Details

Time bar (total: 24.7s)

analyze5.3s (21.4%)

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
1.2%98.6%0.2%11
1.4%98.4%0.2%12
10.8%88.9%0.2%13
10.8%88.9%0.2%14
Compiler

Compiled 39 to 24 computations (38.5% saved)

sample430.0ms (1.7%)

Algorithm
intervals
Results
195.0ms116×body1024valid
45.0ms47×body512valid
17.0ms68×body128valid
14.0ms25×body256valid
Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify52.0ms (0.2%)

Algorithm
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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
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 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
Compiler

Compiled 146 to 78 computations (46.6% 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)))))))

series145.0ms (0.6%)

Counts
4 → 132
Calls

4 calls:

74.0ms
(-.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)))))))
52.0ms
(*.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))))))
10.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
8.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

rewrite16.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 72
Calls

4 calls:

4.0ms
(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms
(*.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))))))
3.0ms
(-.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)))))))
1.0ms
(asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify189.0ms (0.8%)

Algorithm
egg-herbie
Rules
447×fma-neg_binary64
377×distribute-rgt-neg-in_binary64
326×distribute-lft-neg-in_binary64
259×associate-*r*_binary64
241×neg-mul-1_binary64
Counts
204 → 185
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02626113
16975704
222285493
347995493
449925493
549275493

prune296.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1769185
Fresh000
Picked101
Done000
Total1779186
Error
0.0b
Counts
186 → 9
Alt Table
StatusErrorProgram
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.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)))))))))
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
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 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
26.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 theta) (sin.f64 delta))) (sqrt.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)))))))))
3.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (*.f64 (*.f64 (sin.f64 delta) (sin.f64 delta)) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
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 (log.f64 (exp.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
Compiler

Compiled 8726 to 1931 computations (77.9% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series1.0s (4.2%)

Counts
4 → 144
Calls

4 calls:

803.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
156.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))
64.0ms
(*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
6.0ms
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

rewrite30.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
11×pow1_binary64
times-frac_binary64
Counts
4 → 92
Calls

4 calls:

7.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
7.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))
4.0ms
(*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
0.0ms
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))

simplify292.0ms (1.2%)

Algorithm
egg-herbie
Rules
601×fma-def_binary64
492×associate-/l*_binary64
470×times-frac_binary64
256×*-commutative_binary64
169×associate-*r*_binary64
Counts
236 → 231
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
071422674
1236521377
2534321377

prune853.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2692271
Fresh178
Picked101
Done000
Total2719280
Error
0.0b
Counts
280 → 9
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.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)))))))))
26.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 theta) (sin.f64 delta))) (sqrt.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)))))))))
3.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (*.f64 (*.f64 (sin.f64 delta) (sin.f64 delta)) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
Compiler

Compiled 32693 to 8263 computations (74.7% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
0.3b
(asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))
0.4b
(*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))
0.5b
(fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))

series1.0s (4%)

Counts
2 → 72
Calls

2 calls:

838.0ms
(/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
161.0ms
(fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))

rewrite9.0ms (0%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

2.0ms
(/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
0.0ms
(fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))

simplify220.0ms (0.9%)

Algorithm
egg-herbie
Rules
466×associate-/l*_binary64
465×times-frac_binary64
425×fma-def_binary64
282×associate-/r*_binary64
206×*-commutative_binary64
Counts
111 → 116
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
055417090
1189016284
2497716284

prune1.1s (4.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2420242
Fresh088
Picked011
Done000
Total2429251
Error
0.0b
Counts
251 → 9
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.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)))))))))
26.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 theta) (sin.f64 delta))) (sqrt.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)))))))))
3.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (*.f64 (*.f64 (sin.f64 delta) (sin.f64 delta)) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
Compiler

Compiled 29456 to 7951 computations (73% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series1.1s (4.4%)

Counts
3 → 108
Calls

3 calls:

851.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
164.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2)))
67.0ms
(pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2)

rewrite19.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
13×add-cube-cbrt_binary64
times-frac_binary64
add-exp-log_binary64
Counts
3 → 69
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))
5.0ms
(-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2)))
2.0ms
(pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2)

simplify249.0ms (1%)

Algorithm
egg-herbie
Rules
596×fma-def_binary64
483×associate-/l*_binary64
468×times-frac_binary64
246×*-commutative_binary64
163×+-commutative_binary64
Counts
177 → 192
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
068218301
1229417646
2517517646

prune784.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2120212
Fresh077
Picked011
Done011
Total2129221
Error
0.0b
Counts
221 → 9
Alt Table
StatusErrorProgram
0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (fma.f64 (cos.f64 delta) (cos.f64 delta) (neg.f64 (*.f64 (pow.f64 (sin.f64 phi1) 2) (*.f64 (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))))))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (*.f64 (sin.f64 phi1) delta) (cos.f64 theta))))))
0.3b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 theta)) (cbrt.f64 (sin.f64 theta))) (*.f64 (cbrt.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)))))))))
26.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (sin.f64 theta) (sin.f64 delta))) (sqrt.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)))))))))
3.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 theta)) (sin.f64 theta)) (*.f64 (*.f64 (sin.f64 delta) (sin.f64 delta)) (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)))))))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.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 (-.f64 (*.f64 (cos.f64 delta) (cos.f64 delta)) (*.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (fma.f64 (sin.f64 delta) (*.f64 (cos.f64 theta) (cos.f64 phi1)) (*.f64 (cos.f64 delta) (sin.f64 phi1))) 2))) (fma.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta))))) (cos.f64 delta)))))
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) (sin.f64 (asin.f64 (fma.f64 (sin.f64 phi1) (cos.f64 delta) (*.f64 (*.f64 (cos.f64 phi1) (cos.f64 theta)) (sin.f64 delta)))))))))))
Compiler

Compiled 23861 to 7809 computations (67.3% saved)

regimes862.0ms (3.5%)

Accuracy

Total 0.1b remaining (70.2%)

Threshold costs 0.1b (70.2%)

Counts
82 → 1
Compiler

Compiled 27683 to 14868 computations (46.3% saved)

simplify6.0ms (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
03099
14599
25399
35899
46099
55899

end1.0ms (0%)

Compiler

Compiled 65 to 29 computations (55.4% saved)

sample10.7s (43.1%)

Algorithm
intervals
Results
7.4s3909×body1024valid
1.5s1287×body512valid
609.0ms2202×body128valid
372.0ms594×body256valid
35.0msbody2048valid
Compiler

Compiled 542 to 288 computations (46.9% saved)

Profiling

Loading profile data...