Details

sample394.0ms

Algorithm

intervals

Results

191.0ms	64×	body	1280	valid
89.0ms	59×	body	640	valid
62.0ms	193×	body	80	valid
21.0ms	19×	body	320	valid
9.0ms	12×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1174
2	189
1	54
0	19

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.8b

localize36.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
3.2b	(/ (tan k) (/ l t))
3.4b	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
11.7b	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
154×	`add-sqr-sqrt`
151×	`add-cbrt-cube` `add-exp-log`
118×	`*-un-lft-identity` `add-cube-cbrt`
58×	`prod-exp` `cbrt-unprod`
57×	`cbrt-undiv` `div-exp`
50×	`associate-r`
46×	`associate-l`
20×	`pow1`
13×	`associate-/r*` `div-inv`
12×	`associate-*l/`
10×	`pow-prod-down`
9×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-/r/` `-commutative` `associate-/l*`
2×	`fma-udef`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `tan-quot` `associate-/l/`

Counts

4 → 289

Calls

4 calls:

37.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
17.0ms	(/ (tan k) (/ l t))
91.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
241.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

148.0ms	(* (/ t (/ l t)) (/ (tan k) (/ l t)))
137.0ms	(/ (tan k) (/ l t))
235.0ms	(* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k))
764.0ms	(* (* (* (/ t (/ l t)) (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify1.9s

Counts

301 → 301

Iterations

Iter	Nodes
done	5002
1	1545
0	465

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* t (/ (tan k) (/ l t))) (sin k))
3.2b	(/ (tan k) (/ l t))
4.1b	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
9.5b	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
103×	`add-cbrt-cube` `add-exp-log`
62×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
43×	`prod-exp` `cbrt-unprod`
33×	`cbrt-undiv` `div-exp`
26×	`associate-/r*`
18×	`pow1`
9×	`pow-prod-down`
8×	`div-inv`
6×	`associate-r`
5×	`associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-*r/`
2×	`clear-num` `frac-2neg` `associate-l` `associate-/r/` `*-commutative` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `distribute-lft-in` `tan-quot`

Counts

4 → 197

Calls

4 calls:

35.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
8.0ms	(/ (tan k) (/ l t))
143.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
130.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (* t (/ (tan k) (/ l t))) (sin k))
179.0ms	(/ (tan k) (/ l t))
388.0ms	(/ (* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2)) (/ l t))
368.0ms	(* (* (* t (/ (tan k) (/ l t))) (sin k)) (fma (/ k t) (/ k t) 2))

simplify2.9s

Counts

209 → 209

Iterations

Iter	Nodes
done	5002
2	4720
1	1073
0	367

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
4.1b	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
5.8b	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
8.8b	(/ (* (* (sin k) t) (* (sin k) t)) l)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

475×	`times-frac`
233×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
77×	`add-cbrt-cube` `add-exp-log`
61×	`associate-/r*`
29×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp` `div-inv`
8×	`associate-/l*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 338

Calls

4 calls:

15.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
12.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
56.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
49.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

series1.6s

Counts

4 → 12

Calls

4 calls:

929.0ms	(/ 2 (/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
381.0ms	(/ (fma 2 (/ (/ (* (* (sin k) t) (* (sin k) t)) l) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
123.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))
123.0ms	(/ (* (* (sin k) t) (* (sin k) t)) l)

simplify2.1s

Counts

350 → 350

Iterations

Iter	Nodes
done	5000
1	1820
0	644

prune3.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 2 (/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
0.8b	(/ l (* (sin k) t))
4.1b	(/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
5.8b	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

475×	`times-frac`
233×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
64×	`add-cbrt-cube` `add-exp-log`
59×	`associate-/r*`
24×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
21×	`cbrt-undiv` `div-exp`
10×	`associate-/l*`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 332

Calls

4 calls:

7.0ms	(/ 2 (/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
8.0ms	(/ l (* (sin k) t))
6.0ms	(/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
46.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

series1.5s

Counts

4 → 12

Calls

4 calls:

930.0ms	(/ 2 (/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t)))
80.0ms	(/ l (* (sin k) t))
363.0ms	(/ (fma 2 (/ (/ (* (sin k) t) (/ l (* (sin k) t))) (cos k)) (/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))) (/ l t))
140.0ms	(/ (* (* (sin k) k) (* (sin k) k)) (* l (cos k)))

simplify2.6s

Counts

344 → 344

Iterations

Iter	Nodes
done	5000
1	1799
0	624

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

regimes468.0ms

Accuracy

0% (2.3b remaining)

Error of 7.0b against oracle of 4.6b and baseline of 7.0b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample15.2s

Algorithm

intervals

Results

7.2s	2075×	body	1280	valid
3.4s	1684×	body	640	valid
2.6s	6010×	body	80	valid
1.1s	826×	body	320	valid
458.0ms	457×	body	160	valid