Details

sample194.0ms

Algorithm

intervals

Results

75.0ms	47×	body	1280	valid
43.0ms	45×	body	640	valid
31.0ms	130×	body	80	valid
15.0ms	22×	body	320	valid
6.0ms	12×	body	160	valid

simplify311.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

311.0ms

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize53.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite125.0ms

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

48.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
29.0ms	(* J (* (cos (/ K 2)) 2))
29.0ms	(* (cos (/ K 2)) (* -2 J))
18.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

379.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
130.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
81.0ms	(* J (* (cos (/ K 2)) 2))
65.0ms	(* (cos (/ K 2)) (* -2 J))

simplify6.9s

Counts

55 → 104

Calls

55 calls:

Slowest

745.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
459.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
434.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
405.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
366.0ms	(* (* (* (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))))

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.6b

localize58.0ms

Local error

Found 4 expressions with local error:

6.5b	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))
0.1b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

Slowest

47.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
20.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
16.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
14.0ms	(* J (* (cos (/ K 2)) 2))

series826.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

366.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
298.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
101.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
60.0ms	(* J (* (cos (/ K 2)) 2))

simplify7.1s

Counts

58 → 105

Calls

58 calls:

Slowest

523.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
473.0ms	(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))))
423.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
406.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
343.0ms	(* (* (* (* (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)) (cos (/ K 2))) (cos (/ K 2)))) (* (* (* -2 J) (* -2 J)) (* -2 J)))

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.6b

localize40.0ms

Local error

Found 4 expressions with local error:

6.4b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.4b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
0.2b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))

rewrite147.0ms

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

107.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
36.0ms	(* (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

377.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J))))
367.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
233.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
231.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify7.1s

Counts

55 → 101

Calls

55 calls:

Slowest

517.0ms	(* (* (* (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)))))
511.0ms	(* (* (* (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)))))
405.0ms	(* (* (* (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)))))
389.0ms	(* (* (* (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)))))
332.0ms	(* (* (* (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)))))) (* (* (* (cos (/ K 2)) (* -2 J)) (* (cos (/ K 2)) (* -2 J))) (* (cos (/ K 2)) (* -2 J))))

prune1.4s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.6b

localize92.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.7b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.7b	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
6.4b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

397.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
370.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
362.0ms	(cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
210.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify2.6s

Counts

26 → 70

Calls

26 calls:

Slowest

469.0ms	(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
371.0ms	(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
370.0ms	(exp (* 1/3 (- (+ (log (/ -1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ -1 U)))))
294.0ms	(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))
260.0ms	(exp (* 1/3 (- (+ (log (/ 1 J)) (log (/ 1/2 (cos (* 1/2 K))))) (log (/ 1 U)))))

prune1.3s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 2.6b

regimes518.0ms

Accuracy

-12.8% (4.1b remaining)

Error of 7.9b against oracle of 3.7b and baseline of 7.4b

bsearch388.0ms

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.7s	1558×	body	1280	valid
1.6s	4247×	body	80	valid
1.5s	1248×	body	640	valid
485.0ms	605×	body	320	valid
216.0ms	344×	body	160	valid