Details

sample347.0ms

Algorithm

intervals

Results

101.0ms	21×	body	320	valid
67.0ms	49×	body	640	valid
54.0ms	46×	body	1280	valid
19.0ms	125×	body	80	valid
7.0ms	15×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
5	37
4	34
3	26
2	21
1	13
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 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))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
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` `pow-plus` `flip3--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip--` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

8.0ms	(- 1.0 (* (tan x) (tan x)))
29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
26.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))

series304.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- 1.0 (* (tan x) (tan x)))
125.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
45.0ms	(* (tan x) (tan x))
71.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1536
1	350
0	138

prune557.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ 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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`pow1`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`tan-quot` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-/r*` `flip3-+` `div-sub` `flip-+`
2×	`pow2` `neg-sub0` `frac-times` `associate-+r-` `sum-log` `pow-plus` `unsub-neg` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `neg-log` `div-inv`

Counts

4 → 110

Calls

4 calls:

7.0ms	(+ 1.0 (- (* (tan x) (tan x))))
21.0ms	(/ (+ 1.0 (- (* (tan x) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
19.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))

series272.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ 1.0 (- (* (tan x) (tan x))))
136.0ms	(/ (+ 1.0 (- (* (tan x) (tan x)))) (+ 1.0 (* (tan x) (tan x))))
58.0ms	(* (tan x) (tan x))
40.0ms	(* (tan x) (tan x))

simplify1.5s

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1849
1	359
0	139

prune466.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

23.0ms	(/ (* (sin x) (tan x)) (cos x))
32.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(* (sin x) (tan x))
23.0ms	(* (tan x) (tan x))

series479.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (* (sin x) (tan x)) (cos x))
210.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
83.0ms	(* (sin x) (tan x))
65.0ms	(* (tan x) (tan x))

simplify1.7s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	2689
1	487
0	190

prune695.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

19.0ms	(/ (* (sin x) (tan x)) (cos x))
48.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
10.0ms	(* (sin x) (tan x))
29.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (* (sin x) (tan x)) (cos x))
159.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ 1.0 (* (/ (sin x) (cos x)) (/ (sin x) (cos x)))))
77.0ms	(* (sin x) (tan x))
66.0ms	(* (/ (sin x) (cos x)) (/ (sin x) (cos x)))

simplify1.1s

Counts

160 → 160

Iterations

Iter	Nodes
done	5000
1	775
0	258

prune999.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes231.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	8

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.0s	1532×	body	1280	valid
1.3s	1251×	body	640	valid
756.0ms	4281×	body	80	valid
223.0ms	603×	body	320	valid
86.0ms	333×	body	160	valid