Details

Time bar (total: 20.0s)

sample84.0ms

Algorithm
intervals
Results
26.0ms148×body80valid
23.0ms51×body1280valid
11.0ms35×body640valid
4.0ms18×body320valid
1.0ms4×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01724
13424
27124
313524
420824
549224
6323624
done500024

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
25.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
33.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
205.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
221.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
318.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
199.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: 2 (411.0ms)

IterNodesCost
01922013
15081800
223681613
done50021613

prune655.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp associate-*r/ sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
29.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
18.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
141.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
63.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series771.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
197.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
285.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
224.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts
94 → 94
Iterations

Useful iterations: 2 (473.0ms)

IterNodesCost
01991983
15441775
224271561
done50021561

prune623.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.5b

localize42.0ms

Local error

Found 4 expressions with local error:

1.5b
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.6b
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
13.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×pow1
13×cbrt-prod add-cbrt-cube add-exp-log
11×add-sqr-sqrt
9×add-cube-cbrt
7×sqrt-prod
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* flip-+ distribute-lft-out
2×rem-sqrt-square sqrt-pow1 sqrt-div
1×pow1/2 associate-*l* *-commutative
Counts
4 → 70
Calls
4 calls:
84.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
47.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
33.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
46.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
362.0ms
(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
124.0ms
(* (* -2.0 (* J (cos (/ K 2.0)))) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
320.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
353.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify904.0ms

Counts
82 → 82
Iterations

Useful iterations: done (898.0ms)

IterNodesCost
01572283
13672144
215551864
done50011809

prune831.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.5b

localize42.0ms

Local error

Found 4 expressions with local error:

6.7b
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.4b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
12×sqrt-prod
11×cbrt-prod add-sqr-sqrt
9×add-cube-cbrt
6×pow1 sqrt-div
4×cbrt-div flip3-+ add-cbrt-cube add-exp-log flip-+ distribute-lft-out add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 63
Calls
4 calls:
28.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
65.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
98.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
53.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
360.0ms
(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
231.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
242.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
329.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify836.0ms

Counts
75 → 75
Iterations

Useful iterations: done (832.0ms)

IterNodesCost
01101821
12121623
24981527
316091513
done50001507

prune666.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.5b

regimes790.0ms

Accuracy

91.4% (0.5b remaining)

Error of 12.8b against oracle of 12.3b and baseline of 17.5b

bsearch4.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
032118
14599
done4599

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.3s1509×body1280valid
1.2s4345×body80valid
971.0ms1203×body640valid
254.0ms645×body320valid
122.0ms299×body160valid