Details

sample302.0ms

Algorithm

intervals

Results

23.0ms	51×	body	1280	valid
11.0ms	36×	body	640	valid
7.0ms	128×	body	80	valid
4.0ms	20×	body	320	valid
4.0ms	21×	body	160	valid

simplify25.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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))

rewrite36.0ms

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:

9.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
39.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify1.6s

Counts

117 → 117

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	138	1632
1	312	1486
2	842	1368
3	2993	1346
done	5000	1345

prune261.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.4b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite32.0ms

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:

2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
17.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series196.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))
95.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: 3 (442.0ms)

Iter	Nodes	Cost
0	164	1427
1	287	1225
2	675	1122
3	2096	1102
done	5000	1102

prune268.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

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))
0.4b	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

rewrite48.0ms

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:

5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))
30.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))
156.0ms	(- (/ 1.0 (+ 1.0 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: 3 (666.0ms)

Iter	Nodes	Cost
0	118	1623
1	264	1425
2	745	1302
3	3151	1269
done	5000	1269

prune238.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan x))
0.4b	(- (/ 1.0 (+ 1.0 (cbrt (pow (tan x) 6)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.7b	(pow (tan x) 6)
7.7b	(cbrt (pow (tan x) 6))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

5.0ms	(* (tan x) (tan x))
77.0ms	(- (/ 1.0 (+ 1.0 (cbrt (pow (tan x) 6)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
2.0ms	(pow (tan x) 6)
1.0ms	(cbrt (pow (tan x) 6))

series295.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (tan x) (tan x))
156.0ms	(- (/ 1.0 (+ 1.0 (cbrt (pow (tan x) 6)))) (/ (* (tan x) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
66.0ms	(pow (tan x) 6)
36.0ms	(cbrt (pow (tan x) 6))

simplify1.9s

Counts

90 → 90

Iterations

Useful iterations: 3 (760.0ms)

Iter	Nodes	Cost
0	156	1384
1	335	1305
2	908	1123
3	4074	1030
done	5001	1030

prune223.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes177.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	10	17
done	10	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

673.0ms	1450×	body	1280	valid
372.0ms	1309×	body	640	valid
253.0ms	4314×	body	80	valid
121.0ms	598×	body	320	valid
44.0ms	329×	body	160	valid