Details

Time bar (total: 3.2m)

sample190.0ms

Algorithm
intervals
Results
78.0ms42×body1280valid
40.0ms46×body640valid
28.0ms133×body80valid
17.0ms25×body320valid
4.0ms10×body160valid

simplify262.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
262.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize36.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.6b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite637.0ms

Algorithm
rewrite-expression-head
Rules
105×add-cbrt-cube add-exp-log
51×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
24×pow1
18×add-sqr-sqrt
15×*-un-lft-identity times-frac add-cube-cbrt
9×pow-prod-down
8×associate-*r* associate-*l*
7×swap-sqr
5×associate-*l/ div-inv
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-prod associate-/l*
2×flip3-+ *-commutative flip-+
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 136
Calls
4 calls:
Slowest
341.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
164.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
105.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
21.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
150.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
123.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
89.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

simplify47.8s

Counts
119 → 148
Calls
119 calls:
Slowest
2.7s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.3s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
1.9s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
1.6s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize64.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.6b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
102×add-cbrt-cube add-exp-log
49×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
21×pow1
19×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
15×times-frac
10×associate-*r*
8×associate-*l*
7×swap-sqr pow-prod-down associate-*l/
5×div-inv
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-prod associate-/l*
2×flip3-+ *-commutative flip-+
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 135
Calls
4 calls:
Slowest
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
152.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
111.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
13.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
134.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
125.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
94.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

simplify46.5s

Counts
118 → 147
Calls
118 calls:
Slowest
2.4s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
2.1s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
1.9s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
1.8s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize55.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
6.5b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))
2.3b
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J))
0.6b
(cbrt J)

rewrite6.3s

Algorithm
rewrite-expression-head
Rules
55×pow1
54×add-exp-log
37×pow-prod-down prod-exp cbrt-unprod
35×add-cbrt-cube
14×associate-*l/
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×associate-*r*
6×cbrt-prod sqrt-div
4×insert-posit16 add-log-exp
3×flip3-+ sqrt-prod flip-+
2×associate-*l* *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 98
Calls
4 calls:
Slowest
4.9s
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J))
1.2s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))
129.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
409.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))
265.0ms
(cbrt J)
253.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J))
161.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify21.1s

Counts
74 → 110
Calls
74 calls:
Slowest
993.0ms
(* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J))))
727.0ms
(* (* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (* (* -2 -2) -2)) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J)))) J)
723.0ms
(* (* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))) (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J)))) J)
647.0ms
(* (* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2)))) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2)))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J)))) J)
621.0ms
(* (* (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2)) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))) (* (* (* (cbrt J) (cbrt J)) (* (cbrt J) (cbrt J))) (* (cbrt J) (cbrt J)))) J)

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.5b

localize70.0ms

Local error

Found 4 expressions with local error:

8.7b
(sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1))
8.6b
(* (* (sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1)) -2) (* (cos (/ K 2)) J))
4.3b
(/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J)))
0.1b
(* U (/ U (* 2 (* (cos (/ K 2)) J))))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
105×add-cbrt-cube add-exp-log
51×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
19×pow1
11×add-sqr-sqrt
10×*-un-lft-identity
9×pow-prod-down
8×associate-*r* add-cube-cbrt
4×times-frac sqrt-div associate-*l* associate-*l/ sqrt-prod insert-posit16 add-log-exp
2×flip3-+ associate-*r/ *-commutative flip-+ div-inv
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 distribute-lft-out associate-/l* unswap-sqr associate-/l/
Counts
4 → 117
Calls
4 calls:
Slowest
263.0ms
(* (* (sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1)) -2) (* (cos (/ K 2)) J))
110.0ms
(sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1))
76.0ms
(/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J)))
49.0ms
(* U (/ U (* 2 (* (cos (/ K 2)) J))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
205.0ms
(* (* (sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1)) -2) (* (cos (/ K 2)) J))
146.0ms
(/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J)))
126.0ms
(sqrt (+ (/ (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* 2 (* (cos (/ K 2)) J))) 1))
74.0ms
(* U (/ U (* 2 (* (cos (/ K 2)) J))))

simplify48.2s

Counts
90 → 129
Calls
90 calls:
Slowest
3.2s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
3.1s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J))))
3.1s
(/ (* (* (* U U) U) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
2.8s
(/ (* (* (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))
2.8s
(/ (* (* (* U U) U) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))

prune1.8s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.5b

regimes689.0ms

Accuracy

5.1% (9.0b remaining)

Error of 17.5b against oracle of 8.6b and baseline of 18.0b

bsearch331.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
2.2s1490×body1280valid
1.9s1275×body640valid
1.6s4268×body80valid
540.0ms653×body320valid
147.0ms315×body160valid