Details

Time bar (total: 28.1s)

sample84.0ms

Algorithm
intervals
Results
23.0ms47×body1280valid
16.0ms41×body640valid
12.0ms129×body80valid
8.0ms28×body320valid
2.0ms11×body160valid

simplify2.6s

Counts
1 → 1

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize27.0ms

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)
5.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite388.0ms

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-*r/ associate-*l* *-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:
19.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
26.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
209.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
132.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series769.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
210.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
275.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
206.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify918.0ms

Counts
97 → 97

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize49.0ms

Local error

Found 4 expressions with local error:

5.3b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
5.3b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite363.0ms

Algorithm
rewrite-expression-head
Rules
32×sqrt-prod
18×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 add-cube-cbrt sqrt-pow1
6×rem-sqrt-square pow1/2
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
4 → 76
Calls
4 calls:
92.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
77.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
84.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
106.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
350.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
355.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
211.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
195.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify714.0ms

Counts
88 → 88

prune710.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.3b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.2b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.7b
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (/ 1 4))

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
21×add-sqr-sqrt
18×add-cube-cbrt
16×pow-unpow sqrt-prod
15×add-exp-log
12×times-frac
11×unpow-prod-down
9×pow1
6×sqrt-div
5×sqrt-pow1 pow-exp
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square pow1/2 div-exp prod-exp distribute-lft-out
2×pow-to-exp pow-pow flip3-+ flip-+ div-inv sqr-pow
Counts
4 → 90
Calls
4 calls:
23.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
102.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
69.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
138.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (/ 1 4))

series1.2s

Counts
4 → 12
Calls
4 calls:
235.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
333.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
244.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
345.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (/ 1 4))

simplify696.0ms

Counts
102 → 102

prune813.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.3b

localize59.0ms

Local error

Found 4 expressions with local error:

13.7b
(pow (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (/ 1 4))
30.8b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
30.8b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
30.8b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
24×unpow-prod-down
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
13×pow-unpow
5×pow1 add-exp-log
4×add-cbrt-cube div-inv add-log-exp sqr-pow
3×pow1/3
1×pow-to-exp pow-pow pow-exp
Counts
4 → 84
Calls
4 calls:
10.0ms
(pow (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (/ 1 4))
10.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
10.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
32.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

series8.3s

Counts
4 → 12
Calls
4 calls:
452.0ms
(pow (+ 1.0 (* (* (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (/ 1 4))
2.4s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
3.0s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
2.5s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

simplify993.0ms

Counts
96 → 96

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.3b

regimes455.0ms

Accuracy

91% (0.5b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 18.0b

bsearch3.0ms

simplify1.6s

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s1298×body640valid
1.2s1474×body1280valid
795.0ms4326×body80valid
213.0ms606×body320valid
79.0ms301×body160valid