Details

Time bar (total: 37.2s)

sample1.0s

Algorithm
intervals
Results
400.0ms153×body1280valid
86.0ms59×body640valid
18.0ms19×body320valid
14.0ms19×body80valid
3.0ms6×body160valid

simplify58.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
12724
24624
37124
47224
done7224

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b
(sin (- lambda1 lambda2))
3.8b
(cos (- lambda1 lambda2))

rewrite104.0ms

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:
22.0ms
(* (cos phi1) (sin phi2))
38.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

series274.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (cos phi1) (sin phi2))
141.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify6.4s

Counts
71 → 71
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
0128709
1284697
2873607
32313599
44027599
done5000599

prune401.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b
(cos (- lambda1 lambda2))

rewrite138.0ms

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 associate-*l/ *-commutative
2×cos-sum unswap-sqr
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in sin-cos-mult flip--
Counts
4 → 69
Calls
4 calls:
60.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms
(* (cos phi1) (sin phi2))
53.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
11.0ms
(cos (- lambda1 lambda2))

series416.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
83.0ms
(* (cos phi1) (sin phi2))
119.0ms
(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms
(cos (- lambda1 lambda2))

simplify2.7s

Counts
81 → 81
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01481030
13561017
21196879
33817871
done5000871

prune647.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

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:
19.0ms
(* (cos phi1) (sin phi2))
13.0ms
(* (sin lambda1) (sin lambda2))
59.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
75.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (cos phi1) (sin phi2))
66.0ms
(* (sin lambda1) (sin lambda2))
148.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
165.0ms
(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts
99 → 99
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01691229
14281203
21704947
done5001943

prune644.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1 add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
13×add-sqr-sqrt
10×associate-*l*
9×add-cube-cbrt *-un-lft-identity
8×associate-*r*
4×*-commutative add-log-exp
3×associate-*r/ sin-mult
2×sin-cos-mult unswap-sqr
1×frac-times associate-*l/ cos-mult
Counts
4 → 84
Calls
4 calls:
12.0ms
(* (cos phi1) (sin phi2))
24.0ms
(* (sin lambda1) (sin lambda2))
62.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
117.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (cos phi1) (sin phi2))
79.0ms
(* (sin lambda1) (sin lambda2))
149.0ms
(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
179.0ms
(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.3s

Counts
96 → 96
Iterations

Useful iterations: 2 (270.0ms)

IterNodesCost
01741156
14331134
21691896
done5000896

prune565.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes372.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02953
14153
done4153

end0.0ms

sample19.3s

Algorithm
intervals
Results
14.1s4588×body1280valid
3.5s2027×body640valid
620.0ms569×body320valid
462.0ms647×body80valid
137.0ms169×body160valid