Details

sample217.0ms

Algorithm

intervals

Results

84.0ms	83×	body	1280	valid
45.0ms	89×	body	640	valid
28.0ms	265×	body	80	valid
17.0ms	51×	body	320	valid
6.0ms	25×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3163
6	1067
5	416
4	202
3	85
2	44
1	24
0	14

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.9b	(- (exp l) (exp (- l)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`prod-diff`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`add-log-exp`
3×	`fma-neg` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `flip3--` `associate-l/` `associate-r/` `log1p-expm1-u` `flip--`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 50

Calls

2 calls:

70.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
21.0ms	(- (exp l) (exp (- l)))

series218.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
63.0ms	(- (exp l) (exp (- l)))

simplify2.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
3	2654
2	804
1	299
0	123

prune461.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* l (fma l (* l 1/3) 2))
0.0b	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
0.1b	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
0.3b	(* l 1/3)

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` `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 → 76

Calls

4 calls:

11.0ms	(* l (fma l (* l 1/3) 2))
34.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
24.0ms	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
5.0ms	(* l 1/3)

series718.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* l (fma l (* l 1/3) 2))
344.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
205.0ms	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
26.0ms	(* l 1/3)

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1110
1	357
0	147

prune648.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))) U)
0.1b	(* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0))))
0.1b	(* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))
0.3b	(* l 1/3)

rewrite62.0ms

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` `log1p-expm1-u`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+`

Counts

4 → 74

Calls

4 calls:

26.0ms	(+ (* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))) U)
14.0ms	(* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0))))
9.0ms	(* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))
11.0ms	(* l 1/3)

series1.0s

Counts

4 → 12

Calls

4 calls:

332.0ms	(+ (* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))) U)
542.0ms	(* J (* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0))))
134.0ms	(* (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2))) (cos (/ K 2.0)))
24.0ms	(* l 1/3)

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5003
2	1084
1	348
0	146

prune692.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(* l (fma l (* l 1/3) 2))
0.0b	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
0.1b	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
0.3b	(* l 1/3)

rewrite42.0ms

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` `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 → 76

Calls

4 calls:

6.0ms	(* l (fma l (* l 1/3) 2))
14.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
15.0ms	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
6.0ms	(* l 1/3)

series790.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* l (fma l (* l 1/3) 2))
374.0ms	(+ (* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0))) U)
265.0ms	(* (* J (fma (pow l 5) 1/60 (* l (fma l (* l 1/3) 2)))) (cos (/ K 2.0)))
22.0ms	(* l 1/3)

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1110
1	357
0	147

prune730.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes629.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample7.8s

Algorithm

intervals

Results

2.2s	2614×	body	1280	valid
2.2s	2545×	body	640	valid
2.1s	8383×	body	80	valid
483.0ms	1442×	body	320	valid
181.0ms	805×	body	160	valid