Details

sample320.0ms

Algorithm

intervals

Results

117.0ms	101×	body	1280	valid
98.0ms	86×	body	640	valid
45.0ms	258×	body	80	valid
20.0ms	38×	body	320	valid
10.0ms	27×	body	160	valid

simplify620.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

620.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.2b

localize50.0ms

Local error

Found 3 expressions with local error:

8.5b	(- (exp l) (exp (- l)))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-r`
5×	`add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
3×	`expm1-log1p-u` `sub-neg` `flip3--` `fma-neg` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 99

Calls

3 calls:

Slowest

74.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
46.0ms	(* J (- (exp l) (exp (- l))))
25.0ms	(- (exp l) (exp (- l)))

series240.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

127.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
70.0ms	(* J (- (exp l) (exp (- l))))
42.0ms	(- (exp l) (exp (- l)))

simplify8.9s

Counts

80 → 108

Calls

80 calls:

Slowest

585.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
337.0ms	(* (* (* (* J (- (exp l) (exp (- l)))) (* J (- (exp l) (exp (- l))))) (* J (- (exp l) (exp (- l))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
336.0ms	(+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))
305.0ms	(* (* J (- (pow (exp l) 3) (pow (exp (- l)) 3))) (cos (/ K 2)))
292.0ms	(* J (- (exp l) (exp (* -1 l))))

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
0.0b	(+ (* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2))) U)
0.0b	(* l (fma 1/3 (* l l) 2))
0.0b	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 82

Calls

4 calls:

Slowest

33.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
26.0ms	(+ (* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2))) U)
6.0ms	(* l (fma 1/3 (* l l) 2))
6.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

series869.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

317.0ms	(+ (* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2))) U)
212.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
201.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
139.0ms	(* l (fma 1/3 (* l l) 2))

simplify9.0s

Counts

47 → 94

Calls

47 calls:

Slowest

861.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
524.0ms	(fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))
497.0ms	(+ (log J) (log (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
476.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
476.0ms	(cbrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 80

Calls

4 calls:

Slowest

28.0ms	(+ (* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))) U)
16.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
12.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
6.0ms	(* l (fma 1/3 (* l l) 2))

series836.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

350.0ms	(+ (* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))) U)
228.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
144.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
114.0ms	(* l (fma 1/3 (* l l) 2))

simplify9.0s

Counts

44 → 92

Calls

44 calls:

Slowest

1.2s	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
967.0ms	(* (* (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
501.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))
455.0ms	(+ (log (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (log (cos (/ K 2))))
446.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.2b	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

17.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

279.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
169.0ms	(cbrt (cos (/ K 2)))
150.0ms	(cbrt (cos (/ K 2)))
136.0ms	(cbrt (cos (/ K 2)))

simplify2.2s

Counts

65 → 97

Calls

65 calls:

Slowest

456.0ms	(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
224.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
212.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
198.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
152.0ms	(pow (pow (cos (* 1/2 K)) 2) 1/3)

prune1.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes618.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample10.0s

Algorithm

intervals

Results

4.1s	2748×	body	1280	valid
2.2s	2617×	body	640	valid
1.9s	8371×	body	80	valid
973.0ms	1436×	body	320	valid
308.0ms	790×	body	160	valid