Details

Time bar (total: 2.6m)

sample248.0ms

Algorithm
intervals
Results
68.0ms259×body80valid
67.0ms17×body1280valid
57.0ms49×body640valid
15.0ms18×body320valid
7.0ms14×body160valid

simplify247.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
247.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize33.0ms

Local error

Found 4 expressions with local error:

41.4b
(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))))

rewrite258.0ms

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
137.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
89.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
13.0ms
(cos (/ (+ phi1 phi2) 2))
9.0ms
(cos (/ (+ phi1 phi2) 2))

series663.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
477.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
117.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
35.0ms
(cos (/ (+ phi1 phi2) 2))
32.0ms
(cos (/ (+ phi1 phi2) 2))

simplify43.9s

Counts
129 → 151
Calls
129 calls:
Slowest
1.3s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (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))))))
1.2s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))) (+ phi1 phi2)) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2)))) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
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))))))
1.0s
(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))))))
944.0ms
(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))))))

prune2.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.7b

localize61.0ms

Local error

Found 4 expressions with local error:

41.4b
(sqrt (+ (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (- phi1 phi2) (- phi1 phi2))))
2.5b
(cos (* (+ phi1 phi2) 1/2))
2.5b
(cos (* (+ phi1 phi2) 1/2))
1.6b
(+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
42×sqrt-div
40×frac-add
36×frac-times
30×flip3-- flip--
26×associate-*r/
24×cos-mult
18×flip3-+ associate-*l/ flip-+
6×add-sqr-sqrt add-log-exp
5×pow1 *-un-lft-identity add-cube-cbrt
4×associate-+r+ add-cbrt-cube add-exp-log insert-posit16
3×sqrt-prod
2×distribute-rgt-in sub-neg distribute-lft-in
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Counts
4 → 88
Calls
4 calls:
Slowest
97.0ms
(sqrt (+ (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (- phi1 phi2) (- phi1 phi2))))
20.0ms
(cos (* (+ phi1 phi2) 1/2))
18.0ms
(cos (* (+ phi1 phi2) 1/2))
18.0ms
(+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))

series924.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
819.0ms
(sqrt (+ (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (- phi1 phi2) (- phi1 phi2))))
40.0ms
(+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))
32.0ms
(cos (* (+ phi1 phi2) 1/2))
32.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify18.5s

Counts
64 → 100
Calls
64 calls:
Slowest
1.0s
(sqrt (+ (* (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* lambda1 (- lambda1 (* lambda2 2))) (* lambda1 (- lambda1 (* lambda2 2)))))) (* (+ phi1 phi2) (+ phi1 phi2))) (* (* 2 (- (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (* phi1 phi1) (* phi2 phi2))))))
905.0ms
(sqrt (+ (* (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* lambda1 (- lambda1 (* lambda2 2))) (* lambda1 (- lambda1 (* lambda2 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2)))) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
767.0ms
(sqrt (+ (* (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (+ (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* 2 (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
699.0ms
(sqrt (+ (* (* (+ (cos (+ (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2))) (cos (- (* (+ phi1 phi2) 1/2) (* (+ phi1 phi2) 1/2)))) (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* lambda1 (- lambda1 (* lambda2 2))) (* lambda1 (- lambda1 (* lambda2 2)))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (* 2 (- (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2))))) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3))))))
678.0ms
(sqrt (+ (* (* (* (cos (* (+ phi1 phi2) 1/2)) (cos (* (+ phi1 phi2) 1/2))) (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* lambda1 (- lambda1 (* lambda2 2))) (* lambda1 (- lambda1 (* lambda2 2)))))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (- (* lambda2 lambda2) (* lambda1 (- lambda1 (* lambda2 2)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.1b

localize76.0ms

Local error

Found 4 expressions with local error:

41.4b
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
28.2b
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
2.5b
(cos (/ (+ phi1 phi2) 2))
2.5b
(cos (/ (+ phi1 phi2) 2))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- 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
126.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
8.0ms
(cos (/ (+ phi1 phi2) 2))
7.0ms
(cos (/ (+ phi1 phi2) 2))
0.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))

series661.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
584.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
31.0ms
(cos (/ (+ phi1 phi2) 2))
24.0ms
(cos (/ (+ phi1 phi2) 2))
22.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))

simplify35.7s

Counts
84 → 117
Calls
84 calls:
Slowest
1.3s
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
1.1s
(sqrt (+ (* (* (* (- (pow lambda1 3) (pow lambda2 3)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))) (+ phi1 phi2)) (* (* (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))) (+ lambda1 lambda2)) (* (- (* phi1 phi1) (* phi2 phi2)) (- phi1 phi2)))))
962.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (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))))))
946.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (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))))))
941.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (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))))))

prune2.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 22.1b

localize100.0ms

Local error

Found 4 expressions with local error:

41.4b
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
28.2b
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
28.2b
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
2.5b
(cos (/ (+ phi1 phi2) 2))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- 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
2×remove-posit16
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 106
Calls
4 calls:
Slowest
84.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
7.0ms
(cos (/ (+ phi1 phi2) 2))
0.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
0.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))

series590.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
524.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
23.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))
21.0ms
(cos (/ (+ phi1 phi2) 2))
21.0ms
(posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))

simplify34.5s

Counts
85 → 118
Calls
85 calls:
Slowest
967.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
965.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
952.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (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))))))
935.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (+ phi1 phi2)) (* (* (+ lambda1 lambda2) (+ lambda1 lambda2)) (* (- (* phi1 phi1) (* phi2 phi2)) (- phi1 phi2)))))
849.0ms
(sqrt (+ (* (* (* (- lambda1 lambda2) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2))))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (posit16->real (real->posit16 (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (+ lambda1 lambda2) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))

prune3.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 21.8b

regimes1.4s

Accuracy

34.3% (11.8b remaining)

Error of 31.4b against oracle of 19.6b and baseline of 37.6b

bsearch115.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.6s8387×body80valid
1.4s758×body1280valid
1.3s1255×body640valid
644.0ms742×body320valid
143.0ms370×body160valid