Details

sample140.0ms

Algorithm

intervals

Results

23.0ms	37×	body	1280	valid
13.0ms	34×	body	640	valid
13.0ms	149×	body	80	valid
7.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid

simplify59.0ms

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: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

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:

29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
4.0ms	(- 1.0 (* (tan x) (tan x)))
11.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
61.0ms	(- 1.0 (* (tan x) (tan x)))
66.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify899.0ms

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1717
1	360
0	141

prune518.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

4.0ms	(- 1.0 (* (tan x) (tan x)))
11.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
63.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 1.0 (* (tan x) (tan x)))
59.0ms	(* (tan x) (tan x))
44.0ms	(* (tan x) (tan x))
142.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))))

simplify972.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1351
1	331
0	166

prune592.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow 1.0 3) (pow (tan x) 6)) (+ (* 1.0 1.0) (* (tan x) (+ (pow (tan x) 3) (* (tan x) 1.0)))))
0.2b	(* (tan x) (tan x))
0.3b	(pow (tan x) 3)
0.6b	(pow (tan x) 6)

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-sqr-sqrt`
48×	`times-frac` `difference-of-squares`
42×	`*-un-lft-identity`
34×	`unpow-prod-down` `add-cube-cbrt`
30×	`sqr-pow`
16×	`associate-/l*`
15×	`cube-prod`
13×	`pow1`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow-unpow`
5×	`tan-quot`
4×	`distribute-lft-out--` `add-log-exp`
3×	`associate-/r` `swap-sqr` `associate-r` `associate-l*`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `associate-/l/`
1×	`cube-div` `pow2` `cube-mult` `frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `flip3--` `unpow3` `div-sub` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `flip--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 153

Calls

4 calls:

102.0ms	(/ (- (pow 1.0 3) (pow (tan x) 6)) (+ (* 1.0 1.0) (* (tan x) (+ (pow (tan x) 3) (* (tan x) 1.0)))))
23.0ms	(* (tan x) (tan x))
6.0ms	(pow (tan x) 3)
6.0ms	(pow (tan x) 6)

series567.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(/ (- (pow 1.0 3) (pow (tan x) 6)) (+ (* 1.0 1.0) (* (tan x) (+ (pow (tan x) 3) (* (tan x) 1.0)))))
63.0ms	(* (tan x) (tan x))
67.0ms	(pow (tan x) 3)
98.0ms	(pow (tan x) 6)

simplify4.2s

Counts

165 → 165

Iterations

Iter	Nodes
done	5000
2	4686
1	785
0	286

prune885.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan x))
0.3b	(pow (tan x) 3)
0.3b	(pow (tan x) 3)
0.6b	(pow (tan x) 6)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
9×	`pow-unpow` `unpow-prod-down` `add-exp-log`
8×	`add-cbrt-cube`
6×	`cube-prod` `tan-quot`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `swap-sqr` `associate-r` `associate-l` `pow-exp` `sqr-pow`
2×	`cube-div` `cube-mult` `unpow3` `rem-cube-cbrt`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

11.0ms	(* (tan x) (tan x))
4.0ms	(pow (tan x) 3)
4.0ms	(pow (tan x) 3)
4.0ms	(pow (tan x) 6)

series301.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (tan x))
52.0ms	(pow (tan x) 3)
84.0ms	(pow (tan x) 3)
120.0ms	(pow (tan x) 6)

simplify3.2s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2685
1	357
0	117

prune701.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes268.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1524×	body	1280	valid
1.2s	1272×	body	640	valid
576.0ms	4241×	body	80	valid
358.0ms	632×	body	320	valid
134.0ms	331×	body	160	valid