Details

sample359.0ms

Algorithm

intervals

Results

120.0ms	91×	body	1280	valid
88.0ms	273×	body	80	valid
77.0ms	86×	body	640	valid
29.0ms	46×	body	320	valid
13.0ms	32×	body	160	valid

simplify261.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

261.0ms

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.7b

localize37.0ms

Local error

Found 4 expressions with local error:

6.0b	(- (exp l) (exp (- l)))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

Slowest

98.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
89.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
43.0ms	(* J (- (exp l) (exp (- l))))
26.0ms	(- (exp l) (exp (- l)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

308.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
119.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
70.0ms	(* J (- (exp l) (exp (- l))))
67.0ms	(- (exp l) (exp (- l)))

simplify9.9s

Counts

85 → 126

Calls

85 calls:

Slowest

671.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
522.0ms	(- (+ U (* (exp l) (* (cos (* 1/2 K)) J))) (* (cos (* 1/2 K)) (* J (exp (- l)))))
335.0ms	(* (* (* (* J (- (exp l) (exp (- l)))) (* J (- (exp l) (exp (- l))))) (* J (- (exp l) (exp (- l))))) (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))))
322.0ms	(+ (* 2 l) (+ (* 1/3 (pow l 3)) (* 1/60 (pow l 5))))
319.0ms	(* (* J (- (pow (exp l) 3) (pow (exp (- l)) 3))) (cos (/ K 2)))

prune1.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

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

rewrite78.0ms

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

31.0ms	(+ (* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2))) U)
22.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
12.0ms	(* l (fma 1/3 (* l l) 2))
11.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))

series884.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

333.0ms	(+ (* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2))) U)
220.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
195.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
137.0ms	(* l (fma 1/3 (* l l) 2))

simplify9.4s

Counts

47 → 94

Calls

47 calls:

Slowest

845.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
804.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
535.0ms	(fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))
512.0ms	(sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
510.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize72.0ms

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

rewrite66.0ms

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

33.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
16.0ms	(+ (* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))) U)
10.0ms	(* (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))

series782.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

322.0ms	(+ (* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))) U)
242.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
128.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
89.0ms	(* l (fma 1/3 (* l l) 2))

simplify8.1s

Counts

44 → 92

Calls

44 calls:

Slowest

857.0ms	(* (* (* (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))))
810.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
495.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))
468.0ms	(sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
465.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))

prune1.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize60.0ms

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))))

rewrite16.0ms

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

12.0ms	(* (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)))

series728.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

252.0ms	(* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))
182.0ms	(cbrt (cos (/ K 2)))
160.0ms	(cbrt (cos (/ K 2)))
134.0ms	(cbrt (cos (/ K 2)))

simplify2.4s

Counts

65 → 97

Calls

65 calls:

Slowest

526.0ms	(- 1 (+ (* 1/25920 (pow K 6)) (* 1/12 (pow K 2))))
274.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
199.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
167.0ms	(- 1 (+ (* 1/1152 (pow K 4)) (* 1/24 (pow K 2))))
162.0ms	(pow (pow (cos (* 1/2 K)) 2) 1/3)

prune1.8s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes985.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch6.0ms

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.4s	2659×	body	1280	valid
2.6s	2653×	body	640	valid
2.2s	8275×	body	80	valid
1.3s	1424×	body	320	valid
257.0ms	777×	body	160	valid