Details

Time bar (total: 1.0m)

sample879.0ms

Algorithm
intervals
Results
529.0ms142×body1280valid
152.0ms80×body640valid
25.0ms20×body320valid
8.0ms9×body160valid
6.0ms1×body2560valid
1.0ms4×body80valid

simplify63.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
62.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize88.0ms

Local error

Found 4 expressions with local error:

3.9b
(cos (- lambda1 lambda2))
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite41.0ms

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*
4×insert-posit16 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 → 59
Calls
4 calls:
Slowest
21.0ms
(* (sin phi1) (sin phi2))
9.0ms
(cos (- lambda1 lambda2))
6.0ms
(* (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)))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
75.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
58.0ms
(* (sin phi1) (sin phi2))
55.0ms
(cos (- lambda1 lambda2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.7s

Counts
35 → 71
Calls
35 calls:
Slowest
579.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (* (* R R) R))
335.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
103.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
68.0ms
(* (acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))) R)
67.0ms
(* (acos (+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))) R)

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize65.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin phi1) (sin phi2))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 76
Calls
4 calls:
Slowest
55.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms
(* (sin phi1) (sin phi2))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series832.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
425.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
312.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
80.0ms
(* (sin phi1) (sin phi2))
15.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify8.0s

Counts
54 → 88
Calls
54 calls:
Slowest
601.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
525.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
426.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
426.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
366.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize92.0ms

Local error

Found 4 expressions with local error:

1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.9b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×insert-posit16
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 62
Calls
4 calls:
Slowest
24.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
9.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
6.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
85.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
72.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
15.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify7.3s

Counts
37 → 74
Calls
37 calls:
Slowest
456.0ms
(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
303.0ms
(* (* (* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
299.0ms
(* (sqrt (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) (sqrt R))
292.0ms
(log (sqrt (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
263.0ms
(exp (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.5b

localize129.0ms

Local error

Found 4 expressions with local error:

1.9b
(log (exp (* (sin phi1) (sin phi2))))
1.4b
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
11×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* cos-mult
5×add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×frac-times log-prod associate-*r/ log-pow
2×flip3-+ frac-add *-commutative flip-+ sin-mult
1×distribute-rgt-in acos-asin exp-prod distribute-lft-in exp-to-pow rem-log-exp associate-*l/ unswap-sqr
Counts
4 → 71
Calls
4 calls:
Slowest
104.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
9.0ms
(log (exp (* (sin phi1) (sin phi2))))
6.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
245.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
95.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
86.0ms
(log (exp (* (sin phi1) (sin phi2))))
29.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify8.6s

Counts
49 → 83
Calls
49 calls:
Slowest
693.0ms
(* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
618.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
515.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
473.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
391.0ms
(* (sqrt (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))

prune2.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

regimes1.2s

Accuracy

0% (0.4b remaining)

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

bsearch6.0ms

end0.0ms

sample24.4s

Algorithm
intervals
Results
16.4s4791×body1280valid
5.6s2077×body640valid
1.6s708×body320valid
257.0ms296×body160valid
81.0ms15×body2560valid
43.0ms113×body80valid