Details

Time bar (total: 27.2s)

sample372.0ms

Algorithm
intervals
Results
230.0ms104×body1280valid
79.0ms78×body640valid
30.0ms40×body320valid
6.0ms15×body160valid
4.0ms19×body80valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done23
223
120
014

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b
(sin (- lambda1 lambda2))
3.3b
(cos (- lambda1 lambda2))

rewrite451.0ms

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)))))
26.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.0ms
(sin (- lambda1 lambda2))
410.0ms
(cos (- lambda1 lambda2))

series199.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
130.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify2.2s

Counts
85 → 85
Iterations
IterNodes
done5002
31952
2729
1376
0195

prune862.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize87.0ms

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)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b
(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:
18.0ms
(* (cos lambda1) (sin lambda2))
0.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms
(cos (- lambda1 lambda2))

series275.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (cos lambda1) (sin lambda2))
11.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
180.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms
(cos (- lambda1 lambda2))

simplify2.2s

Counts
84 → 84
Iterations
IterNodes
done5001
32765
2894
1405
0198

prune976.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize112.0ms

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) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.5b
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite58.0ms

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:
12.0ms
(* (cos 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))))))
25.0ms
(* (sin lambda1) (sin lambda2))
20.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series503.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (cos lambda1) (sin lambda2))
30.0ms
(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
83.0ms
(* (sin lambda1) (sin lambda2))
329.0ms
(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify2.7s

Counts
84 → 84
Iterations
IterNodes
done5000
34211
21015
1350
0145

prune880.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize134.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos phi1))
0.3b
(cbrt (cos phi1))
0.3b
(cbrt (cos phi1))
0.5b
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
2.0ms
(cbrt (cos phi1))
2.0ms
(cbrt (cos phi1))
3.0ms
(cbrt (cos phi1))
1.0ms
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series760.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (cos phi1))
111.0ms
(cbrt (cos phi1))
127.0ms
(cbrt (cos phi1))
391.0ms
(fma (* (cbrt (cos phi1)) (cbrt (cos phi1))) (cbrt (cos phi1)) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.5s

Counts
65 → 65
Iterations
IterNodes
done5003
42311
3765
2284
1133
067

prune552.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes815.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
done35
135
026

end0.0ms

sample11.4s

Algorithm
intervals
Results
7.5s3533×body1280valid
2.2s2331×body640valid
642.0ms975×body320valid
546.0ms439×body160valid
156.0ms722×body80valid