Details

sample576.0ms

Algorithm

intervals

Results

179.0ms	47×	body	1280	valid
112.0ms	13×	body	160	valid
75.0ms	147×	body	80	valid
52.0ms	36×	body	640	valid
14.0ms	13×	body	320	valid

simplify106.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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))

rewrite671.0ms

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:

599.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
9.0ms	(- 1 (* (tan x) (tan x)))
28.0ms	(* (tan x) (tan x))
31.0ms	(* (tan x) (tan x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))
39.0ms	(- 1 (* (tan x) (tan x)))
46.0ms	(* (tan x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
3	2002
2	964
1	376
0	144

prune500.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))))

rewrite113.0ms

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:

29.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))
44.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (tan x) (tan x))
34.0ms	(* (tan x) (tan x))
48.0ms	(* (tan x) (tan x))
161.0ms	(- (/ 1 (+ 1 (* (tan x) (tan x)))) (/ (* (tan x) (tan x)) (+ 1 (* (tan x) (tan x)))))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	2000
3	2000
2	902
1	308
0	121

prune431.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

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

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

39×	`associate-*r/`
36×	`tan-quot`
25×	`pow1`
22×	`add-sqr-sqrt` `frac-sub`
21×	`frac-times` `flip3-+` `flip-+`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-*l/`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`associate--l+` `sub-div`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `diff-log` `flip--`

Counts

4 → 126

Calls

4 calls:

23.0ms	(* (tan x) (tan x))
13.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))
69.0ms	(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))

series214.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (tan x) (tan x))
39.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))
60.0ms	(- (* 1 (+ 1 (* (tan x) (tan x)))) (* (+ 1 (* (tan x) (tan x))) (* (tan x) (tan x))))

simplify1.1s

Counts

138 → 138

Iterations

Iter	Nodes
done	2003
2	2003
1	623
0	187

prune618.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

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))))))

rewrite53.0ms

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:

4.0ms	(- 1 (* (tan x) (tan x)))
13.0ms	(* (tan x) (tan x))
14.0ms	(* (tan x) (tan x))
20.0ms	(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))

series241.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1 (* (tan x) (tan x)))
52.0ms	(* (tan x) (tan x))
58.0ms	(* (tan x) (tan x))
96.0ms	(log (exp (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x))))))

simplify1.5s

Counts

120 → 120

Iterations

Iter	Nodes
done	2003
4	2003
3	1622
2	684
1	344
0	172

prune554.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes306.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	10

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.5s	1492×	body	1280	valid
1.4s	1274×	body	640	valid
939.0ms	4311×	body	80	valid
562.0ms	328×	body	160	valid
397.0ms	595×	body	320	valid