Details

Time bar (total: 12.5s)

sample259.0ms

Algorithm
intervals
Results
180.0ms140×body1280valid
48.0ms63×body640valid
7.0ms14×body320valid
4.0ms33×body80valid
2.0ms6×body160valid

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02715
14615
27115
37715
47715

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b
(sin (- lambda1 lambda2))
2.6b
(cos (- lambda1 lambda2))

rewrite67.0ms

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×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×sub-neg cos-sum sin-sum *-commutative
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff sin-cos-mult unswap-sqr
Counts
4 → 59
Calls
4 calls:
11.0ms
(* (cos phi1) (sin phi2))
33.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms
(sin (- lambda1 lambda2))
11.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (cos phi1) (sin phi2))
98.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms
(sin (- lambda1 lambda2))
19.0ms
(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0286430
11077367
24907367
35001367

prune375.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin lambda1) (cos lambda2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b
(cos (- lambda1 lambda2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×cos-diff *-commutative
2×cos-sum sin-cos-mult unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in associate-*l/
Counts
4 → 68
Calls
4 calls:
13.0ms
(* (sin lambda1) (cos lambda2))
11.0ms
(* (cos phi1) (sin phi2))
29.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms
(cos (- lambda1 lambda2))

series207.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin lambda1) (cos lambda2))
44.0ms
(* (cos phi1) (sin phi2))
97.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms
(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0340481
11343409
25002409

prune441.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-exp-log add-cbrt-cube
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
4×*-commutative sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult unswap-sqr
Counts
4 → 87
Calls
4 calls:
11.0ms
(* (cos phi1) (sin phi2))
12.0ms
(* (sin lambda1) (sin lambda2))
42.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
47.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos phi1) (sin phi2))
52.0ms
(* (sin lambda1) (sin lambda2))
120.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
108.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify58.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0420777
11833599
25001599

prune464.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.9b
(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
30×add-exp-log add-cbrt-cube
17×pow-prod-down prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
5×associate-*r* associate-*l* add-log-exp
4×sin-cos-mult
3×log-prod log-pow *-commutative sin-mult
2×frac-times associate-*r/ associate-*l/ cos-mult
1×exp-prod exp-to-pow rem-log-exp unswap-sqr
Counts
4 → 83
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
42.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
42.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
11.0ms
(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin lambda1) (sin lambda2))
123.0ms
(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
109.0ms
(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
106.0ms
(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0355838
11625649
25002649

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes454.0ms

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
03943
13943

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.9s4525×body1280valid
1.5s2040×body640valid
292.0ms585×body320valid
104.0ms637×body80valid
61.0ms213×body160valid