Details

Time bar (total: 14.0s)

analyze2.9s (20.9%)

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)

sample313.0ms (2.2%)

Algorithm
1×intervals
Results
144.0ms141×body1024valid
24.0ms50×body512valid
11.0ms5×body2048valid
7.0ms23×body256valid
6.0ms37×body128valid
Compiler

Compiled 53 to 33 computations (37.7% saved)

simplify35.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
284×fma-def_binary64
141×fma-neg_binary64
44×distribute-rgt-in_binary64
38×cancel-sign-sub-inv_binary64
37×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01532
12130
22830
33530
44230
56830
69830
713230
817630
922030
1028830
1131030
1234630
1339330
1440330
1542130
1644230
1744930
1847030
1947830
2048030
2145330

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
Compiler

Compiled 137 to 71 computations (48.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
✓0.4b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
✓4.4b
(sin.f64 (-.f64 lambda1 lambda2))
✓4.5b
(cos.f64 (-.f64 lambda1 lambda2))

series57.0ms (0.4%)

Counts
4 → 76
Calls

4 calls:

31.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
17.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
4.0ms
(cos.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
39×sin-sum_binary64
36×add-sqr-sqrt_binary64
36×prod-diff_binary64
34×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
Counts
4 → 102
Calls

4 calls:

8.0ms
(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
5.0ms
(cos.f64 (-.f64 lambda1 lambda2))
4.0ms
(sin.f64 (-.f64 lambda1 lambda2))
0.0ms
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))

simplify161.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
394×fma-neg_binary64
343×distribute-rgt-neg-in_binary64
318×associate-*r*_binary64
302×distribute-lft-neg-in_binary64
294×associate-*l*_binary64
Counts
178 → 207
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03844373
17473586
222483335
346143218
449503210
550313210

prune353.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New19413207
Fresh101
Picked101
Done000
Total19613209
Error
0.6b
Counts
209 → 13
Alt Table
StatusErrorProgram
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.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))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
14.8b
(+.f64 lambda1 (atan2.f64 (+.f64 (*.f64 (*.f64 (sin.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 phi2)) (*.f64 (*.f64 (cos.f64 (fma.f64 1 lambda1 (neg.f64 (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (sin.f64 (fma.f64 (neg.f64 (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)) (*.f64 (cbrt.f64 lambda2) (*.f64 (cbrt.f64 lambda2) (cbrt.f64 lambda2)))))) (cos.f64 phi2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (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) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.2b
(+.f64 lambda1 (atan2.f64 (-.f64 (+.f64 (*.f64 (cos.f64 phi2) (sin.f64 (neg.f64 lambda2))) (*.f64 (cos.f64 phi2) (*.f64 (cos.f64 (neg.f64 lambda2)) lambda1))) (*.f64 1/2 (*.f64 (cos.f64 phi2) (*.f64 (sin.f64 (neg.f64 lambda2)) (pow.f64 lambda1 2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
5.5b
(+.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))))
14.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (*.f64 lambda2 lambda2) -1/2)))))))
5.5b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
26.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (-.f64 (+.f64 (*.f64 1/24 (pow.f64 phi1 4)) (+.f64 1 (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))) (+.f64 (*.f64 1/2 (pow.f64 phi1 2)) (*.f64 1/720 (pow.f64 phi1 6))))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
Compiler

Compiled 8394 to 2281 computations (72.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))
✓0.2b
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.4b
(fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))
4.5b
(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms (0.4%)

Counts
2 → 84
Calls

2 calls:

39.0ms
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
12.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))

rewrite10.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
6×add-sqr-sqrt_binary64
4×*-un-lft-identity_binary64
4×add-cube-cbrt_binary64
4×add-cbrt-cube_binary64
4×add-exp-log_binary64
Counts
2 → 37
Calls

2 calls:

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

simplify150.0ms (1.1%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
01674328
14354135
215204072
341934062
447774062
549514062

prune433.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1755180
Fresh6612
Picked101
Done000
Total18211193
Error
0.0b
Counts
193 → 11
Alt Table
StatusErrorProgram
1.2b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
▶0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.5b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
14.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (*.f64 lambda2 lambda2) -1/2)))))))
Compiler

Compiled 7807 to 1794 computations (77% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b
(*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
✓0.2b
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
✓0.4b
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))

series86.0ms (0.6%)

Counts
3 → 104
Calls

3 calls:

61.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
15.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))
10.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite7.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
7×add-sqr-sqrt_binary64
5×*-un-lft-identity_binary64
5×add-cube-cbrt_binary64
5×add-cbrt-cube_binary64
5×add-exp-log_binary64
Counts
3 → 40
Calls

3 calls:

4.0ms
(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.0ms
(fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))
0.0ms
(atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1)))

simplify144.0ms (1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
02105476
15815020
218904940
346314940
453164940

prune431.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1810181
Fresh01010
Picked011
Done000
Total18111192
Error
0.0b
Counts
192 → 11
Alt Table
StatusErrorProgram
1.2b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
▶0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
✓0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.5b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
14.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (*.f64 lambda2 lambda2) -1/2)))))))
Compiler

Compiled 8760 to 1821 computations (79.2% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))
✓0.4b
(fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))
✓0.5b
(expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))
4.5b
(cos.f64 (-.f64 lambda1 lambda2))

series49.0ms (0.4%)

Counts
3 → 96
Calls

3 calls:

31.0ms
(fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))
12.0ms
(expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))

rewrite2.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
4×log1p-expm1-u_binary64
3×*-un-lft-identity_binary64
3×add-sqr-sqrt_binary64
3×add-cube-cbrt_binary64
3×add-cbrt-cube_binary64
Counts
3 → 32
Calls

3 calls:

0.0ms
(fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))
0.0ms
(expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))
0.0ms
(log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2))))

simplify87.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
718×cancel-sign-sub-inv_binary64
360×associate--l+_binary64
329×neg-sub0_binary64
325×neg-mul-1_binary64
277×unsub-neg_binary64
Counts
128 → 112
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02032242
15952117
220622006
343301994
449991994

prune327.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1540154
Fresh099
Picked011
Done011
Total15411165
Error
0.0b
Counts
165 → 11
Alt Table
StatusErrorProgram
1.2b
(+.f64 lambda1 (*.f64 (*.f64 (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))) (cbrt.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (sin.f64 (-.f64 lambda1 lambda2))))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
1.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (*.f64 (*.f64 (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)))) (cbrt.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
✓0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (log1p.f64 (expm1.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
✓0.1b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (+.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (log.f64 (exp.f64 (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))))
5.5b
(+.f64 lambda1 (atan2.f64 (cbrt.f64 (pow.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) 3)) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
0.7b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (fma.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)) (cos.f64 phi1))))
0.9b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cbrt.f64 (cos.f64 (-.f64 lambda1 lambda2)))) (cos.f64 phi1))))
0.8b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (-.f64 (*.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (fma.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2) (cos.f64 phi1)) 3))))
14.5b
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (fma.f64 (cos.f64 lambda1) (cos.f64 phi2) (cos.f64 phi1)) (*.f64 (cos.f64 phi2) (fma.f64 lambda2 (sin.f64 lambda1) (*.f64 (cos.f64 lambda1) (*.f64 (*.f64 lambda2 lambda2) -1/2)))))))
Compiler

Compiled 6568 to 1637 computations (75.1% saved)

regimes1.4s (9.8%)

Accuracy

Total 0.1b remaining (49.7%)

Threshold costs 0.1b (49.7%)

Counts
157 → 1
Compiler

Compiled 35077 to 20429 computations (41.8% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
7×*-commutative_binary64
5×+-commutative_binary64
4×sub-neg_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02052
13052
24052
34652
45052
55152
65152

end1.0ms (0%)

Compiler

Compiled 36 to 19 computations (47.2% saved)

sample6.9s (49.1%)

Algorithm
1×intervals
Results
4.6s4457×body1024valid
901.0ms1766×body512valid
305.0ms111×body2048valid
252.0ms739×body256valid
155.0ms927×body128valid
Compiler

Compiled 489 to 245 computations (49.9% saved)

Profiling

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