Details

sample485.0ms

Algorithm

intervals

Results

206.0ms	71×	body	1280	valid
127.0ms	49×	body	640	valid
74.0ms	176×	body	80	valid
39.0ms	29×	body	320	valid
10.0ms	12×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2003
4	2003
3	1174
2	189
1	54
0	19

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.3b	(/ t (* (/ l t) (/ l t)))
2.7b	(* (/ t (* (/ l t) (/ l t))) (sin k))
4.6b	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
15.3b	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite771.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

17.0ms	(/ t (* (/ l t) (/ l t)))
44.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
154.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
552.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

series826.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ t (* (/ l t) (/ l t)))
125.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
209.0ms	(* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k))
428.0ms	(* (* (* (/ t (* (/ l t) (/ l t))) (sin k)) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
2	2000
1	672
0	235

prune877.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 2 (* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)))
3.5b	(* (/ (cbrt t) (/ l t)) (sin k))
4.6b	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
15.3b	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

455×	`add-exp-log`
375×	`add-cbrt-cube`
239×	`prod-exp` `cbrt-unprod`
143×	`cbrt-undiv` `div-exp`
141×	`times-frac`
94×	`add-sqr-sqrt`
85×	`associate-l`
78×	`*-un-lft-identity` `add-cube-cbrt`
42×	`associate-*l/`
41×	`cbrt-prod`
29×	`pow1`
17×	`pow-prod-down`
15×	`frac-times`
12×	`tan-quot`
9×	`associate-r` `associate-*r/`
8×	`associate-/r/` `div-inv`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`fma-udef`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 322

Calls

4 calls:

848.0ms	(/ 2 (* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)))
28.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
186.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
736.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ 2 (* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2)))
179.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
233.0ms	(* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
590.0ms	(* (* (* (/ (* (cbrt t) (cbrt t)) (/ l t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify2.2s

Counts

334 → 334

Iterations

Iter	Nodes
done	2005
2	2005
1	1620
0	535

prune2.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.9b

localize98.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
3.5b	(* (/ (cbrt t) (/ l t)) (sin k))
6.9b	(* (/ 2 (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))) (/ l t))
13.6b	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite4.2s

Algorithm

rewrite-expression-head

Rules

276×	`add-exp-log`
226×	`add-cbrt-cube`
165×	`prod-exp` `cbrt-unprod`
151×	`times-frac`
106×	`add-sqr-sqrt`
95×	`associate-l`
85×	`*-un-lft-identity` `add-cube-cbrt`
61×	`cbrt-undiv` `div-exp`
51×	`pow1`
41×	`cbrt-prod`
34×	`pow-prod-down`
22×	`associate-r`
17×	`associate-*l/`
10×	`associate-*r/`
9×	`div-inv`
7×	`unswap-sqr`
6×	`tan-quot`
4×	`expm1-log1p-u` `frac-times` `associate-/r/` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 285

Calls

4 calls:

187.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
27.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
3.2s	(* (/ 2 (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))) (/ l t))
797.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

271.0ms	(* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k))
227.0ms	(* (/ (cbrt t) (/ l t)) (sin k))
411.0ms	(* (/ 2 (* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))) (/ l t))
619.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt t) (/ l t)) (sin k))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify1.9s

Counts

297 → 297

Iterations

Iter	Nodes
done	2004
2	2004
1	1482
0	488

prune2.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.9b

localize114.0ms

Local error

Found 4 expressions with local error:

13.2b	(cbrt (/ l t))
13.2b	(cbrt (/ l t))
13.2b	(cbrt (/ l t))
13.6b	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt (* (cbrt t) (cbrt t))) (* (cbrt (/ l t)) (cbrt (/ l t)))) (* (/ (cbrt (cbrt t)) (cbrt (/ l t))) (sin k)))) (tan k)) (fma (/ k t) (/ k t) 2))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

153×	`add-exp-log`
109×	`prod-exp` `cbrt-unprod`
97×	`add-cbrt-cube`
42×	`pow1`
39×	`cbrt-prod`
30×	`pow-prod-down`
27×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`cbrt-undiv` `div-exp`
16×	`associate-*l/`
9×	`associate-*r/`
5×	`frac-times`
4×	`expm1-log1p-u` `tan-quot` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-r` `div-inv`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

4 → 151

Calls

4 calls:

2.0ms	(cbrt (/ l t))
2.0ms	(cbrt (/ l t))
2.0ms	(cbrt (/ l t))
3.3s	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt (* (cbrt t) (cbrt t))) (* (cbrt (/ l t)) (cbrt (/ l t)))) (* (/ (cbrt (cbrt t)) (cbrt (/ l t))) (sin k)))) (tan k)) (fma (/ k t) (/ k t) 2))

series901.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (/ l t))
96.0ms	(cbrt (/ l t))
110.0ms	(cbrt (/ l t))
614.0ms	(* (* (* (* (cbrt t) (cbrt t)) (* (/ (cbrt (* (cbrt t) (cbrt t))) (* (cbrt (/ l t)) (cbrt (/ l t)))) (* (/ (cbrt (cbrt t)) (cbrt (/ l t))) (sin k)))) (tan k)) (fma (/ k t) (/ k t) 2))

simplify2.1s

Counts

163 → 163

Iterations

Iter	Nodes
done	2000
2	2000
1	1042
0	350

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.9b

regimes970.0ms

Accuracy

60.5% (2.9b remaining)

Error of 8.8b against oracle of 5.9b and baseline of 13.2b

bsearch923.0ms

Steps

Iters	Range		Point
10	2.9113178253619213e-72	7.890370861757397e-58	1.5813717718336364e-60
11	-8.962244879641589e+45	-3.5315641353691205e+25	-4.5086094187532317e+30

simplify34.0ms

Iterations

Iter	Nodes
done	65
1	65
0	48

end0.0ms

sample16.3s

Algorithm

intervals

Results

7.6s	2115×	body	1280	valid
3.5s	1654×	body	640	valid
2.7s	5971×	body	80	valid
1.6s	841×	body	320	valid
534.0ms	436×	body	160	valid