Details

sample350.0ms

Algorithm

intervals

Results

116.0ms	83×	body	640	valid
107.0ms	69×	body	1280	valid
55.0ms	267×	body	80	valid
26.0ms	41×	body	320	valid
14.0ms	30×	body	160	valid

simplify212.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

212.0ms

(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize51.0ms

Local error

Found 3 expressions with local error:

5.2b	(- (exp l) (exp (- l)))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`sub-neg` `flip3--` `insert-posit16` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

Slowest

71.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
39.0ms	(* J (- (exp l) (exp (- l))))
24.0ms	(- (exp l) (exp (- l)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

157.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
77.0ms	(* J (- (exp l) (exp (- l))))
67.0ms	(- (exp l) (exp (- l)))

simplify4.2s

Counts

42 → 72

Calls

42 calls:

Slowest

650.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
268.0ms	(* (* (* (* J (- (exp l) (exp (- l)))) (* J (- (exp l) (exp (- l))))) (* J (- (exp l) (exp (- l))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
262.0ms	(* (* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
261.0ms	(+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))
246.0ms	(* J (- (exp l) (exp (* -1 l))))

prune966.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/3 l)
0.1b	(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
0.1b	(* l (* 1/3 l))
0.0b	(* (pow l 5) 1/60)

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
18×	`add-sqr-sqrt` `add-cbrt-cube`
16×	`pow1`
14×	`associate-l`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-r` `prod-exp`
8×	`cbrt-unprod`
7×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`associate-l/` `associate-r/` `sqr-pow`
1×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 85

Calls

4 calls:

Slowest

180.0ms	(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
27.0ms	(* l (* 1/3 l))
17.0ms	(* (pow l 5) 1/60)
10.0ms	(* 1/3 l)

series423.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
96.0ms	(* (pow l 5) 1/60)
48.0ms	(* l (* 1/3 l))
27.0ms	(* 1/3 l)

simplify5.5s

Counts

58 → 97

Calls

58 calls:

Slowest

788.0ms	(* (* (* (* J J) J) (* (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
685.0ms	(* (* (* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)))) (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
436.0ms	(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
378.0ms	(* (* J (+ (pow (* l (+ (* l (* 1/3 l)) 2)) 3) (pow (* (pow l 5) 1/60) 3))) (cos (/ K 2)))
352.0ms	(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.4b	(* 1/3 l)
0.1b	(* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2)))
0.1b	(* l (* 1/3 l))
0.1b	(* J (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2))))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`associate-l/` `-commutative` `insert-posit16` `add-log-exp`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

Slowest

122.0ms	(* J (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2))))
121.0ms	(* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2)))
13.0ms	(* l (* 1/3 l))
10.0ms	(* 1/3 l)

series353.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

182.0ms	(* J (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2))))
114.0ms	(* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (cos (/ K 2)))
36.0ms	(* l (* 1/3 l))
22.0ms	(* 1/3 l)

simplify8.7s

Counts

52 → 92

Calls

52 calls:

Slowest

713.0ms	(* (* (* J J) J) (* (* (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2)))))
608.0ms	(* (cbrt (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cbrt (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))))
558.0ms	(+ (log (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (log (cos (/ K 2))))
550.0ms	(* (* (* (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60)) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
503.0ms	(* (sqrt (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (sqrt (cos (/ K 2))))

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

5.2b	(- (* J (exp l)) (/ J (exp l)))
0.0b	(/ J (exp l))
0.0b	(* J (exp l))
0.0b	(* (- (* J (exp l)) (/ J (exp l))) (cos (/ K 2)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
10×	`add-cbrt-cube`
9×	`times-frac`
8×	`pow1` `add-exp-log`
7×	`associate-l`
6×	`associate-r` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`flip3--` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp`

Counts

4 → 83

Calls

4 calls:

Slowest

64.0ms	(* (- (* J (exp l)) (/ J (exp l))) (cos (/ K 2)))
23.0ms	(- (* J (exp l)) (/ J (exp l)))
9.0ms	(* J (exp l))
5.0ms	(/ J (exp l))

series270.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

138.0ms	(* (- (* J (exp l)) (/ J (exp l))) (cos (/ K 2)))
67.0ms	(- (* J (exp l)) (/ J (exp l)))
33.0ms	(/ J (exp l))
32.0ms	(* J (exp l))

simplify3.7s

Counts

61 → 95

Calls

61 calls:

Slowest

474.0ms	(* (- (pow (* J (exp l)) 3) (pow (/ J (exp l)) 3)) (cos (/ K 2)))
404.0ms	(* -1 (* (cos (* 1/2 K)) (* J (- (/ 1 (exp l)) (exp l)))))
396.0ms	(/ (* (* J J) J) (* (* (exp l) (exp l)) (exp l)))
394.0ms	(* (* (* (- (* J (exp l)) (/ J (exp l))) (- (* J (exp l)) (/ J (exp l)))) (- (* J (exp l)) (/ J (exp l)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
335.0ms	(* (* (* J J) J) (* (* (exp l) (exp l)) (exp l)))

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes322.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample10.1s

Algorithm

intervals

Results

3.6s	2587×	body	1280	valid
2.8s	2630×	body	640	valid
2.0s	8320×	body	80	valid
907.0ms	1419×	body	320	valid
363.0ms	762×	body	160	valid