theta))) (*.f64 1/720 (*.f64 (cos.f64 phi1) (pow.f64 theta 6))))) (-.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (*.f64 1/24 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)))))))))
Compiler

Compiled 8503 to 2083 computations (75.5% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1))
✓0.3b
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
✓0.5b
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
✓54.4b
(fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))

series412.0ms (1.6%)

Counts
3 → 108
Calls

3 calls:

309.0ms
(fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
55.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
47.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))

rewrite136.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
373×fma-neg_binary64
301×expm1-udef_binary64
301×log1p-udef_binary64
181×add-sqr-sqrt_binary64
168×log1p-expm1-u_binary64
Counts
3 → 80
Calls

3 calls:

133.0ms
(*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))
133.0ms
(-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
133.0ms
(fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
016111
1341106
24069106
34966106
45282106

simplify205.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
720×fma-def_binary64
689×cancel-sign-sub-inv_binary64
615×associate-*r*_binary64
584×associate-*l*_binary64
333×sub-neg_binary64
Counts
188 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01082464
13562354
211942263
344522263
449522263
550452263

prune645.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2190219
Fresh088
Picked011
Done000
Total2199228
Error
0.0b
Counts
228 → 9
Alt Table
StatusErrorProgram
✓0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (expm1.f64 (log1p.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
10.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 phi1) delta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (+.f64 (pow.f64 (cos.f64 delta) 2) (*.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 delta)) 2) (cbrt.f64 (cos.f64 delta)) (neg.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
▶0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)))))
0.3b
(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
26.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (*.f64 1/2 (*.f64 (cos.f64 phi1) (*.f64 theta theta))) (*.f64 1/720 (*.f64 (cos.f64 phi1) (pow.f64 theta 6))))) (-.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (*.f64 1/24 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)))))))))
Compiler

Compiled 16773 to 2418 computations (85.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series197.0ms (0.8%)

Counts
3 → 76
Calls

3 calls:

117.0ms
(-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))
77.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)
3.0ms
(pow.f64 (cos.f64 delta) 2)

rewrite82.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
321×expm1-udef_binary64
321×log1p-udef_binary64
180×add-sqr-sqrt_binary64
173×log1p-expm1-u_binary64
173×expm1-log1p-u_binary64
Counts
3 → 85
Calls

3 calls:

80.0ms
(pow.f64 (cos.f64 delta) 2)
80.0ms
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)
80.0ms
(-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01772
136072
2427972
3518972

simplify99.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
528×fma-neg_binary64
380×distribute-rgt-neg-in_binary64
352×unswap-sqr_binary64
348×distribute-lft-neg-in_binary64
339×associate-*r*_binary64
Counts
161 → 140
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01834781
16234765
225764765
351054765

prune940.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2264230
Fresh257
Picked101
Done011
Total22910239
Error
0.0b
Counts
239 → 10
Alt Table
StatusErrorProgram
✓0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
10.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 phi1) delta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))) 3)))))
0.3b
(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (+.f64 (pow.f64 (cos.f64 delta) 2) (*.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (pow.f64 (cos.f64 delta) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))) 1))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 delta) 2))) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))))))
▶0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (+.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)) (fma.f64 (neg.f64 (pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)) (pow.f64 (sin.f64 phi1) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)))))
26.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (*.f64 1/2 (*.f64 (cos.f64 phi1) (*.f64 theta theta))) (*.f64 1/720 (*.f64 (cos.f64 phi1) (pow.f64 theta 6))))) (-.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (*.f64 1/24 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)))))))))
Compiler

Compiled 17546 to 5058 computations (71.2% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)
✓0.4b
(pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)
0.4b
(-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))
✓44.5b
(fma.f64 (neg.f64 (pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)) (pow.f64 (sin.f64 phi1) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))

series656.0ms (2.6%)

Counts
2 → 72
Calls

2 calls:

596.0ms
(fma.f64 (neg.f64 (pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)) (pow.f64 (sin.f64 phi1) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))
60.0ms
(pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)

rewrite77.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
322×expm1-udef_binary64
322×log1p-udef_binary64
193×add-sqr-sqrt_binary64
182×log1p-expm1-u_binary64
182×expm1-log1p-u_binary64
Counts
2 → 55
Calls

2 calls:

74.0ms
(pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)
74.0ms
(fma.f64 (neg.f64 (pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)) (pow.f64 (sin.f64 phi1) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01987
139184
2418884
3505984

simplify94.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
568×sub-neg_binary64
537×*-commutative_binary64
515×cancel-sign-sub-inv_binary64
333×associate--l+_binary64
314×associate-+l+_binary64
Counts
127 → 81
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01311446
14241444
214891396
341691396
448271396
551021396

prune1.1s (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2440244
Fresh088
Picked011
Done011
Total24410254
Error
0.0b
Counts
254 → 10
Alt Table
StatusErrorProgram
✓0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (fma.f64 (neg.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (sin.f64 phi1) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))))))
10.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (*.f64 (cos.f64 phi1) (-.f64 (cos.f64 phi1) (*.f64 (cos.f64 theta) (*.f64 (sin.f64 phi1) delta))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))) 3)))))
0.3b
(+.f64 lambda1 (atan2.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 phi1) (*.f64 (sin.f64 delta) (sin.f64 theta)))) 3) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)) (+.f64 (pow.f64 (cos.f64 delta) 2) (*.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (+.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) (cos.f64 delta)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (pow.f64 (cos.f64 delta) 2) (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))) 1))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (-.f64 (expm1.f64 (log1p.f64 (pow.f64 (cos.f64 delta) 2))) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2))))))
✓0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 1 (/.f64 (+.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))))) (+.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)) (fma.f64 (neg.f64 (pow.f64 (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta))) 2)) (pow.f64 (sin.f64 phi1) 2) (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 2)))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (fma.f64 (cos.f64 delta) (sin.f64 phi1) (*.f64 (*.f64 (sin.f64 delta) (cos.f64 phi1)) (cos.f64 theta)))) 3)))))
26.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (+.f64 (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (*.f64 1/2 (*.f64 (cos.f64 phi1) (*.f64 theta theta))) (*.f64 1/720 (*.f64 (cos.f64 phi1) (pow.f64 theta 6))))) (-.f64 (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi1)) (cos.f64 delta)) (*.f64 (*.f64 (sin.f64 phi1) (sin.f64 delta)) (+.f64 (cos.f64 phi1) (*.f64 1/24 (*.f64 (cos.f64 phi1) (pow.f64 theta 4)))))))))
Compiler

Compiled 29324 to 7723 computations (73.7% saved)

regimes2.0s (8.1%)

Accuracy

Total 0.1b remaining (68.5%)

Threshold costs 0.1b (68.5%)

Counts
193 → 1
Compiler

Compiled 71244 to 36288 computations (49.1% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
8×*-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
023105
139105
248105
353105
455105
555105

end286.0ms (1.1%)

Compiler

Compiled 754 to 332 computations (56% saved)

Profiling

Loading profile data...