Details

Time bar (total: 7.7s)

sample57.0ms

Algorithm
intervals
Results
18.0ms41×body1280valid
9.0ms147×body80valid
9.0ms37×body640valid
4.0ms21×body320valid
1.0ms10×body160valid

simplify43.0ms

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: 15.4b

localize15.0ms

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)
5.8b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite241.0ms

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:
17.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
140.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
59.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series547.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
138.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
195.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
153.0ms
(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 (11.0ms)

IterNodesCost
04531006
11965898
25001898

prune267.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.5b

localize17.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
5.7b
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite231.0ms

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:
58.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
57.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
57.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
57.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series756.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
225.0ms
(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
153.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
154.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
01891016
1461986
21696986
35001962

prune355.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.5b

localize31.0ms

Local error

Found 4 expressions with local error:

8.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
12×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+ distribute-lft-out add-log-exp
3×pow1/3
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
58.0ms
(sqrt (+ 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)))
29.0ms
(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)))

series842.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
230.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
233.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
231.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0179931
1406873
21387861
35002850

prune456.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.5b

localize25.0ms

Local error

Found 4 expressions with local error:

5.7b
(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))))))
8.8b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.1b
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
8×pow1 cbrt-prod add-sqr-sqrt
7×add-cube-cbrt
6×cbrt-div sqrt-div
5×sqrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×sqrt-pow1 distribute-lft-out
2×pow1/2 pow1/3 associate-*r/
1×rem-sqrt-square pow-prod-down
Counts
4 → 57
Calls
4 calls:
35.0ms
(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))))))
59.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
29.0ms
(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)))

series912.0ms

Counts
4 → 12
Calls
4 calls:
306.0ms
(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))))))
146.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
231.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
229.0ms
(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
02491053
1623993
22353985
35002977

prune399.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 10.5b

regimes425.0ms

Accuracy

83.1% (1.0b remaining)

Error of 13.4b against oracle of 12.4b and baseline of 18.1b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04550
14550

end0.0ms

sample1.6s

Algorithm
intervals
Results
541.0ms1489×body1280valid
306.0ms1216×body640valid
297.0ms4381×body80valid
109.0ms610×body320valid
39.0ms307×body160valid