Details

Time bar (total: 17.3s)

analyze2.8s (16.2%)

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)

sample8.0s (46%)

Results
5.7s4623×body1024valid
1.3s1803×body512valid
380.0ms767×body256valid
279.0ms111×body2048valid
249.0ms952×body128valid
Compiler

Compiled 74 to 44 computations (40.5% saved)

simplify27.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
284×fma-def_binary64
141×fma-neg_binary64
44×distribute-rgt-in_binary64
39×cancel-sign-sub-inv_binary64
35×sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01532
12130
22830
33530
44530
57130
611530
716830
824030
932730
1045430
1160030
1264630
1374830
1485230
1587430
1690730
1795130
1899430
19101530
20101730
Stop Event
1×saturated
Counts
1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.5b
(+.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))))
0.5b
(+.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)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
✓0.5b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓3.0b
(sin.f64 (-.f64 lambda1 lambda2))
✓3.2b
(cos.f64 (-.f64 lambda1 lambda2))

series45.0ms (0.3%)

Counts
4 → 64
Calls

4 calls:

27.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
8.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
6.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))

rewrite61.0ms (0.4%)

Algorithm
1×batch-egg-rewrite
Rules
671×prod-diff_binary64
268×log1p-udef_binary64
147×add-sqr-sqrt_binary64
137×log1p-expm1-u_binary64
137×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01353
127453
2359953
Stop Event
1×node limit
Counts
4 → 117
Calls

4 calls:

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

simplify35.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
609×cancel-sign-sub-inv_binary64
482×fma-def_binary64
475×associate-*r*_binary64
458×associate-*l*_binary64
200×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01211354
13911249
213431165
Stop Event
1×node limit
Counts
181 → 178

prune299.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16711178
Fresh011
Picked101
Done000
Total16812180
Error
0.3b
Counts
180 → 12
Alt Table
StatusErrorProgram
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
0.5b
(+.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))))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (log.f64 (exp.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
12.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
3.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
6.1b
(+.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))))
28.3b
(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3) 1/3))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
2.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (pow.f64 (cos.f64 phi1) 2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))
▶0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 6360 to 1643 computations (74.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
✓0.5b
(fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))
✓0.6b
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
3.0b
(sin.f64 (-.f64 lambda1 lambda2))

series834.0ms (4.8%)

Counts
3 → 96
Calls

3 calls:

789.0ms
(fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))
25.0ms
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)
19.0ms
(*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

rewrite44.0ms (0.3%)

Algorithm
1×batch-egg-rewrite
Rules
268×log1p-expm1-u_binary64
268×expm1-log1p-u_binary64
263×add-cbrt-cube_binary64
252×add-log-exp_binary64
251×add-cube-cbrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02497
155895
Stop Event
1×node limit
Counts
3 → 47
Calls

3 calls:

43.0ms
(*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
43.0ms
(fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))
43.0ms
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)

simplify126.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
766×fma-def_binary64
761×cancel-sign-sub-inv_binary64
452×unswap-sqr_binary64
301×associate-*r*_binary64
216×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02017863
16567823
228227608
Stop Event
1×node limit
Counts
143 → 116

prune538.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1773180
Fresh2911
Picked101
Done000
Total18012192
Error
0.0b
Counts
192 → 12
Alt Table
StatusErrorProgram
28.3b
(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3) 1/3))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (log.f64 (exp.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3))) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))))
12.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
3.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
2.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (pow.f64 (cos.f64 phi1) 2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))
▶0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))))
6.1b
(+.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))))
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (*.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)))) (cos.f64 phi1))))
Compiler

Compiled 15820 to 4349 computations (72.5% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.4b
(*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
0.5b
(fma.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) (cos.f64 phi1))
0.6b
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)

series314.0ms (1.8%)

Counts
1 → 24
Calls

1 calls:

314.0ms
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite28.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
222×log1p-expm1-u_binary64
222×expm1-log1p-u_binary64
221×add-sqr-sqrt_binary64
217×add-cbrt-cube_binary64
206×add-log-exp_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01967
146165
Stop Event
1×node limit
Counts
1 → 18
Calls

1 calls:

27.0ms
(/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (+.f64 (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (-.f64 (*.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (*.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify41.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
634×unswap-sqr_binary64
494×fma-neg_binary64
410×distribute-rgt-neg-in_binary64
384×distribute-lft-neg-in_binary64
321×associate-*r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0571394
11931388
26091284
325911282
Stop Event
1×node limit
Counts
42 → 35

prune431.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1492151
Fresh2911
Picked101
Done000
Total15211163
Error
0.0b
Counts
163 → 11
Alt Table
StatusErrorProgram
28.3b
(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3) 1/3))
▶0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)) (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) -1) (cos.f64 phi1))))
12.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
3.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
6.1b
(+.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))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (*.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)))) (cos.f64 phi1))))
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
2.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (pow.f64 (cos.f64 phi1) 2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 13017 to 3875 computations (70.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
✓0.4b
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)
✓0.5b
(fma.f64 (cos.f64 phi2) (pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)) (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) -1) (cos.f64 phi1))
0.6b
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3)

series1.3s (7.3%)

Counts
3 → 96
Calls

3 calls:

1.2s
(fma.f64 (cos.f64 phi2) (pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)) (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) -1) (cos.f64 phi1))
25.0ms
(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
17.0ms
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)

rewrite37.0ms (0.2%)

Algorithm
1×batch-egg-rewrite
Rules
265×log1p-expm1-u_binary64
265×expm1-log1p-u_binary64
258×add-cbrt-cube_binary64
250×add-cube-cbrt_binary64
250×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02598
156498
Stop Event
1×node limit
Counts
3 → 48
Calls

3 calls:

36.0ms
(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
36.0ms
(pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)
36.0ms
(fma.f64 (cos.f64 phi2) (pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)) (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) -1) (cos.f64 phi1))

simplify128.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
789×fma-def_binary64
482×unswap-sqr_binary64
312×associate-*r*_binary64
278×fma-neg_binary64
217×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02107911
16867875
229477674
Stop Event
1×node limit
Counts
144 → 115

prune407.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1460146
Fresh01010
Picked011
Done000
Total14611157
Error
0.0b
Counts
157 → 11
Alt Table
StatusErrorProgram
28.3b
(+.f64 lambda1 (pow.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3) 1/3))
✓0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (pow.f64 (/.f64 (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)) (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))) -1) (cos.f64 phi1))))
12.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (pow.f64 (sqrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2)))
3.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (*.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (*.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
6.1b
(+.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))))
0.2b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (fma.f64 (sin.f64 lambda1) (cos.f64 lambda2) (neg.f64 (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))) (+.f64 (*.f64 (cos.f64 phi2) (/.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 3) (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)) (fma.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (-.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (pow.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) 2)))) (cos.f64 phi1))))
0.6b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) 3))))
0.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
2.4b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (/.f64 (-.f64 (*.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) (pow.f64 (cos.f64 phi1) 2)) (-.f64 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (cos.f64 phi1)))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (pow.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 2))))
6.2b
(+.f64 lambda1 (cbrt.f64 (pow.f64 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) 3)))
Compiler

Compiled 12498 to 4095 computations (67.2% saved)

regimes1.5s (8.7%)

Accuracy

Total 0.1b remaining (55.2%)

Threshold costs 0.1b (55.2%)

Counts
144 → 1
Compiler

Compiled 45885 to 23719 computations (48.3% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
031104
148104
265104
374104
479104
580104
Stop Event
1×saturated

end267.0ms (1.5%)

Compiler

Compiled 563 to 278 computations (50.6% saved)

Profiling

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