Details

Time bar (total: 12.4s)

sample86.0ms

Algorithm
intervals
Results
31.0ms52×body1280valid
16.0ms38×body640valid
15.0ms132×body80valid
8.0ms25×body320valid
2.0ms9×body160valid

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03413
17413
213813
320313
436813
5136113
6500113

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

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)
7.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite101.0ms

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:
6.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
57.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
27.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series504.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
137.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
181.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
139.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04531006
11965898
25001898

prune299.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

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)
7.2b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite87.0ms

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/ associate-*r* pow-exp 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:
6.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
48.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series690.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
125.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
380.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
139.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify55.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0488987
12021866
25002866

prune285.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.0b

localize19.0ms

Local error

Found 4 expressions with local error:

7.2b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.2b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite97.0ms

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:
23.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
25.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
212.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
136.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
142.0ms
(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

prune346.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.0b

localize20.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (+ 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)))))
31.6b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
31.6b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
31.6b
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod
21×unpow-prod-down
15×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
9×times-frac
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod div-inv sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 72
Calls
4 calls:
2.0ms
(sqrt (+ 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)))))
6.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
3.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
4.0ms
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

series5.2s

Counts
4 → 12
Calls
4 calls:
281.0ms
(sqrt (+ 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)))))
1.7s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
1.7s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))
1.6s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

simplify64.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
08132131
119232055
250022055

prune695.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 11.0b

regimes364.0ms

Accuracy

91.2% (0.5b remaining)

Error of 12.8b against oracle of 12.3b and baseline of 18.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04950
14950

end0.0ms

sample2.5s

Algorithm
intervals
Results
896.0ms1435×body1280valid
585.0ms1275×body640valid
530.0ms4349×body80valid
215.0ms612×body320valid
80.0ms332×body160valid