Details

sample216.0ms

Algorithm

intervals

Results

93.0ms	52×	body	1280	valid
23.0ms	46×	body	640	valid
13.0ms	128×	body	80	valid
7.0ms	19×	body	320	valid
3.0ms	11×	body	160	valid

simplify44.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite104.0ms

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:

11.0ms	(- 1.0 (* (tan x) (tan x)))
49.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
16.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series351.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (* (tan x) (tan x)))
159.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
70.0ms	(* (tan x) (tan x))
77.0ms	(* (tan x) (tan x))

simplify596.0ms

Counts: 117 → 117

prune410.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt 1.0) (tan x))
0.2b	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
37×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-r`
16×	`difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-prod` `distribute-lft-out--`
7×	`associate-l`
6×	`associate-/l*` `add-log-exp`
4×	`tan-quot` `flip3-+` `associate-/r/` `flip-+`
3×	`frac-times` `swap-sqr` `associate-l/` `prod-exp` `associate-/r` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip--` `div-inv` `associate-/l/`
1×	`pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `distribute-lft-out`

Counts

4 → 135

Calls

4 calls:

9.0ms	(- (sqrt 1.0) (tan x))
31.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
88.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
22.0ms	(* (tan x) (tan x))

series527.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (sqrt 1.0) (tan x))
163.0ms	(/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x))))
257.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
55.0ms	(* (tan x) (tan x))

simplify1.2s

Counts: 147 → 147

prune518.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.7b	(pow (tan x) 6)
9.5b	(cbrt (pow (tan x) 6))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

69.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
31.0ms	(* (tan x) (tan x))
4.0ms	(pow (tan x) 6)
3.0ms	(cbrt (pow (tan x) 6))

series381.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- 1.0 (cbrt (pow (tan x) 6))) (+ 1.0 (* (tan x) (tan x))))
65.0ms	(* (tan x) (tan x))
109.0ms	(pow (tan x) 6)
42.0ms	(cbrt (pow (tan x) 6))

simplify675.0ms

Counts: 124 → 124

prune527.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
0.2b	(* (tan x) (- (tan x) (sqrt 1.0)))
0.3b	(* (tan x) (tan x))
0.4b	(pow (tan x) 3)

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
15×	`*-un-lft-identity`
14×	`pow1`
13×	`add-cube-cbrt`
11×	`frac-times`
9×	`flip3-+` `associate-r` `flip-+`
8×	`tan-quot` `associate-/r/` `associate-/l/`
7×	`associate-*r/`
6×	`associate-l` `associate-*l/` `prod-exp` `cbrt-unprod`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `swap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-prod-down` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`cube-div` `pow2` `cube-mult` `pow-to-exp` `pow-pow` `frac-2neg` `times-frac` `pow-plus` `unpow3` `pow-exp` `clear-num` `associate-/r` `sqrt-prod` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l` `distribute-lft-out--` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 119

Calls

4 calls:

171.0ms	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
89.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
31.0ms	(* (tan x) (tan x))
9.0ms	(pow (tan x) 3)

series837.0ms

Counts

4 → 12

Calls

4 calls:

604.0ms	(/ (* (+ (pow (sqrt 1.0) 3) (pow (tan x) 3)) (- (sqrt 1.0) (tan x))) (* (+ 1.0 (* (tan x) (tan x))) (+ (* (tan x) (- (tan x) (sqrt 1.0))) 1.0)))
102.0ms	(* (tan x) (- (tan x) (sqrt 1.0)))
63.0ms	(* (tan x) (tan x))
68.0ms	(pow (tan x) 3)

simplify554.0ms

Counts: 131 → 131

prune566.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes393.0ms

Accuracy

10.3% (0.3b remaining)

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

bsearch0.0ms

simplify1.3s

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.4s	1530×	body	1280	valid
1.4s	1199×	body	640	valid
1.1s	4329×	body	80	valid
289.0ms	617×	body	320	valid
81.0ms	325×	body	160	valid