Details

Time bar (total: 28.0s)

sample375.0ms

Algorithm
intervals
Results
225.0ms111×body1280valid
88.0ms80×body640valid
16.0ms22×body320valid
14.0ms12×body160valid
8.0ms31×body80valid

simplify19.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
120
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.4b
(cos (- lambda1 lambda2))
1.5b
(sin (- lambda1 lambda2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×cos-diff
2×cos-sum associate-+r+ sub-neg sin-sum
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 44
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms
(cos (- lambda1 lambda2))
30.0ms
(sin (- lambda1 lambda2))

series209.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
156.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))
24.0ms
(sin (- lambda1 lambda2))

simplify2.4s

Counts
56 → 56
Iterations
IterNodes
done5001
42616
31179
2486
1211
0101

prune534.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.1b

localize65.0ms

Local error

Found 4 expressions with local error:

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)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.4b
(cos (- lambda1 lambda2))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
4×insert-posit16
3×distribute-rgt-in cos-diff sub-neg distribute-lft-in associate-*r* associate-*l*
2×cos-sum associate-+r+ associate-*r/
1×+-commutative sum-log flip3-+ flip3-- pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 58
Calls
4 calls:
99.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
9.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms
(cos (- lambda1 lambda2))

series446.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
11.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
162.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms
(cos (- lambda1 lambda2))

simplify2.5s

Counts
70 → 70
Iterations
IterNodes
done5001
33300
2917
1312
0128

prune790.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×insert-posit16
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative sum-log flip3-+ flip3-- flip-+ flip-- sin-mult
Counts
4 → 65
Calls
4 calls:
12.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
72.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
18.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (sin lambda1) (sin lambda2))
27.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
172.0ms
(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
165.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify3.3s

Counts
77 → 77
Iterations
IterNodes
done5001
34287
21171
1379
0147

prune867.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize120.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (* (* (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
0.6b
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
30×flip3-+ flip-+
28×frac-times
26×cbrt-div
14×associate-*l/
10×add-log-exp
8×associate-*r/
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
3×+-commutative sum-log
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 73
Calls
4 calls:
75.0ms
(cbrt (* (* (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
25.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
21.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
20.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series761.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (* (* (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))) (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))))
215.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
197.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))
178.0ms
(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify2.3s

Counts
85 → 85
Iterations
IterNodes
done5003
22018
1418
0139

prune798.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes749.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify17.0ms

Iterations
IterNodes
done51
151
035

end0.0ms

sample10.7s

Algorithm
intervals
Results
5.9s3624×body1280valid
3.5s2363×body640valid
666.0ms937×body320valid
145.0ms407×body160valid
105.0ms669×body80valid