Details

Time bar (total: 8.8s)

sample172.0ms

Algorithm
intervals
Results
104.0ms117×body1280valid
39.0ms76×body640valid
8.0ms28×body320valid
3.0ms13×body160valid
2.0ms22×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02012
12312
22312

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b
(sin (- lambda1 lambda2))
3.9b
(cos (- lambda1 lambda2))

rewrite41.0ms

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:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(sin (- lambda1 lambda2))
13.0ms
(cos (- lambda1 lambda2))

series145.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(sin (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune293.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b
(cos (- lambda1 lambda2))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×cos-sum prod-diff
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u
3×cos-diff sub-neg fma-def associate-*r* associate-*l*
2×associate-+r+ associate-*r/
1×+-commutative flip3-- flip3-+ pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod flip-+ unswap-sqr
Counts
4 → 76
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
59.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
13.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(cos (- lambda1 lambda2))

series237.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
122.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
87.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
15.0ms
(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04271128
11340942
25001940

prune437.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.2b
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative sin-mult
1×associate-*l/ fma-udef unswap-sqr
Counts
4 → 61
Calls
4 calls:
28.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
11.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series233.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (* (sin lambda1) (sin lambda2)) (cos phi2))
16.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
39.0ms
(* (sin lambda1) (sin lambda2))
109.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify100.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0226727
1898621
24339620
35002620

prune380.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
3.9b
(cos (- lambda1 lambda2))
3.9b
(cos (- lambda1 lambda2))
3.9b
(cos (- lambda1 lambda2))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
33×cos-sum
30×prod-diff
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×cos-diff
4×pow1 add-exp-log expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u
2×associate--l+
1×distribute-rgt-in flip3-- distribute-lft-in fma-neg diff-log flip--
Counts
4 → 83
Calls
4 calls:
16.0ms
(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
13.0ms
(cos (- lambda1 lambda2))
13.0ms
(cos (- lambda1 lambda2))
15.0ms
(cos (- lambda1 lambda2))

series141.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(- (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
14.0ms
(cos (- lambda1 lambda2))
17.0ms
(cos (- lambda1 lambda2))
15.0ms
(cos (- lambda1 lambda2))

simplify89.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
03001229
1737925
23213916
35001840

prune444.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes413.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02923
12923

end0.0ms

sample5.3s

Algorithm
intervals
Results
3.2s3584×body1280valid
1.2s2332×body640valid
313.0ms914×body320valid
103.0ms445×body160valid
69.0ms725×body80valid