Details

Time bar (total: 27.2s)

sample91.0ms

Algorithm
intervals
Results
35.0ms262×body80valid
16.0ms44×body640valid
10.0ms18×body1280valid
6.0ms22×body320valid
2.0ms10×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
017466
134361
276361
3259361
41037361
done5001361

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
8.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
36.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
9.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
542.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
727.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
110.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
40.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.5s

Counts
75 → 75
Iterations

Useful iterations: done (1.5s)

IterNodesCost
014226234
136224716
2159324376
done500224246

prune798.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
2.2b
(cos (* 0.5 (+ phi1 phi2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
12×distribute-rgt-in distribute-lft-in
8×pow1 add-cbrt-cube associate-*r* add-exp-log
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cos-sum sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
12.0ms
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
50.0ms
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
8.0ms
(cos (* 0.5 (+ phi1 phi2)))

series1.9s

Counts
4 → 12
Calls
4 calls:
969.0ms
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
709.0ms
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
181.0ms
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
50.0ms
(cos (* 0.5 (+ phi1 phi2)))

simplify1.9s

Counts
99 → 99
Iterations

Useful iterations: done (1.9s)

IterNodesCost
019544136
142640163
2192936589
done500136279

prune677.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (* phi1 0.5)) (cos (* phi2 0.5)))
0.1b
(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
0.2b
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
0.2b
(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
19×prod-diff
11×distribute-rgt-in distribute-lft-in associate-*r*
10×pow1 add-cbrt-cube add-exp-log
9×flip3-- associate-*l* cos-mult flip-- sin-mult
8×frac-times
6×add-log-exp
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*r/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 118
Calls
4 calls:
35.0ms
(* (cos (* phi1 0.5)) (cos (* phi2 0.5)))
77.0ms
(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
25.0ms
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
185.0ms
(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

series782.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(* (cos (* phi1 0.5)) (cos (* phi2 0.5)))
167.0ms
(- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
114.0ms
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
429.0ms
(* (- (* (cos (* phi1 0.5)) (cos (* phi2 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

simplify3.6s

Counts
130 → 130
Iterations

Useful iterations: done (3.5s)

IterNodesCost
025084566
161378868
2298674984
done500073537

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
0.1b
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
0.2b
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
0.2b
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
19×prod-diff
11×distribute-rgt-in distribute-lft-in associate-*r*
10×pow1 add-cbrt-cube add-exp-log
9×flip3-- associate-*l* cos-mult flip-- sin-mult
8×frac-times
6×add-log-exp
4×expm1-log1p-u associate-*l/ frac-sub log1p-expm1-u sub-div
3×sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*r/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 118
Calls
4 calls:
20.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
58.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
23.0ms
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
162.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

series839.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* (cos (* phi2 0.5)) (cos (* phi1 0.5)))
158.0ms
(- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5))))
119.0ms
(* (sin (* phi1 0.5)) (sin (* phi2 0.5)))
477.0ms
(* (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi1 0.5)) (sin (* phi2 0.5)))) (- lambda1 lambda2))

simplify2.7s

Counts
130 → 130
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
025486166
164180483
2347876694
done500176694

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes763.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
023796
130796
done30796

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.9s8366×body80valid
1.2s1309×body640valid
799.0ms782×body1280valid
333.0ms768×body320valid
181.0ms398×body160valid