Details

sample308.0ms

Algorithm

intervals

Results

76.0ms	88×	body	1280	valid
73.0ms	307×	body	80	valid
62.0ms	106×	body	640	valid
21.0ms	51×	body	320	valid
9.0ms	30×	body	160	valid

simplify307.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

307.0ms

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize52.0ms

Local error

Found 4 expressions with local error:

5.6b	(- (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)

rewrite249.0ms

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

102.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
62.0ms	(* J (- (exp l) (exp (- l))))
58.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
26.0ms	(- (exp l) (exp (- l)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

321.0ms	(+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2))) U)
121.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2)))
74.0ms	(* J (- (exp l) (exp (- l))))
53.0ms	(- (exp l) (exp (- l)))

simplify25.7s

Counts

159 → 126

Calls

159 calls:

Slowest

864.0ms	(* (* (* J (- (exp l) (exp (- l)))) (* J (- (exp l) (exp (- l))))) (* J (- (exp l) (exp (- l)))))
620.0ms	(* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l))))
555.0ms	(* (* (* J J) J) (* (* (- (exp l) (exp (- l))) (- (exp l) (exp (- l)))) (- (exp l) (exp (- l)))))
520.0ms	(* J (- (* (exp l) (exp l)) (* (exp (- l)) (exp (- l)))))
499.0ms	(- (+ U (* (exp l) (* (cos (* 1/2 K)) J))) (* (cos (* 1/2 K)) (* J (exp (- l)))))

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

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)))
0.0b	(fma 1/3 (* l l) 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))))

rewrite47.0ms

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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `fma-udef`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

Slowest

34.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
6.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
6.0ms	(* l (fma 1/3 (* l l) 2))
0.0ms	(fma 1/3 (* l l) 2)

series520.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(* (* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (cos (/ K 2)))
153.0ms	(* J (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))))
105.0ms	(* l (fma 1/3 (* l l) 2))
60.0ms	(fma 1/3 (* l l) 2)

simplify18.3s

Counts

93 → 90

Calls

93 calls:

Slowest

878.0ms	(* (* (* l (fma 1/3 (* l l) 2)) (* l (fma 1/3 (* l l) 2))) (* l (fma 1/3 (* l l) 2)))
764.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
574.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
560.0ms	(* (sqrt J) (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))
486.0ms	(+ (log J) (log (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* l l))
0.1b	(* (* J (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))) (cos (/ K 2)))
0.1b	(* l (* 1/3 (* l l)))
0.0b	(fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

Slowest

37.0ms	(* l (* 1/3 (* l l)))
27.0ms	(* 1/3 (* l l))
21.0ms	(* (* J (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))) (cos (/ K 2)))
0.0ms	(fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

244.0ms	(* (* J (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))) (cos (/ K 2)))
83.0ms	(fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))
56.0ms	(* l (* 1/3 (* l l)))
48.0ms	(* 1/3 (* l l))

simplify17.3s

Counts

88 → 90

Calls

88 calls:

Slowest

935.0ms	(expm1 (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2))))
650.0ms	(cbrt (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2))))
648.0ms	(* (* (* l l) l) (* (* (* 1/3 (* l l)) (* 1/3 (* l l))) (* 1/3 (* l l))))
608.0ms	(* (* (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2))) (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2)))) (fma 1/60 (pow l 5) (+ (* l (* 1/3 (* l l))) (* l 2))))
573.0ms	(* (* (* l (* 1/3 (* l l))) (* l (* 1/3 (* l l)))) (* l (* 1/3 (* l l))))

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 76

Calls

4 calls:

Slowest

33.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
11.0ms	(* l (fma 1/3 (* l l) 2))
7.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
0.0ms	(fma 1/3 (* l l) 2)

series511.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

199.0ms	(* J (* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2))))
120.0ms	(* (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2))) (cos (/ K 2)))
115.0ms	(* l (fma 1/3 (* l l) 2))
77.0ms	(fma 1/3 (* l l) 2)

simplify18.0s

Counts

89 → 88

Calls

89 calls:

Slowest

875.0ms	(* (* (* l (fma 1/3 (* l l) 2)) (* l (fma 1/3 (* l l) 2))) (* l (fma 1/3 (* l l) 2)))
862.0ms	(* (* (* (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))))
861.0ms	(* (* (* l l) l) (* (* (fma 1/3 (* l l) 2) (fma 1/3 (* l l) 2)) (fma 1/3 (* l l) 2)))
523.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))
520.0ms	(* (sqrt (fma 1/60 (pow l 5) (* l (fma 1/3 (* l l) 2)))) (sqrt (cos (/ K 2))))

prune1.5s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes546.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample10.1s

Algorithm

intervals

Results

4.0s	2615×	body	1280	valid
2.4s	2581×	body	640	valid
2.1s	8337×	body	80	valid
798.0ms	1437×	body	320	valid
282.0ms	764×	body	160	valid