Details

sample169.0ms

Algorithm

intervals

Results

38.0ms	44×	body	1280	valid
20.0ms	148×	body	80	valid
18.0ms	29×	body	640	valid
10.0ms	24×	body	320	valid
3.0ms	11×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	38
5	38
4	36
3	28
2	23
1	15
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`pow1`
15×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`associate-/l*`
4×	`insert-posit16`
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 → 114

Calls

4 calls:

28.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (* (tan x) (tan x)))
33.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))

series342.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
60.0ms	(- 1 (* (tan x) (tan x)))
66.0ms	(* (tan x) (tan x))
76.0ms	(* (tan x) (tan x))

simplify2.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	5070
3	3113
2	964
1	376
0	144

prune487.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

136×	`pow1`
44×	`tan-quot`
39×	`pow-prod-up`
26×	`pow-prod-down`
25×	`pow-sqr`
22×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
21×	`pow-plus`
20×	`frac-times`
16×	`pow2` `*-un-lft-identity` `add-cube-cbrt`
14×	`associate-l/` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`swap-sqr` `associate-r` `associate-l`
4×	`*-commutative` `insert-posit16` `add-log-exp` `unswap-sqr`

Counts

4 → 166

Calls

4 calls:

14.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))
68.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
53.0ms	(* (tan x) (tan x))
78.0ms	(* (* (tan x) (tan x)) (* (tan x) (tan x)))

simplify2.3s

Counts

178 → 178

Iterations

Iter	Nodes
done	5000
3	1922
2	954
1	318
0	108

prune712.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

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 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`pow1`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
8×	`times-frac`
6×	`add-log-exp` `difference-of-squares`
5×	`distribute-rgt-out--` `div-inv`
4×	`associate-/r/` `insert-posit16`
3×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 115

Calls

4 calls:

27.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))
57.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))
41.0ms	(* (tan x) (tan x))
193.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify2.4s

Counts

127 → 127

Iterations

Iter	Nodes
done	5010
3	2951
2	902
1	308
0	121

prune523.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`log-pow` `add-cube-cbrt`
21×	`exp-prod`
19×	`pow1`
15×	`times-frac`
8×	`add-cbrt-cube` `tan-quot` `add-exp-log` `difference-of-squares`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
4×	`insert-posit16`
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 → 108

Calls

4 calls:

9.0ms	(- 1 (* (tan x) (tan x)))
27.0ms	(* (tan x) (tan x))
28.0ms	(* (tan x) (tan x))
40.0ms	(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- 1 (* (tan x) (tan x)))
58.0ms	(* (tan x) (tan x))
64.0ms	(* (tan x) (tan x))
119.0ms	(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))

simplify3.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
4	4565
3	1622
2	684
1	344
0	172

prune617.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes303.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	1494×	body	1280	valid
1.3s	1210×	body	640	valid
981.0ms	4324×	body	80	valid
945.0ms	626×	body	320	valid
183.0ms	346×	body	160	valid