Details

Time bar (total: 40.3s)

sample252.0ms

Algorithm
intervals
Results
99.0ms296×body80valid
53.0ms50×body640valid
31.0ms21×body1280valid
26.0ms24×body320valid
6.0ms12×body160valid

simplify904.0ms

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize34.0ms

Local error

Found 4 expressions with local error:

36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite244.0ms

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
131.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
76.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
16.0ms
(cos (/ (+ phi1 phi2) 2))
15.0ms
(cos (/ (+ phi1 phi2) 2))

series781.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
577.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
135.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
42.0ms
(cos (/ (+ phi1 phi2) 2))
27.0ms
(cos (/ (+ phi1 phi2) 2))

simplify974.0ms

Counts
151 → 151

prune2.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.9b

localize56.0ms

Local error

Found 4 expressions with local error:

36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))
0.3b
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))

rewrite156.0ms

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
126.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
9.0ms
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))

series658.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
551.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
43.0ms
(* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))
37.0ms
(cos (/ (+ phi1 phi2) 2))
27.0ms
(cos (/ (+ phi1 phi2) 2))

simplify1.6s

Counts
208 → 208

prune4.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 24.9b

localize60.0ms

Local error

Found 4 expressions with local error:

36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (* (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))) (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
558×associate-*l/
532×frac-times
402×flip3-- flip--
288×cos-mult
282×sqrt-div
280×frac-add
230×associate-*r/
216×cbrt-div
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 320
Calls
4 calls:
Slowest
178.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (* (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))) (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
8.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))

series716.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
601.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (* (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))) (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
40.0ms
(cos (/ (+ phi1 phi2) 2))
38.0ms
(cos (/ (+ phi1 phi2) 2))
36.0ms
(cos (/ (+ phi1 phi2) 2))

simplify4.0s

Counts
332 → 332

prune10.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.3b

localize81.0ms

Local error

Found 4 expressions with local error:

36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
27.3b
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
96×flip3-- associate-*l/ flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ remove-posit16
Counts
4 → 105
Calls
4 calls:
Slowest
84.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
8.0ms
(cos (/ (+ phi1 phi2) 2))
8.0ms
(cos (/ (+ phi1 phi2) 2))
0.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))

series578.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
495.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
33.0ms
(cos (/ (+ phi1 phi2) 2))
26.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
23.0ms
(cos (/ (+ phi1 phi2) 2))

simplify771.0ms

Counts
117 → 117

prune3.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 23.3b

regimes902.0ms

Accuracy

35.9% (8.6b remaining)

Error of 32.7b against oracle of 24.1b and baseline of 37.5b

bsearch326.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.0s8272×body80valid
1.8s1275×body640valid
1.4s747×body1280valid
603.0ms727×body320valid
168.0ms427×body160valid