Details

sample218.0ms

Algorithm

intervals

Results

71.0ms	50×	body	1280	valid
45.0ms	21×	body	320	valid
43.0ms	40×	body	640	valid
38.0ms	139×	body	80	valid
3.0ms	6×	body	160	valid

simplify286.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

286.0ms

(* (* (* -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

localize32.0ms

Local error

Found 4 expressions with local error:

8.5b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* J (* (cos (/ K 2)) 2))
0.2b	(* (cos (/ K 2)) (* -2 J))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite124.0ms

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

65.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
29.0ms	(* J (* (cos (/ K 2)) 2))
17.0ms	(* (cos (/ K 2)) (* -2 J))
13.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series607.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

354.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
119.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
73.0ms	(* (cos (/ K 2)) (* -2 J))
62.0ms	(* J (* (cos (/ K 2)) 2))

simplify6.8s

Counts

55 → 104

Calls

55 calls:

Slowest

543.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
531.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J)))
429.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
375.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))
363.0ms	(* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J)))

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

localize39.0ms

Local error

Found 4 expressions with local error:

8.6b	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
0.2b	(* J (* (cos (/ K 2)) 2))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))
0.0b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

rewrite107.0ms

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

38.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
28.0ms	(* J (* (cos (/ K 2)) 2))
26.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
13.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

367.0ms	(* (* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2))) (* -2 J))
249.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (cos (/ K 2)))
92.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
61.0ms	(* J (* (cos (/ K 2)) 2))

simplify7.2s

Counts

58 → 105

Calls

58 calls:

Slowest

540.0ms	(* (* (* (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))))
441.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
437.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
358.0ms	(/ (* (* U U) U) (* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2))))
350.0ms	(- (log U) (+ (log J) (+ (log (cos (/ K 2))) (log 2))))

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.5b

localize48.0ms

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)))))
0.2b	(* J (* (cos (/ K 2)) 2))
0.2b	(* J (* (cos (/ K 2)) 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
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 → 74

Calls

4 calls:

Slowest

14.0ms	(* J (* (cos (/ K 2)) 2))
14.0ms	(* J (* (cos (/ K 2)) 2))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
1.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

269.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
264.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
74.0ms	(* J (* (cos (/ K 2)) 2))
63.0ms	(* J (* (cos (/ K 2)) 2))

simplify3.2s

Counts

38 → 86

Calls

38 calls:

Slowest

535.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
451.0ms	(+ (log J) (log (* (cos (/ K 2)) 2)))
444.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
416.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
400.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.5b

localize74.0ms

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

Slowest

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

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

307.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
259.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
223.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
214.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify1.2s

Counts

32 → 76

Calls

32 calls:

Slowest

102.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
101.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
95.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
77.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
77.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

prune1.3s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.5b

regimes557.0ms

Accuracy

-40.3% (5.5b remaining)

Error of 9.4b against oracle of 3.8b and baseline of 7.8b

bsearch435.0ms

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.1s	1490×	body	1280	valid
1.8s	1231×	body	640	valid
1.6s	4372×	body	80	valid
406.0ms	622×	body	320	valid
131.0ms	288×	body	160	valid