Details

sample197.0ms

Algorithm

intervals

Results

73.0ms	42×	body	1280	valid
44.0ms	46×	body	640	valid
32.0ms	133×	body	80	valid
17.0ms	25×	body	320	valid
5.0ms	10×	body	160	valid

simplify647.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

646.0ms

(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize44.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (cos (/ K 2)) (* -2 J))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

Slowest

57.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
27.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
21.0ms	(* (cos (/ K 2)) (* -2 J))
15.0ms	(* J (* (cos (/ K 2)) 2))

series647.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

374.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
130.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
78.0ms	(* J (* (cos (/ K 2)) 2))
65.0ms	(* (cos (/ K 2)) (* -2 J))

simplify6.9s

Counts

55 → 104

Calls

55 calls:

Slowest

479.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
443.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
391.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
383.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))
375.0ms	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
0.2b	(/ 1 (* J (* (cos (/ K 2)) 2)))
0.1b	(* J (* (cos (/ K 2)) 2))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
41×	`add-cbrt-cube`
37×	`prod-exp`
26×	`pow1`
19×	`cbrt-unprod`
13×	`add-sqr-sqrt` `pow-prod-down`
12×	`div-exp`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`cbrt-undiv` `rec-exp` `times-frac` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `pow-flip` `associate-/l`
2×	`div-inv`
1×	`clear-num` `associate-/r` `frac-2neg` `associate-r/` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 120

Calls

4 calls:

Slowest

83.0ms	(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
72.0ms	(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
22.0ms	(/ 1 (* J (* (cos (/ K 2)) 2)))
14.0ms	(* J (* (cos (/ K 2)) 2))

series596.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

343.0ms	(* (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
106.0ms	(* U (/ 1 (* J (* (cos (/ K 2)) 2))))
96.0ms	(/ 1 (* J (* (cos (/ K 2)) 2)))
50.0ms	(* J (* (cos (/ K 2)) 2))

simplify14.0s

Counts

81 → 132

Calls

81 calls:

Slowest

487.0ms	(+ (log (hypot 1 (* U (/ 1 (* J (* (cos (/ K 2)) 2)))))) (+ (log (cos (/ K 2))) (log (* -2 J))))
487.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
483.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
479.0ms	(+ (log U) (- (log 1) (log (* J (* (cos (/ K 2)) 2)))))
478.0ms	(* (* (* U U) U) (/ (* (* 1 1) 1) (* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))))

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

8.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.6b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.1b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-l` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 89

Calls

4 calls:

Slowest

129.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
70.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

365.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
314.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
295.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
231.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify7.6s

Counts

55 → 101

Calls

55 calls:

Slowest

526.0ms	(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))))
440.0ms	(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))
423.0ms	(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J)))))
417.0ms	(* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))))
347.0ms	(+ (log (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (+ (log (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))) (+ (log (cos (/ K 2))) (+ (log -2) (log J)))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.2b

localize40.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
32×	`pow1`
22×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
12×	`associate-l`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `-commutative` `sqrt-prod` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 101

Calls

4 calls:

Slowest

130.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
53.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
16.0ms	(* J (* (cos (/ K 2)) 2))
13.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series617.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

373.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
125.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
63.0ms	(* J (* (cos (/ K 2)) 2))
56.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))

simplify9.8s

Counts

65 → 113

Calls

65 calls:

Slowest

628.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
510.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
456.0ms	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* (sqrt (cos (/ K 2))) (* -2 J)) (* (sqrt (cos (/ K 2))) (* -2 J))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
453.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
419.0ms	(* (* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* (sqrt (cos (/ K 2))) (sqrt (cos (/ K 2)))) (sqrt (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))))

prune1.7s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

regimes429.0ms

Accuracy

0% (3.9b remaining)

Error of 7.7b against oracle of 3.8b and baseline of 7.7b

bsearch3.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	1490×	body	1280	valid
1.3s	1275×	body	640	valid
1.1s	4268×	body	80	valid
818.0ms	653×	body	320	valid
184.0ms	315×	body	160	valid