Details

Time bar (total: 36.0s)

sample497.0ms

Algorithm
intervals
Results
308.0ms115×body1280valid
131.0ms85×body640valid
21.0ms21×body320valid
8.0ms26×body80valid
6.0ms9×body160valid

simplify20.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize100.0ms

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))))
2.4b
(cos (- lambda1 lambda2))
2.6b
(sin (- lambda1 lambda2))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
18×prod-diff
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
11×cos-sum sin-sum
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cos-diff fma-def
2×associate-+r+ sub-neg
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ sin-diff flip-+
Counts
4 → 73
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
21.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms
(cos (- lambda1 lambda2))
19.0ms
(sin (- lambda1 lambda2))

series279.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
184.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
37.0ms
(cos (- lambda1 lambda2))
40.0ms
(sin (- lambda1 lambda2))

simplify2.5s

Counts
85 → 85
Iterations
IterNodes
done5001
31948
2723
1376
0195

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.9b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))))
2.4b
(cos (- lambda1 lambda2))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cos-diff fma-def associate-*r* associate-*l*
2×associate-+r+
1×distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 72
Calls
4 calls:
23.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
22.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(cos (- lambda1 lambda2))

series253.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (cos lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
149.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms
(cos (- lambda1 lambda2))

simplify2.4s

Counts
84 → 84
Iterations
IterNodes
done5001
32765
2894
1405
0198

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def
2×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in flip3-+ flip-+ sin-mult
Counts
4 → 72
Calls
4 calls:
21.0ms
(* (cos lambda1) (sin lambda2))
23.0ms
(* (sin lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
18.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series509.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (cos lambda1) (sin lambda2))
69.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
361.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify3.2s

Counts
84 → 84
Iterations
IterNodes
done5000
34209
21009
1350
0145

prune935.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize133.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))
0.4b
(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))
0.4b
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))
1.3b
(- (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
171×pow1
77×pow-prod-down
57×add-cbrt-cube add-exp-log
39×prod-exp cbrt-unprod
34×pow-prod-up
12×pow-sqr
6×pow-plus add-log-exp
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow2 prod-diff
2×associate-*r* associate-*l* *-commutative
1×sub-neg flip3-- fma-neg diff-log cube-unmult swap-sqr fma-udef flip--
Counts
4 → 133
Calls
4 calls:
148.0ms
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))
0.0ms
(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))
57.0ms
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))
11.0ms
(- (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

series1.7s

Counts
4 → 12
Calls
4 calls:
276.0ms
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2))))
893.0ms
(fma (cos phi1) (* (cos phi1) (cos phi1)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))))
220.0ms
(* (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)))
325.0ms
(- (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1))

simplify2.7s

Counts
145 → 145
Iterations
IterNodes
done5028
22419
1631
0213

prune938.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

regimes965.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done35
135
028

end0.0ms

sample16.2s

Algorithm
intervals
Results
9.4s3541×body1280valid
4.4s2316×body640valid
1.2s985×body320valid
621.0ms742×body80valid
243.0ms416×body160valid