Details

sample168.0ms

Algorithm

intervals

Results

31.0ms	45×	body	1280	valid
19.0ms	42×	body	640	valid
14.0ms	133×	body	80	valid
8.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid

simplify785.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	45
6	45
5	43
4	37
3	29
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

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))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-neg` `prod-diff`
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 → 119

Calls

4 calls:

28.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
23.0ms	(- 1.0 (* (tan x) (tan x)))
25.0ms	(* (tan x) (tan x))
29.0ms	(* (tan x) (tan x))

series346.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
64.0ms	(- 1.0 (* (tan x) (tan x)))
58.0ms	(* (tan x) (tan x))
80.0ms	(* (tan x) (tan x))

simplify1.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1700
1	376
0	151

prune600.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

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))
44.1b	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1`
22×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
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`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

25.0ms	(* (tan x) (tan x))
12.0ms	(* (tan x) (tan x))
11.0ms	(* (tan x) (tan x))
0.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (tan x) (tan x))
62.0ms	(* (tan x) (tan x))
59.0ms	(* (tan x) (tan x))
146.0ms	(fma (- (tan x)) (tan x) (* (tan x) (tan x)))

simplify6.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4739
2	635
1	144
0	64

prune658.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`prod-diff`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`times-frac`
6×	`associate-r` `associate-l` `tan-quot` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/r` `fma-neg` `swap-sqr` `prod-exp` `associate-r/` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`pow2` `frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `associate-l/` `pow-sqr` `pow-prod-up` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

18.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
16.0ms	(/ (* (sin x) (tan x)) (cos x))
10.0ms	(* (sin x) (tan x))
15.0ms	(* (tan x) (tan x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
84.0ms	(/ (* (sin x) (tan x)) (cos x))
61.0ms	(* (sin x) (tan x))
40.0ms	(* (tan x) (tan x))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5000
2	3043
1	492
0	192

prune822.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(/ (* (sin x) (tan x)) (cos x))
0.2b	(* (sin x) (tan x))
0.2b	(* (sin x) (tan x))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-/r` `times-frac` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `tan-quot` `associate-*r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr` `associate-/l/`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (* (sin x) (tan x)) (cos x))
11.0ms	(/ (* (sin x) (tan x)) (cos x))
21.0ms	(* (sin x) (tan x))
18.0ms	(* (sin x) (tan x))

series321.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (* (sin x) (tan x)) (cos x))
96.0ms	(/ (* (sin x) (tan x)) (cos x))
55.0ms	(* (sin x) (tan x))
68.0ms	(* (sin x) (tan x))

simplify1.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1165
1	201
0	90

prune586.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes427.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	10

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.4s	1467×	body	1280	valid
1.3s	1249×	body	640	valid
650.0ms	626×	body	320	valid
649.0ms	4349×	body	80	valid
142.0ms	309×	body	160	valid