Details

Time bar (total: 10.3s)

sample78.0ms

Algorithm
intervals
Results
26.0ms46×body1280valid
16.0ms44×body640valid
12.0ms131×body80valid
5.0ms19×body320valid
3.0ms16×body160valid

simplify48.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite253.0ms

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:
18.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
146.0ms
(* (* (* -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)))

series470.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
122.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
174.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
127.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify60.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04531006
11965898
25001898

prune482.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.0b

localize22.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite247.0ms

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:
61.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
61.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
60.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
62.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
199.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
130.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
128.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
01891016
1461986
21696986
35001962

prune770.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.0b

localize29.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
12.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.6b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
13×*-un-lft-identity
12×pow1 cbrt-prod
9×sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt add-cube-cbrt
4×add-exp-log frac-times add-cbrt-cube add-log-exp
3×distribute-lft-out
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 69
Calls
4 calls:
67.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
31.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
30.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
32.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series827.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(sqrt (* (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))) (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
203.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
200.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
200.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify98.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
02101282
15641214
225741208
350011182

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.3b
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×sqrt-prod
15×add-exp-log add-sqr-sqrt
12×add-cube-cbrt
11×unpow-prod-down
9×pow1
6×pow-unpow sqrt-div
5×sqrt-pow1 pow-exp
4×add-cbrt-cube add-log-exp
3×rem-sqrt-square times-frac pow1/2 div-exp prod-exp distribute-lft-out
2×pow-to-exp pow-pow flip3-+ flip-+ sqr-pow
1×div-inv
Counts
4 → 80
Calls
4 calls:
22.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
61.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
60.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
64.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

series656.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
200.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
128.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
200.0ms
(pow (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) 1/4)

simplify44.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0394980
11269945
25002943

prune724.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 10.0b

regimes677.0ms

Accuracy

79.5% (1.1b remaining)

Error of 13.7b against oracle of 12.6b and baseline of 18.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample2.2s

Algorithm
intervals
Results
863.0ms1502×body1280valid
487.0ms1280×body640valid
387.0ms4292×body80valid
170.0ms626×body320valid
55.0ms303×body160valid