Details

sample51.0ms

Algorithm

intervals

Results

17.0ms	255×	body	80	valid
15.0ms	237×	body	80	overflowed
0.0ms	1×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1361	13
6	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite96.0ms

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)))
8.0ms	(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))))
22.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
133.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
194.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
150.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	453	1007
1	1964	898
2	5001	898

prune296.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.6b

localize18.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.5b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.4b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite96.0ms

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:

24.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms	(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)))

series728.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
219.0ms	(sqrt (sqrt (+ 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)))
141.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	189	1016
1	461	986
2	1696	986
3	5001	962

prune359.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 13.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.7b	(* (* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
29×	`pow1`
27×	`add-cbrt-cube`
19×	`prod-exp`
16×	`*-un-lft-identity` `pow-prod-down` `cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt`
11×	`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 → 94

Calls

4 calls:

24.0ms	(* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0))))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
123.0ms	(* (* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (cos (/ K 2.0))))
132.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
200.0ms	(* (* (* (* -2.0 J) (sqrt (cos (/ K 2.0)))) (sqrt (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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	513	1269
1	2313	1048
2	5002	1048

prune313.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 13.6b

localize27.0ms

Local error

Found 4 expressions with local error:

4.0b	(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
4.2b	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
15.2b	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
22.4b	(/ (* (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (* (* -2.0 J) (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`sqrt-div`
6×	`pow1` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
5×	`distribute-lft-out`
4×	`cbrt-undiv` `unpow-prod-down` `flip3-+` `cube-prod` `div-exp` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*l/` `associate-/r/` `associate-/l/`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `frac-2neg` `diff-log` `clear-num` `sum-cubes` `flip--` `div-inv` `associate-/l*`

Counts

4 → 84

Calls

4 calls:

72.0ms	(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
44.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
103.0ms	(/ (* (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (* (* -2.0 J) (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

130.0ms	(sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3)))
505.0ms	(sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
497.0ms	(- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
1.1s	(/ (* (sqrt (+ (pow 1.0 3) (pow (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) 3))) (* (* -2.0 J) (cos (/ K 2.0)))) (sqrt (+ (* 1.0 1.0) (- (* (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)) (* 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))

simplify114.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	707	3127
1	3501	2783
2	5002	2783

prune495.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.6b

regimes255.0ms

Accuracy

76.7% (1.3b remaining)

Error of 14.3b against oracle of 13.0b and baseline of 18.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	61
1	50	61

end0.0ms

sample1.2s

Algorithm

intervals

Results

531.0ms	7992×	body	80	valid
354.0ms	6703×	body	80	overflowed
2.0ms	10×	body	160	valid