Details

Time bar (total: 26.1s)

sample84.0ms

Algorithm
intervals
Results
24.0ms47×body1280valid
15.0ms145×body80valid
13.0ms35×body640valid
6.0ms22×body320valid
1.0ms7×body160valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
13424
27224
313624
421424
549824
6335624
done500224

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.3b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
22×add-cbrt-cube
18×add-sqr-sqrt
16×*-un-lft-identity
15×pow1
12×add-cube-cbrt prod-exp
9×cbrt-unprod
8×unpow-prod-down sqrt-prod
7×associate-*r*
6×times-frac div-exp pow-prod-down
4×expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow hypot-def associate-/l*
2×flip3-+ associate-*r/ flip-+ div-inv distribute-lft-out sqr-pow
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*l* clear-num associate-/r* *-commutative
Counts
4 → 101
Calls
4 calls:
19.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
40.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
219.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
83.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series775.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
191.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
256.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
190.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02222298
16132082
228831877
done50011875

prune539.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.1b
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
6.9b
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-*l* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 88
Calls
4 calls:
30.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
19.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
97.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.0s

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
55.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
115.0ms
(/ U (* (* 2.0 J) (cos (/ K 2.0))))
800.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.9s

Counts
100 → 100
Iterations

Useful iterations: 2 (493.0ms)

IterNodesCost
01931843
14981816
229781437
done50011437

prune572.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
6.9b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.9b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite876.0ms

Algorithm
rewrite-expression-head
Rules
29×pow1
27×add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
12×add-sqr-sqrt associate-*r* sqrt-prod
10×add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative
Counts
4 → 85
Calls
4 calls:
328.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
541.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
2.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.8s

Counts
4 → 12
Calls
4 calls:
645.0ms
(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
783.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
664.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
740.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.8s

Counts
97 → 97
Iterations

Useful iterations: 2 (371.0ms)

IterNodesCost
01563825
14073009
221542451
done50002451

prune649.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
6.9b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.9b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.9b
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
13×add-exp-log add-cbrt-cube
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*l* *-commutative
Counts
4 → 71
Calls
4 calls:
112.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series3.0s

Counts
4 → 12
Calls
4 calls:
844.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
732.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
696.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
762.0ms
(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.0s

Counts
83 → 83
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01242323
13052079
214031861
done50001851

prune498.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.1b

regimes433.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 7.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01926
12426
done2426

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.2s1448×body1280valid
1.1s1227×body640valid
758.0ms4429×body80valid
290.0ms590×body320valid
127.0ms309×body160valid