Details

Time bar (total: 31.7s)

sample688.0ms

Algorithm
intervals
Results
387.0ms152×body1280valid
84.0ms70×body640valid
19.0ms23×body320valid
4.0ms9×body160valid
0.0ms2×body80valid

simplify31.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.2b
(cos (- lambda1 lambda2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
29.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
24.0ms
(cos (- lambda1 lambda2))

series167.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* (sin phi1) (sin phi2))
59.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
29.0ms
(cos (- lambda1 lambda2))

simplify1.9s

Counts
67 → 67

prune581.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin (- lambda2)))
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin sin-neg distribute-rgt-neg-out
Counts
4 → 65
Calls
4 calls:
17.0ms
(* (sin lambda1) (sin (- lambda2)))
26.0ms
(* (sin phi1) (sin phi2))
14.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (sin lambda1) (sin (- lambda2)))
60.0ms
(* (sin phi1) (sin phi2))
98.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.6s

Counts
77 → 77

prune699.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 58
Calls
4 calls:
32.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
7.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
12.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
96.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
24.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
36.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.8s

Counts
70 → 70

prune810.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))) R)
0.4b
(exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))
0.7b
(log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))))
1.0b
(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 58
Calls
4 calls:
31.0ms
(* (log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))) R)
18.0ms
(exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))
19.0ms
(log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))))
34.0ms
(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))) R)
57.0ms
(exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2))))))))
21.0ms
(log (exp (acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))))
20.0ms
(acos (- (+ (* (sin phi1) (sin phi2)) (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2))))) (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin (* -1 lambda2)))))))

simplify1.2s

Counts
70 → 70

prune629.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify958.0ms

end0.0ms

sample18.0s

Algorithm
intervals
Results
13.2s4751×body1280valid
3.1s2117×body640valid
787.0ms683×body320valid
153.0ms323×body160valid
72.0ms14×body2560valid
29.0ms114×body80valid