Details

Time bar (total: 3.7m)

sample229.0ms

Algorithm
intervals
Results
94.0ms272×body80valid
55.0ms51×body640valid
24.0ms17×body1280valid
21.0ms28×body320valid
5.0ms9×body160valid

simplify332.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
331.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize44.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.4b
(cos (/ (+ phi1 phi2) 2))
2.4b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-cbrt-cube add-exp-log
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×pow-sqr pow-prod-up insert-posit16 add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 139
Calls
4 calls:
Slowest
107.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
96.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))

series836.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
602.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
159.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
38.0ms
(cos (/ (+ phi1 phi2) 2))
36.0ms
(cos (/ (+ phi1 phi2) 2))

simplify43.1s

Counts
129 → 151
Calls
129 calls:
Slowest
1.1s
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
1.1s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))
971.0ms
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (+ phi1 phi2)) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
900.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
872.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.8b

localize41.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
2.4b
(cos (/ (+ phi1 phi2) 2))
2.4b
(cos (/ (+ phi1 phi2) 2))
0.3b
(* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
97×flip3-- flip--
82×associate-*l/ associate-*r/
66×sqrt-div
64×frac-times frac-add
10×pow1
9×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×insert-posit16 add-log-exp
3×associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* *-commutative flip-+
Counts
4 → 117
Calls
4 calls:
Slowest
140.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
60.0ms
(* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
17.0ms
(cos (/ (+ phi1 phi2) 2))
14.0ms
(cos (/ (+ phi1 phi2) 2))

series884.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
605.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
218.0ms
(* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
35.0ms
(cos (/ (+ phi1 phi2) 2))
26.0ms
(cos (/ (+ phi1 phi2) 2))

simplify40.2s

Counts
94 → 129
Calls
94 calls:
Slowest
999.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))
952.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
926.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))) (+ phi1 phi2)) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
898.0ms
(sqrt (+ (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
877.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.4b

localize52.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))
2.4b
(cos (/ (+ phi1 phi2) 2))
2.4b
(cos (/ (+ phi1 phi2) 2))
0.5b
(log (exp (cos (/ (+ phi1 phi2) 2))))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
96×flip3-- flip--
80×associate-*l/ associate-*r/
66×sqrt-div
64×frac-times frac-add
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×pow1
4×add-cbrt-cube add-exp-log log-pow insert-posit16 add-log-exp
3×log-prod exp-prod sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp flip-+
Counts
4 → 112
Calls
4 calls:
Slowest
169.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))
14.0ms
(cos (/ (+ phi1 phi2) 2))
13.0ms
(cos (/ (+ phi1 phi2) 2))
13.0ms
(log (exp (cos (/ (+ phi1 phi2) 2))))

series622.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (- phi1 phi2) (- phi1 phi2))))
38.0ms
(cos (/ (+ phi1 phi2) 2))
37.0ms
(log (exp (cos (/ (+ phi1 phi2) 2))))
36.0ms
(cos (/ (+ phi1 phi2) 2))

simplify36.7s

Counts
90 → 124
Calls
90 calls:
Slowest
1.2s
(sqrt (+ (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
910.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (pow lambda1 3) (pow lambda2 3)) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))
885.0ms
(sqrt (+ (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
885.0ms
(sqrt (+ (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
852.0ms
(sqrt (+ (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (log (exp (cos (/ (+ phi1 phi2) 2))))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.4b

localize58.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
31.9b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
2.4b
(cos (/ (+ phi1 phi2) 2))
2.4b
(cos (/ (+ phi1 phi2) 2))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
192×flip3-- flip--
160×associate-*l/ associate-*r/
132×sqrt-div
128×frac-times frac-add
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 176
Calls
4 calls:
Slowest
135.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
121.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
12.0ms
(cos (/ (+ phi1 phi2) 2))
9.0ms
(cos (/ (+ phi1 phi2) 2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
575.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
546.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
27.0ms
(cos (/ (+ phi1 phi2) 2))
22.0ms
(cos (/ (+ phi1 phi2) 2))

simplify1.3m

Counts
154 → 188
Calls
154 calls:
Slowest
1.3s
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3))))))
1.2s
(sqrt (+ (* (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2)) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
932.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))
928.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
888.0ms
(sqrt (+ (* (* (- (pow lambda1 3) (pow lambda2 3)) (* (cos (/ (+ phi1 phi2) 2)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))

prune5.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 21.4b

regimes1.1s

Accuracy

63.8% (4.4b remaining)

Error of 29.4b against oracle of 24.9b and baseline of 37.1b

bsearch10.0ms

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.6s8342×body80valid
1.9s1316×body640valid
1.2s781×body1280valid
657.0ms755×body320valid
249.0ms355×body160valid