Details

sample297.0ms

Algorithm

intervals

Results

43.0ms	40×	body	1280	valid
36.0ms	46×	body	640	valid
20.0ms	138×	body	80	valid
10.0ms	22×	body	320	valid
3.0ms	10×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	15
1	13	15
2	21	15
3	26	15
4	34	15
5	37	15
done	37	15

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

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:

39.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
11.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
51.0ms	(* (tan x) (tan x))

series398.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
76.0ms	(- 1.0 (* (tan x) (tan x)))
63.0ms	(* (tan x) (tan x))
89.0ms	(* (tan x) (tan x))

simplify1.4s

Counts

117 → 117

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	138	1632
1	351	1506
2	1541	1370
done	5002	1360

prune608.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

9.0ms	(- 1.0 (* (tan x) (tan x)))
52.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
33.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- 1.0 (* (tan x) (tan x)))
171.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
60.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

112 → 112

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	164	1427
1	327	1245
2	1226	1122
done	5000	1114

prune613.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

35.0ms	(/ (* (sin x) (tan x)) (cos x))
26.0ms	(* (sin x) (tan x))
16.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
29.0ms	(* (tan x) (tan x))

series323.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (* (sin x) (tan x)) (cos x))
78.0ms	(* (sin x) (tan x))
86.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
57.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

95 → 95

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	134	997
1	334	914
2	2003	823
done	5000	813

prune576.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-exp-log` `add-cbrt-cube`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `distribute-rgt-out--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
98.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series455.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))
278.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify1.1s

Counts

118 → 118

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	118	1623
1	295	1455
2	1236	1306
done	5000	1295

prune502.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes661.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
done	13	18

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.5s	1544×	body	1280	valid
1.2s	1260×	body	640	valid
887.0ms	624×	body	320	valid
830.0ms	4254×	body	80	valid
179.0ms	318×	body	160	valid