Details

sample206.0ms

Algorithm

intervals

Results

71.0ms	41×	body	1280	valid
20.0ms	145×	body	80	valid
18.0ms	35×	body	640	valid
9.0ms	27×	body	320	valid
2.0ms	8×	body	160	valid

simplify184.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
5	36
4	34
3	26
2	21
1	13
0	7

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize139.0ms

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)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite157.0ms

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×	`insert-posit16` `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 → 109

Calls

4 calls:

42.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
13.0ms	(- 1.0 (* (tan x) (tan x)))
37.0ms	(* (tan x) (tan x))
52.0ms	(* (tan x) (tan x))

series663.0ms

Counts

4 → 12

Calls

4 calls:

331.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
105.0ms	(- 1.0 (* (tan x) (tan x)))
119.0ms	(* (tan x) (tan x))
107.0ms	(* (tan x) (tan x))

simplify7.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5019
3	3745
2	1002
1	352
0	141

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize157.0ms

Local error

Found 4 expressions with local error:

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

rewrite321.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`associate-r`
19×	`times-frac` `add-cube-cbrt`
13×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp` `difference-of-squares`
7×	`associate-l`
4×	`flip3-+` `tan-quot` `sqrt-prod` `flip-+` `insert-posit16` `distribute-lft-out--`
3×	`frac-times` `swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`pow-prod-down` `associate-r/` `associate-/r/` `-commutative` `distribute-lft-out`
1×	`pow2` `cbrt-undiv` `+-commutative` `sum-log` `sub-neg` `pow-plus` `flip3--` `diff-log` `div-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 107

Calls

4 calls:

30.0ms	(- (sqrt 1.0) (tan x))
36.0ms	(+ (sqrt 1.0) (tan x))
175.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
73.0ms	(* (tan x) (tan x))

series836.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (sqrt 1.0) (tan x))
104.0ms	(+ (sqrt 1.0) (tan x))
524.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
114.0ms	(* (tan x) (tan x))

simplify4.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
2	1828
1	542
0	191

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize154.0ms

Local error

Found 4 expressions with local error:

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

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
6×	`associate-r` `associate-l` `tan-quot` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `times-frac` `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` `div-inv` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares` `associate-/l/`

Counts

4 → 87

Calls

4 calls:

63.0ms	(* (sin x) (tan x))
38.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
72.0ms	(/ (* (sin x) (tan x)) (cos x))
67.0ms	(* (tan x) (tan x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (sin x) (tan x))
158.0ms	(- 1.0 (/ (* (sin x) (tan x)) (cos x)))
200.0ms	(/ (* (sin x) (tan x)) (cos x))
101.0ms	(* (tan x) (tan x))

simplify7.0s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
3	3521
2	1020
1	335
0	138

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize153.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (tan x))
0.2b	(- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x)))))
0.2b	(* (tan x) (tan x))
0.3b	(/ 1 (/ (cos x) (* (sin x) (tan x))))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `times-frac`
31×	`*-un-lft-identity`
29×	`add-exp-log`
27×	`add-cube-cbrt`
17×	`add-cbrt-cube`
14×	`pow1`
12×	`div-exp`
9×	`tan-quot`
8×	`associate-/r*`
6×	`associate-r` `associate-l` `associate-*r/` `div-inv` `add-log-exp`
5×	`cbrt-undiv` `prod-exp` `associate-/r/`
4×	`insert-posit16`
3×	`rec-exp` `1-exp` `swap-sqr` `cbrt-unprod` `associate-/l*` `difference-of-squares`
2×	`pow-prod-down` `*-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`pow2` `frac-times` `clear-num` `sub-neg` `frac-2neg` `pow-plus` `flip3--` `diff-log` `associate-*l/` `pow-sqr` `pow-prod-up` `pow-flip` `flip--` `inv-pow`

Counts

4 → 128

Calls

4 calls:

57.0ms	(* (sin x) (tan x))
74.0ms	(- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x)))))
36.0ms	(* (tan x) (tan x))
74.0ms	(/ 1 (/ (cos x) (* (sin x) (tan x))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (sin x) (tan x))
113.0ms	(- 1.0 (/ 1 (/ (cos x) (* (sin x) (tan x)))))
120.0ms	(* (tan x) (tan x))
176.0ms	(/ 1 (/ (cos x) (* (sin x) (tan x))))

simplify4.6s

Counts

140 → 140

Iterations

Iter	Nodes
done	5001
2	1506
1	510
0	209

prune996.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes1.3s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	1509×	body	1280	valid
1.4s	1338×	body	640	valid
596.0ms	4234×	body	80	valid
307.0ms	600×	body	320	valid
177.0ms	319×	body	160	valid