Details

Time bar (total: 45.9s)

sample843.0ms

Algorithm
intervals
Results
591.0ms148×body1280valid
188.0ms64×body640valid
23.0ms17×body320valid
10.0ms23×body80valid
3.0ms4×body160valid

simplify68.0ms

Counts
1 → 1
Iterations
IterNodes
580
480
377
247
128
017

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b
(cos (- lambda1 lambda2))
5.2b
(sin (- lambda1 lambda2))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×prod-diff
11×pow1 cos-sum add-cbrt-cube sin-sum add-exp-log
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cos-diff
2×sub-neg *-commutative sin-cos-mult
1×distribute-rgt-in distribute-lft-in associate-*l/ sin-diff unswap-sqr
Counts
4 → 90
Calls
4 calls:
44.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
71.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms
(cos (- lambda1 lambda2))
21.0ms
(sin (- lambda1 lambda2))

series326.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* (sin (- lambda1 lambda2)) (cos phi2))
153.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms
(cos (- lambda1 lambda2))
31.0ms
(sin (- lambda1 lambda2))

simplify1.9s

Counts
102 → 102
Iterations
IterNodes
33293
2978
1425
0214

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.9b

localize114.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (cos lambda1) (sin lambda2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b
(cos (- lambda1 lambda2))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×pow1 add-cbrt-cube add-exp-log
11×cos-sum
9×associate-*r* prod-diff
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cos-diff associate-*l/ *-commutative
2×unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- sin-cos-mult flip--
Counts
4 → 90
Calls
4 calls:
76.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
15.0ms
(* (cos lambda1) (sin lambda2))
53.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms
(cos (- lambda1 lambda2))

series453.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
77.0ms
(* (cos lambda1) (sin lambda2))
129.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms
(cos (- lambda1 lambda2))

simplify4.9s

Counts
102 → 102
Iterations
IterNodes
34666
21328
1481
0225

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize104.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1 add-cbrt-cube add-exp-log
18×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt
8×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u sin-cos-mult add-log-exp
3×sin-mult
2×frac-times associate-*l/ associate-*r/ cos-mult unswap-sqr
Counts
4 → 99
Calls
4 calls:
44.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
21.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (cos lambda1) (sin lambda2))
44.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
69.0ms
(* (sin lambda1) (sin lambda2))
58.0ms
(* (cos lambda1) (sin lambda2))
134.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify3.3s

Counts
111 → 111
Iterations
IterNodes
37124
21509
1441
0167

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize104.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-cbrt-cube add-exp-log
16×pow-prod-down prod-exp cbrt-unprod
13×add-sqr-sqrt
10×associate-*l*
9×*-un-lft-identity add-cube-cbrt
8×associate-*r*
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r/ sin-mult
2×sin-cos-mult unswap-sqr
1×frac-times associate-*l/ cos-mult
Counts
4 → 96
Calls
4 calls:
18.0ms
(* (sin lambda1) (sin lambda2))
16.0ms
(* (cos lambda1) (sin lambda2))
81.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
66.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series419.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (sin lambda1) (sin lambda2))
58.0ms
(* (cos lambda1) (sin lambda2))
156.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
142.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify2.9s

Counts
108 → 108
Iterations
IterNodes
37285
21539
1439
0172

prune861.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes632.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
241
141
029

end0.0ms

sample24.6s

Algorithm
intervals
Results
17.4s4509×body1280valid
5.3s2043×body640valid
978.0ms555×body320valid
320.0ms664×body80valid
185.0ms229×body160valid