Details

sample199.0ms

Algorithm

intervals

Results

65.0ms	43×	body	1280	valid
58.0ms	154×	body	80	valid
34.0ms	32×	body	640	valid
17.0ms	21×	body	320	valid
3.0ms	6×	body	160	valid

simplify215.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

214.0ms

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.8b

localize46.0ms

Local error

Found 4 expressions with local error:

8.8b	(* (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)))

rewrite94.0ms

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

35.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
26.0ms	(* J (* (cos (/ K 2)) 2))
19.0ms	(* (cos (/ K 2)) (* -2 J))
13.0ms	(/ U (* J (* (cos (/ K 2)) 2)))

series634.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

384.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (cos (/ K 2)) (* -2 J)))
126.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
66.0ms	(* (cos (/ K 2)) (* -2 J))
57.0ms	(* J (* (cos (/ K 2)) 2))

simplify6.6s

Counts

55 → 104

Calls

55 calls:

Slowest

517.0ms	(* (* (* (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)))
432.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
369.0ms	(+ (* 1/16 (/ (* (pow K 2) U) J)) (* 1/2 (/ U J)))
356.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.0b

localize65.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.8b	(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	(* J (* (cos (/ K 2)) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `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 → 80

Calls

4 calls:

Slowest

40.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
29.0ms	(* 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)))))

series898.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

309.0ms	(* (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (* (cos (/ K 2)) (* -2 J)))
285.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
237.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
67.0ms	(* J (* (cos (/ K 2)) 2))

simplify3.9s

Counts

45 → 92

Calls

45 calls:

Slowest

475.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
414.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
290.0ms	(* (* (* (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))))
271.0ms	(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 J) (* -2 J)) (* -2 J))))
247.0ms	(* (* (* (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)) (cos (/ K 2))) (cos (/ K 2))) (* (* (* -2 -2) -2) (* (* J J) J))))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize94.0ms

Local error

Found 4 expressions with local error:

8.8b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.8b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.8b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
8.8b	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

rewrite11.0ms

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

3.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
2.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

series956.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

273.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
250.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
230.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
202.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))

simplify1.2s

Counts

32 → 76

Calls

32 calls:

Slowest

103.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
103.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))
88.0ms	(sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))
77.0ms	(sqrt (sqrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))))
76.0ms	(sqrt (* (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2))))) (cbrt (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))))))

prune1.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.0b

localize69.0ms

Local error

Found 4 expressions with local error:

6.9b	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
0.1b	(* J (* (cos (/ K 2)) 2))
0.1b	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
0.1b	(/ U (* J (* (cos (/ K 2)) 2)))

rewrite249.0ms

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

147.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
59.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
27.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
13.0ms	(* J (* (cos (/ K 2)) 2))

series597.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

313.0ms	(* (hypot 1 (/ U (* J (* (cos (/ K 2)) 2)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))
139.0ms	(/ U (* J (* (cos (/ K 2)) 2)))
75.0ms	(* J (* (cos (/ K 2)) 2))
69.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))

simplify9.2s

Counts

65 → 113

Calls

65 calls:

Slowest

470.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* 2 2) 2)))
439.0ms	(* (* (* (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))) (* -2 J))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))))
415.0ms	(* (* (* J J) J) (* (* (* (cos (/ K 2)) 2) (* (cos (/ K 2)) 2)) (* (cos (/ K 2)) 2)))
408.0ms	(* (* (* (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)))))
394.0ms	(/ (* (* U U) U) (* (* (* J (* (cos (/ K 2)) 2)) (* J (* (cos (/ K 2)) 2))) (* J (* (cos (/ K 2)) 2))))

prune1.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.0b

regimes492.0ms

Accuracy

-13.8% (4.6b remaining)

Error of 8.4b against oracle of 3.8b and baseline of 7.9b

bsearch406.0ms

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.4s	1496×	body	1280	valid
1.3s	1233×	body	640	valid
1.1s	4337×	body	80	valid
893.0ms	635×	body	320	valid
165.0ms	303×	body	160	valid