Details

Time bar (total: 3.2m)

sample177.0ms

Algorithm
intervals
Results
65.0ms257×body80valid
37.0ms33×body1280valid
34.0ms33×body640valid
12.0ms16×body320valid
6.0ms15×body160valid

simplify369.0ms

Calls
1 calls:
Slowest
369.0ms
(* R (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2)))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize43.0ms

Local error

Found 4 expressions with local error:

35.8b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
3.8b
(cos (/ (+ phi1 phi2) 2))
3.8b
(cos (/ (+ phi1 phi2) 2))
0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
276×*-un-lft-identity
142×associate-*l/
113×associate-*l*
102×flip3-- flip--
92×swap-sqr
75×distribute-lft-out--
68×frac-times
66×sqrt-div
64×frac-add
51×sqrt-prod
48×distribute-lft-out
46×add-sqr-sqrt
44×pow1
34×associate-*r/
26×associate-*r*
17×pow-prod-down add-cube-cbrt
16×add-cbrt-cube add-exp-log
12×unswap-sqr
8×prod-exp cbrt-unprod
5×*-commutative
4×pow-sqr pow-prod-up insert-posit16 add-log-exp difference-of-squares
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
887.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
276.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
17.0ms
(cos (/ (+ phi1 phi2) 2))
17.0ms
(cos (/ (+ phi1 phi2) 2))

series767.0ms

Calls
4 calls:
Slowest
576.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
124.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))
37.0ms
(cos (/ (+ phi1 phi2) 2))
30.0ms
(cos (/ (+ phi1 phi2) 2))

simplify49.8s

Calls
246 calls:
Slowest
1.3s
(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 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))))))
979.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (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))))))
940.0ms
(sqrt (+ (* (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (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))))))

prune4.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.6b

localize18.0ms

Local error

Found 4 expressions with local error:

35.8b
(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
27.2b
(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
3.8b
(cos (/ (+ phi1 phi2) 2))
3.8b
(cos (/ (+ phi1 phi2) 2))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
72×log-div
68×frac-times
66×sqrt-div
64×exp-diff frac-add
57×log-prod
49×*-un-lft-identity
47×add-sqr-sqrt
45×pow1
44×associate-*l*
34×associate-*r/
26×associate-*r*
20×swap-sqr
18×add-cube-cbrt
17×pow-prod-down add-exp-log
16×log-pow
12×unswap-sqr
9×distribute-lft-out--
8×prod-exp
6×sqrt-prod
5×rem-log-exp *-commutative
4×add-cbrt-cube pow-sqr pow-prod-up insert-posit16 add-log-exp difference-of-squares
3×distribute-lft-out
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
1.7s
(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
472.0ms
(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
17.0ms
(cos (/ (+ phi1 phi2) 2))
17.0ms
(cos (/ (+ phi1 phi2) 2))

series826.0ms

Calls
4 calls:
Slowest
569.0ms
(sqrt (+ (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
199.0ms
(log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))
33.0ms
(cos (/ (+ phi1 phi2) 2))
25.0ms
(cos (/ (+ phi1 phi2) 2))

simplify42.5s

Calls
166 calls:
Slowest
1.1s
(sqrt (+ (* (exp (log (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- (pow lambda1 3) (pow lambda2 3)) (cos (/ (+ phi1 phi2) 2)))))) (+ phi1 phi2)) (* (exp (log (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))))) (* (- phi1 phi2) (- (* phi1 phi1) (* phi2 phi2))))))
817.0ms
(sqrt (+ (* (exp (log (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (exp (log (+ lambda1 lambda2))) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
815.0ms
(sqrt (+ (* (exp (log (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (exp (log (* (+ lambda1 lambda2) (+ lambda1 lambda2)))) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
814.0ms
(sqrt (+ (* (exp (log (* (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2))) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2)))))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ phi1 phi2))) (* (exp (log (* (+ lambda1 lambda2) (+ lambda1 lambda2)))) (* (- (pow phi1 3) (pow phi2 3)) (- (* phi1 phi1) (* phi2 phi2))))))
812.0ms
(sqrt (+ (* (exp (log (* (* (- 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))))) (* (exp (log (+ (* lambda1 lambda1) (+ (* lambda2 lambda2) (* lambda1 lambda2))))) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))

prune4.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 26.6b

localize39.0ms

Local error

Found 4 expressions with local error:

35.8b
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
1.6b
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
0.0b
(* (- phi1 phi2) (- phi1 phi2))
0.0b
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
244×*-un-lft-identity
128×associate-*l*
110×distribute-lft-out
61×sqrt-prod
52×distribute-lft-out--
38×associate-*r*
36×sqrt-div
32×frac-add
30×flip3-- flip--
28×associate-*r/
27×add-sqr-sqrt
20×frac-times
19×flip3-+ flip-+
14×pow1
12×add-cube-cbrt
10×associate-*l/
8×add-cbrt-cube add-exp-log
7×swap-sqr
6×add-log-exp
4×insert-posit16 difference-of-squares
3×unswap-sqr
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod
1×pow2 +-commutative rem-sqrt-square sum-log sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up
Calls
4 calls:
Slowest
1.6s
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))
775.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
104.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
36.0ms
(* (- phi1 phi2) (- phi1 phi2))

series556.0ms

Calls
4 calls:
Slowest
283.0ms
(* R (sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2)))))
197.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
45.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
31.0ms
(* (- phi1 phi2) (- phi1 phi2))

simplify39.3s

Calls
179 calls:
Slowest
922.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (+ phi1 phi2)) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (* phi1 phi1) (* phi2 phi2)) (- phi1 phi2)))))
714.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
696.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
651.0ms
(sqrt (+ (* (+ (pow (* lambda2 lambda2) 3) (pow (* (- lambda1 (* lambda2 2)) lambda1) 3)) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* (* lambda2 lambda2) (* lambda2 lambda2)) (- (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1)) (* (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)))) (* (- phi1 phi2) (- (pow phi1 3) (pow phi2 3))))))
637.0ms
(sqrt (+ (* (+ (pow (* lambda2 lambda2) 3) (pow (* (- lambda1 (* lambda2 2)) lambda1) 3)) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* (* lambda2 lambda2) (* lambda2 lambda2)) (- (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1)) (* (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))

prune3.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 23.4b

localize9.0ms

Local error

Found 4 expressions with local error:

35.8b
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
35.8b
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
1.6b
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
1.6b
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
244×*-un-lft-identity
132×associate-*l*
118×distribute-lft-out
60×sqrt-prod
50×distribute-lft-out--
36×sqrt-div
32×frac-add
24×flip3-- flip--
20×flip3-+ flip-+
16×frac-times
8×add-sqr-sqrt associate-*l/ associate-*r/ add-log-exp
6×pow1 add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16
2×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
817.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
741.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
100.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
73.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))

series492.0ms

Calls
4 calls:
Slowest
205.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
193.0ms
(sqrt (+ (+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- phi1 phi2) (- phi1 phi2))))
52.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))
42.0ms
(+ (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1))

simplify24.9s

Calls
130 calls:
Slowest
1.1s
(sqrt (+ (* (+ (pow (* lambda2 lambda2) 3) (pow (* (- lambda1 (* lambda2 2)) lambda1) 3)) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* (* lambda2 lambda2) (* lambda2 lambda2)) (- (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1)) (* (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))
728.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ phi1 phi2) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (* phi1 phi1) (* phi2 phi2)) (- (pow phi1 3) (pow phi2 3))))))
695.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
670.0ms
(sqrt (+ (* (- (* (* lambda2 lambda2) (* lambda2 lambda2)) (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1))) (* (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2))))) (* (- (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)) (* (- (pow phi1 3) (pow phi2 3)) (- (pow phi1 3) (pow phi2 3))))))
669.0ms
(sqrt (+ (* (+ (pow (* lambda2 lambda2) 3) (pow (* (- lambda1 (* lambda2 2)) lambda1) 3)) (+ (* phi1 phi1) (+ (* phi2 phi2) (* phi1 phi2)))) (* (+ (* (* lambda2 lambda2) (* lambda2 lambda2)) (- (* (* (- lambda1 (* lambda2 2)) lambda1) (* (- lambda1 (* lambda2 2)) lambda1)) (* (* lambda2 lambda2) (* (- lambda1 (* lambda2 2)) lambda1)))) (* (- (pow phi1 3) (pow phi2 3)) (- phi1 phi2)))))

prune3.2s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 23.4b

regimes1.4s

Accuracy

54.4% (6.8b remaining)

Error of 29.0b against oracle of 22.2b and baseline of 37.2b

bsearch14.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.8s8250×body80valid
1.6s808×body1280valid
1.4s1312×body640valid
563.0ms702×body320valid
226.0ms378×body160valid