Details

sample1.1s

Algorithm

intervals

Results

167.0ms	55×	body	640	valid
136.0ms	121×	body	80	valid
100.0ms	42×	body	1280	valid
35.0ms	27×	body	320	valid
8.0ms	11×	body	160	valid

simplify140.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
5	36
4	34
3	26
2	21
1	13
0	7

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
41.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
41.0ms	(* (tan x) (tan x))
75.0ms	(* (tan x) (tan x))

series568.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- 1.0 (* (tan x) (tan x)))
211.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
70.0ms	(* (tan x) (tan x))
162.0ms	(* (tan x) (tan x))

simplify5.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
3	3786
2	1000
1	350
0	138

prune827.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
9.0b	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

204×	`tan-quot`
132×	`frac-times`
90×	`associate-*l/`
63×	`cbrt-div`
58×	`associate-*r/`
25×	`pow1`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
4×	`pow-prod-down` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`pow3`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 157

Calls

4 calls:

31.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))
405.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

series256.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (tan x) (tan x))
61.0ms	(* (tan x) (tan x))
66.0ms	(* (tan x) (tan x))
61.0ms	(cbrt (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan x) (tan x)) (tan x))))

simplify7.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
3	3325
2	1785
1	545
0	209

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `associate-*r/` `swap-sqr` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*l/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 109

Calls

4 calls:

34.0ms	(/ (* (sin x) (tan x)) (cos x))
25.0ms	(* (sin x) (tan x))
64.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(* (tan x) (tan x))

series621.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (* (sin x) (tan x)) (cos x))
92.0ms	(* (sin x) (tan x))
324.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
75.0ms	(* (tan x) (tan x))

simplify2.8s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	1540
1	486
0	190

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
0.5b	(pow (* (tan x) (tan x)) 3)

rewrite254.0ms

Algorithm

rewrite-expression-head

Rules

137×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
23×	`add-exp-log` `add-cbrt-cube`
21×	`pow-plus`
20×	`frac-times`
17×	`add-sqr-sqrt`
16×	`pow2`
14×	`associate-r/` `associate-l/`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`prod-exp` `cbrt-unprod`
7×	`swap-sqr` `associate-r` `associate-l`
6×	`pow-pow`
4×	`add-log-exp`
3×	`cube-div` `pow-unpow` `*-commutative` `unswap-sqr`
2×	`pow-exp` `rem-cube-cbrt`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`

Counts

4 → 163

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))
150.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
27.0ms	(pow (* (tan x) (tan x)) 3)

series379.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))
96.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))
124.0ms	(pow (* (tan x) (tan x)) 3)

simplify5.1s

Counts

175 → 175

Iterations

Iter	Nodes
done	5083
3	3828
2	1495
1	472
0	145

prune1.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 0.0b

regimes669.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.5s	1508×	body	1280	valid
1.9s	1255×	body	640	valid
1.3s	4280×	body	80	valid
446.0ms	643×	body	320	valid
203.0ms	314×	body	160	valid