Details

sample466.0ms

Algorithm

intervals

Results

140.0ms	60×	body	640	valid
132.0ms	51×	body	1280	valid
114.0ms	202×	body	80	valid
46.0ms	30×	body	320	valid
6.0ms	7×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
4	6501
3	1077
2	185
1	54
0	19

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize44.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
4.0b	(* (sin k) (/ t l))
5.5b	(* (tan k) (* (/ t l) t))
8.1b	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

rewrite595.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-cbrt-cube` `add-exp-log`
68×	`prod-exp` `cbrt-unprod`
52×	`pow1`
34×	`pow-prod-down`
24×	`associate-*l/`
19×	`add-sqr-sqrt`
18×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cbrt-undiv` `div-exp`
10×	`times-frac` `associate-*r/`
8×	`associate-l` `tan-quot`
7×	`frac-times`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `div-inv`

Counts

4 → 150

Calls

4 calls:

427.0ms	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
24.0ms	(* (sin k) (/ t l))
27.0ms	(* (tan k) (* (/ t l) t))
114.0ms	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

series844.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
69.0ms	(* (sin k) (/ t l))
171.0ms	(* (tan k) (* (/ t l) t))
279.0ms	(* (* (tan k) (* (/ t l) t)) (fma (/ k t) (/ k t) 2))

simplify1.3s

Counts

162 → 162

Iterations

Iter	Nodes
2	3583
1	768
0	262

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.0b

localize75.0ms

Local error

Found 4 expressions with local error:

3.9b	(* (* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
4.0b	(* (tan k) (/ t l))
4.0b	(* (sin k) (/ t l))
8.1b	(* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2))

rewrite579.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-cbrt-cube` `add-exp-log`
65×	`prod-exp` `cbrt-unprod`
49×	`pow1`
32×	`pow-prod-down`
31×	`add-sqr-sqrt`
30×	`associate-r`
25×	`associate-*l/`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
11×	`cbrt-undiv` `div-exp`
10×	`associate-*r/`
8×	`associate-l` `tan-quot`
7×	`frac-times`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 161

Calls

4 calls:

399.0ms	(* (* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
18.0ms	(* (tan k) (/ t l))
24.0ms	(* (sin k) (/ t l))
134.0ms	(* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2))

series845.0ms

Counts

4 → 12

Calls

4 calls:

382.0ms	(* (* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2)) (* (sin k) (/ t l)))
153.0ms	(* (tan k) (/ t l))
77.0ms	(* (sin k) (/ t l))
233.0ms	(* (* (* (tan k) (/ t l)) t) (fma (/ k t) (/ k t) 2))

simplify1.4s

Counts

173 → 173

Iterations

Iter	Nodes
2	3773
1	829
0	275

prune2.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize46.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l)))
4.0b	(* (tan k) (/ t l))
4.0b	(* (sin k) (/ t l))
8.3b	(* (* (* (tan k) (/ t l)) t) (* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l))))

rewrite309.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-cbrt-cube` `add-exp-log`
65×	`prod-exp` `cbrt-unprod`
49×	`pow1`
32×	`pow-prod-down`
31×	`add-sqr-sqrt`
28×	`associate-r`
21×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
15×	`associate-*r/`
12×	`associate-*l/`
11×	`cbrt-undiv` `div-exp`
10×	`associate-l`
6×	`frac-times` `tan-quot`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`div-inv`

Counts

4 → 157

Calls

4 calls:

44.0ms	(* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l)))
16.0ms	(* (tan k) (/ t l))
13.0ms	(* (sin k) (/ t l))
229.0ms	(* (* (* (tan k) (/ t l)) t) (* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l)))
164.0ms	(* (tan k) (/ t l))
83.0ms	(* (sin k) (/ t l))
351.0ms	(* (* (* (tan k) (/ t l)) t) (* (fma (/ k t) (/ k t) 2) (* (sin k) (/ t l))))

simplify1.3s

Counts

169 → 169

Iterations

Iter	Nodes
2	3664
1	782
0	262

prune2.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (* t (sin k)) l)
3.1b	(fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l)))
4.0b	(* (tan k) (/ t l))
8.3b	(* (* (* (tan k) (/ t l)) t) (fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-cbrt-cube` `add-exp-log`
20×	`add-sqr-sqrt`
16×	`associate-r`
15×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
8×	`associate-*l/`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-l` `tan-quot` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `fma-udef`
2×	`frac-times` `associate-r/` `-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `associate-/l*`

Counts

4 → 103

Calls

4 calls:

12.0ms	(/ (* t (sin k)) l)
0.0ms	(fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l)))
20.0ms	(* (tan k) (/ t l))
113.0ms	(* (* (* (tan k) (/ t l)) t) (fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l))))

series688.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (* t (sin k)) l)
130.0ms	(fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l)))
178.0ms	(* (tan k) (/ t l))
293.0ms	(* (* (* (tan k) (/ t l)) t) (fma (/ (sin k) t) (/ k (/ l k)) (* 2 (/ (* t (sin k)) l))))

simplify883.0ms

Counts

115 → 115

Iterations

Iter	Nodes
2	2615
1	639
0	227

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.5b

regimes423.0ms

Accuracy

34.9% (4.2b remaining)

Error of 9.2b against oracle of 5.0b and baseline of 11.5b

bsearch836.0ms

Steps

Iters	Range		Point
10	3.3320211160609306e-240	1.7935617744860337e-229	1.7648188831972625e-229
8	-7.399531600622762e-32	-1.3564347619784578e-34	-1.3735352912821898e-34

simplify18.0ms

Iterations

Iter	Nodes
2	50
1	50
0	37

end0.0ms

sample16.1s

Algorithm

intervals

Results

6.6s	2113×	body	1280	valid
4.0s	1733×	body	640	valid
2.6s	5886×	body	80	valid
2.2s	843×	body	320	valid
371.0ms	412×	body	160	valid