Details

Time bar (total: 25.3s)

sample107.0ms

Algorithm
intervals
Results
34.0ms46×body640valid
24.0ms274×body80valid
12.0ms23×body1280valid
7.0ms24×body320valid
1.0ms7×body160valid

simplify44.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
4.2b
(cos (/ (+ phi1 phi2) 2.0))
34.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite239.0ms

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-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up 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 → 135
Calls
4 calls:
76.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
125.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series640.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
468.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify54.0ms

Counts
147 → 147

prune518.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 23.3b

localize43.0ms

Local error

Found 4 expressions with local error:

4.2b
(cos (* 0.5 (+ phi2 phi1)))
4.2b
(cos (* 0.5 (+ phi2 phi1)))
4.2b
(cos (* 0.5 (+ phi2 phi1)))
34.5b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
20×flip3-- flip--
18×sqrt-div
16×frac-add
8×frac-times
6×add-sqr-sqrt cos-sum
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log associate-*r/ associate-*l/ add-cbrt-cube add-log-exp
3×distribute-rgt-in distribute-lft-in sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 58
Calls
4 calls:
11.0ms
(cos (* 0.5 (+ phi2 phi1)))
10.0ms
(cos (* 0.5 (+ phi2 phi1)))
11.0ms
(cos (* 0.5 (+ phi2 phi1)))
293.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series671.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(cos (* 0.5 (+ phi2 phi1)))
34.0ms
(cos (* 0.5 (+ phi2 phi1)))
29.0ms
(cos (* 0.5 (+ phi2 phi1)))
579.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify88.0ms

Counts
70 → 70

prune461.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.0b

localize54.0ms

Local error

Found 4 expressions with local error:

3.8b
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.2b
(cos (* 0.5 (+ phi2 phi1)))
4.2b
(cos (* 0.5 (+ phi2 phi1)))
34.5b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
9×add-log-exp
8×frac-times
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log cos-sum associate-*r/ associate-*l/ add-cbrt-cube
3×sqrt-prod
2×distribute-rgt-in distribute-lft-in diff-log
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate--l+ sum-log flip-+
Counts
4 → 63
Calls
4 calls:
400.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
11.0ms
(cos (* 0.5 (+ phi2 phi1)))
11.0ms
(cos (* 0.5 (+ phi2 phi1)))
708.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series3.7s

Counts
4 → 12
Calls
4 calls:
621.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
28.0ms
(cos (* 0.5 (+ phi2 phi1)))
303.0ms
(cos (* 0.5 (+ phi2 phi1)))
2.8s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify117.0ms

Counts
75 → 75

prune706.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.0b

localize97.0ms

Local error

Found 4 expressions with local error:

4.8b
(* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2)))
5.4b
(- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2))))))))
8.6b
(* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))
34.5b
(sqrt (+ (- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite6.9s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log
66×prod-exp
50×sqrt-div
48×frac-add
45×flip3-- flip--
40×add-log-exp
37×flip3-+ flip-+
36×frac-sub
34×pow-to-exp pow-exp
30×add-sqr-sqrt
24×frac-times
18×sum-log
17×unpow-prod-down
16×associate-*l* unswap-sqr
13×*-un-lft-identity
12×associate-*r/ associate-*l/
11×add-cube-cbrt add-cbrt-cube unpow2 sqr-pow
9×diff-log associate-*r*
5×pow1
4×cbrt-unprod
3×pow-prod-down sqrt-prod
2×*-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate--l+ associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 192
Calls
4 calls:
63.0ms
(* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2)))
1.1s
(- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2))))))))
31.0ms
(* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))
5.6s
(sqrt (+ (- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

series2.2s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2)))
768.0ms
(- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2))))))))
75.0ms
(* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))
1.2s
(sqrt (+ (- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify242.0ms

Counts
204 → 204

prune2.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 16.7b

regimes994.0ms

Accuracy

47.8% (11.1b remaining)

Error of 28.5b against oracle of 17.4b and baseline of 38.6b

bsearch4.0ms

simplify2.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.1s8453×body80valid
937.0ms1284×body640valid
493.0ms832×body1280valid
431.0ms347×body160valid
294.0ms708×body320valid