Details

Time bar (total: 9.4s)

sample189.0ms

Algorithm
intervals
Results
120.0ms125×body1280valid
36.0ms69×body640valid
12.0ms31×body320valid
4.0ms13×body160valid
3.0ms18×body80valid

simplify5.0ms

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: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b
(sin (- lambda1 lambda2))
3.5b
(cos (- lambda1 lambda2))

rewrite24.0ms

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)))))
7.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms
(sin (- lambda1 lambda2))
8.0ms
(cos (- lambda1 lambda2))

series149.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
99.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(sin (- lambda1 lambda2))
18.0ms
(cos (- lambda1 lambda2))

simplify68.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
03651011
1800787
22597784
35002735

prune297.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
3.5b
(sin (- lambda1 lambda2))

rewrite14.0ms

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:
4.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
8.0ms
(sin (- lambda1 lambda2))

series202.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
13.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1)) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
122.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
21.0ms
(sin (- lambda1 lambda2))

simplify72.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0310819
1773667
22958665
35002641

prune377.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×sub-neg associate-*r/ prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- fma-udef sin-mult
Counts
4 → 68
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
18.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(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)))))
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

series323.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin lambda1) (sin lambda2))
136.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
19.0ms
(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)))))
122.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))

simplify125.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0292936
11106822
24839821
35001821

prune438.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))
7.2b
(cbrt (* (sin lambda1) (sin lambda2)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod cbrt-div pow1/3 sin-mult
1×fma-udef
Counts
4 → 46
Calls
4 calls:
0.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
2.0ms
(cbrt (* (sin lambda1) (sin lambda2)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(fma (cos lambda1) (* (cos lambda2) (cos phi2)) (cos phi1))
89.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
91.0ms
(cbrt (* (sin lambda1) (sin lambda2)))
96.0ms
(cbrt (* (sin lambda1) (sin lambda2)))

simplify167.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
0129413
1321369
21044344
34460329
45001329

prune344.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes458.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03330
13330

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.4s3565×body1280valid
1.3s2381×body640valid
366.0ms935×body320valid
108.0ms403×body160valid
100.0ms715×body80valid
2.0ms1×body2560valid