Details

Time bar (total: 8.6s)

sample66.0ms

Algorithm
intervals
Results
20.0ms46×body1280valid
13.0ms42×body640valid
12.0ms133×body80valid
5.0ms21×body320valid
2.0ms14×body160valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 19.4b

Counts
2 → 1

localize16.0ms

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)
8.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
97×associate-*l*
70×unpow-prod-down
66×times-frac
59×*-un-lft-identity
55×add-cube-cbrt
37×associate-*r*
32×unswap-sqr
28×add-exp-log
20×pow1
18×add-cbrt-cube
12×prod-exp
11×sqrt-prod *-commutative
9×pow-prod-down cbrt-unprod
4×sqrt-div pow-exp add-log-exp
3×pow-unpow div-exp
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 188
Calls
4 calls:
8.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
25.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
34.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
132.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
185.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
141.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify103.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011512379
141852271
250022271

prune684.0ms

Filtered
200 candidates to 144 candidates (72.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New19010200
Fresh000
Picked011
Done000
Total19011201

Merged error: 14.4b

Counts
201 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (/ U (* 2.0 J)) 2.0)
0.3b
(pow (/ 1 (cos (/ K 2.0))) 2.0)
8.6b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0)))))
9.6b
(sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
53×unpow-prod-down
51×*-un-lft-identity
48×associate-*l*
45×times-frac
43×add-cube-cbrt
24×add-exp-log
23×associate-*r*
19×unswap-sqr
17×pow1
13×sqrt-prod add-cbrt-cube
7×pow-exp prod-exp
6×pow-unpow pow-prod-down *-commutative cbrt-unprod
4×pow-pow sqrt-div div-exp distribute-lft-out add-log-exp
2×pow-to-exp flip3-+ associate-*r/ flip-+ div-inv sqr-pow
1×rem-sqrt-square rec-exp pow-flip sqrt-pow1 pow1/2 1-exp inv-pow
Counts
4 → 160
Calls
4 calls:
12.0ms
(pow (/ U (* 2.0 J)) 2.0)
7.0ms
(pow (/ 1 (cos (/ K 2.0))) 2.0)
62.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0)))))
47.0ms
(sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(pow (/ U (* 2.0 J)) 2.0)
151.0ms
(pow (/ 1 (cos (/ K 2.0))) 2.0)
301.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0)))))
286.0ms
(sqrt (+ 1.0 (* (pow (/ 1 (cos (/ K 2.0))) 2.0) (pow (/ U (* 2.0 J)) 2.0))))

simplify95.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
010152028
137541915
250011915

prune599.0ms

Filtered
172 candidates to 116 candidates (67.4%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1684172
Fresh279
Picked011
Done011
Total17013183

Merged error: 14.4b

Counts
183 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.6b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite126.0ms

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:
31.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
34.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
30.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
30.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series731.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
224.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
141.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
145.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
01891016
1461986
21696986
35001962

prune376.0ms

Filtered
88 candidates to 62 candidates (70.5%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New87188
Fresh1910
Picked011
Done022
Total8813101

Merged error: 14.4b

Counts
101 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

8.6b
(sqrt (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
9.6b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
16.0b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
36×sqrt-prod
26×add-sqr-sqrt
20×*-un-lft-identity
14×cbrt-prod
12×add-cube-cbrt
10×associate-*r*
8×pow1
6×cbrt-div sqrt-div unswap-sqr
5×rem-sqrt-square
4×add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×sqrt-pow1 associate-*l*
2×pow1/2 pow1/3 associate-*r/
1×pow-prod-down *-commutative
Counts
4 → 81
Calls
4 calls:
40.0ms
(sqrt (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
30.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
34.0ms
(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)))

series943.0ms

Counts
4 → 12
Calls
4 calls:
312.0ms
(sqrt (* (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))) (sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
160.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
236.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
234.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify84.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
03091705
17821645
229791631
350011615

prune528.0ms

Filtered
93 candidates to 70 candidates (75.3%)
Pruning

13 alts after pruning (9 fresh and 4 done)

PrunedKeptTotal
New93093
Fresh099
Picked011
Done033
Total9313106

Merged error: 14.4b

Counts
106 → 13

regimes437.0ms

Accuracy

92% (0.4b remaining)

Error of 12.5b against oracle of 12.1b and baseline of 17.3b

bsearch7.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample1.9s

Algorithm
intervals
Results
703.0ms1426×body1280valid
416.0ms1218×body640valid
366.0ms4440×body80valid
148.0ms586×body320valid
56.0ms332×body160valid