Details

Time bar (total: 40.5s)

sample144.0ms

Algorithm
intervals
Results
56.0ms266×body80valid
26.0ms39×body640valid
24.0ms27×body1280valid
11.0ms24×body320valid
4.0ms11×body160valid

simplify976.0ms

Counts
1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize42.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.7b
(cos (/ (+ phi1 phi2) 2))
2.7b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite216.0ms

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
97.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
94.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
10.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
607.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
147.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
31.0ms
(cos (/ (+ phi1 phi2) 2))
27.0ms
(cos (/ (+ phi1 phi2) 2))

simplify912.0ms

Counts
151 → 151

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.0b

localize56.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.7b
(cos (/ (+ phi1 phi2) 2))
2.7b
(cos (/ (+ phi1 phi2) 2))
0.4b
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
198×flip3-- flip--
196×frac-times
138×sqrt-div
136×frac-add
130×associate-*l/
74×associate-*r/
73×cos-mult
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×insert-posit16 add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqr-cos sqrt-pow1 flip3-+ pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 196
Calls
4 calls:
Slowest
116.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
17.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
14.0ms
(cos (/ (+ phi1 phi2) 2))

series639.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
521.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
44.0ms
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
37.0ms
(cos (/ (+ phi1 phi2) 2))
36.0ms
(cos (/ (+ phi1 phi2) 2))

simplify1.8s

Counts
208 → 208

prune5.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 25.0b

localize68.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))) (* (- phi1 phi2) (- phi1 phi2))))
2.7b
(cos (* 1/2 (+ phi2 phi1)))
2.7b
(cos (* 1/2 (+ phi2 phi1)))
0.4b
(* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
198×flip3-- flip--
196×frac-times
138×sqrt-div
136×frac-add
130×associate-*l/
74×associate-*r/
73×cos-mult
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×cos-sum insert-posit16 add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
2×distribute-rgt-in distribute-lft-in
1×pow2 rem-sqrt-square sqr-cos sqrt-pow1 flip3-+ pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 200
Calls
4 calls:
Slowest
147.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))) (* (- phi1 phi2) (- phi1 phi2))))
36.0ms
(* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))
12.0ms
(cos (* 1/2 (+ phi2 phi1)))
8.0ms
(cos (* 1/2 (+ phi2 phi1)))

series659.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
557.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))) (* (- phi1 phi2) (- phi1 phi2))))
39.0ms
(cos (* 1/2 (+ phi2 phi1)))
37.0ms
(* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1))))
26.0ms
(cos (* 1/2 (+ phi2 phi1)))

simplify1.7s

Counts
212 → 212

prune6.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.1b

localize81.0ms

Local error

Found 4 expressions with local error:

35.4b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cbrt (* (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1)))) (cos (* 1/2 (+ phi2 phi1))))))) (* (- phi1 phi2) (- phi1 phi2))))
2.7b
(cos (* 1/2 (+ phi2 phi1)))
2.7b
(cos (* 1/2 (+ phi2 phi1)))
2.7b
(cos (* 1/2 (+ phi2 phi1)))

rewrite470.0ms

Algorithm
rewrite-expression-head
Rules
202×associate-*l/
198×flip3-- flip--
196×frac-times
146×associate-*r/
138×sqrt-div
136×frac-add
72×cbrt-div cos-mult
6×add-sqr-sqrt cos-sum
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×distribute-rgt-in distribute-lft-in sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 182
Calls
4 calls:
Slowest
430.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cbrt (* (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1)))) (cos (* 1/2 (+ phi2 phi1))))))) (* (- phi1 phi2) (- phi1 phi2))))
14.0ms
(cos (* 1/2 (+ phi2 phi1)))
9.0ms
(cos (* 1/2 (+ phi2 phi1)))
8.0ms
(cos (* 1/2 (+ phi2 phi1)))

series697.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
581.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (* 1/2 (+ phi2 phi1))) (cbrt (* (* (cos (* 1/2 (+ phi2 phi1))) (cos (* 1/2 (+ phi2 phi1)))) (cos (* 1/2 (+ phi2 phi1))))))) (* (- phi1 phi2) (- phi1 phi2))))
40.0ms
(cos (* 1/2 (+ phi2 phi1)))
38.0ms
(cos (* 1/2 (+ phi2 phi1)))
37.0ms
(cos (* 1/2 (+ phi2 phi1)))

simplify2.4s

Counts
194 → 194

prune5.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.1b

regimes1.1s

Accuracy

43% (12.8b remaining)

Error of 27.6b against oracle of 14.7b and baseline of 37.3b

bsearch426.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.1s8377×body80valid
1.5s1260×body640valid
1.4s775×body1280valid
541.0ms694×body320valid
162.0ms331×body160valid