Details

Time bar (total: 9.5s)

sample174.0ms

Algorithm
intervals
Results
101.0ms112×body1280valid
35.0ms69×body640valid
13.0ms37×body320valid
8.0ms17×body160valid
2.0ms21×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.2b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.3b
(sin (- lambda1 lambda2))
5.3b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
11×cos-sum sin-sum
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cos-diff fma-def
2×sub-neg associate-+r+
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 69
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
6.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms
(sin (- lambda1 lambda2))
5.0ms
(cos (- lambda1 lambda2))

series151.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify71.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune325.0ms

Filtered
81 candidates to 55 candidates (67.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New661581
Fresh000
Picked101
Done000
Total671582

Merged error: 1.0b

Counts
82 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
5.3b
(sin (- lambda1 lambda2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×sin-sum
9×prod-diff
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×sub-neg pow-prod-down prod-exp sin-diff *-commutative cbrt-unprod fma-udef sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
1.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
5.0ms
(sin (- lambda1 lambda2))

series213.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
50.0ms
(* (sin lambda1) (sin lambda2))
128.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms
(sin (- lambda1 lambda2))

simplify73.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0310819
1773667
22958665
35002641

prune342.0ms

Filtered
73 candidates to 52 candidates (71.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New71273
Fresh31114
Picked101
Done000
Total751388

Merged error: 0.1b

Counts
88 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin lambda1) (sin lambda2))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×fma-udef
1×+-commutative associate-+l+ flip3-+ pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
4.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
1.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
5.0ms
(* (sin lambda1) (sin lambda2))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series397.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
49.0ms
(* (sin lambda1) (sin lambda2))
129.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify152.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0261833
1919744
24867738
35001738

prune372.0ms

Filtered
69 candidates to 57 candidates (82.6%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh21012
Picked101
Done000
Total691382

Merged error: 0.1b

Counts
82 → 13

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
0.7b
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow cube-prod fma-udef
1×cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 55
Calls
4 calls:
1.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
1.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

series559.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(fma (cos lambda1) (* (cos phi2) (cos lambda2)) (cos phi1))
126.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
128.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
180.0ms
(pow (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) 3)

simplify181.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0170548
1633507
24290499
35001499

prune399.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New63467
Fresh21012
Picked101
Done000
Total661480

Merged error: 0.1b

Counts
80 → 14

regimes569.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04059
14059

end0.0ms

sample5.4s

Algorithm
intervals
Results
3.3s3547×body1280valid
1.3s2372×body640valid
342.0ms944×body320valid
96.0ms417×body160valid
82.0ms720×body80valid