Details

sample191.0ms

Algorithm

intervals

Results

32.0ms	50×	body	1280	valid
19.0ms	40×	body	640	valid
14.0ms	135×	body	80	valid
6.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	37
5	37
4	34
3	26
2	21
1	13
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

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×	`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 → 105

Calls

4 calls:

52.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
4.0ms	(- 1.0 (* (tan x) (tan x)))
12.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series343.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
51.0ms	(- 1.0 (* (tan x) (tan x)))
63.0ms	(* (tan x) (tan x))
82.0ms	(* (tan x) (tan x))

simplify970.0ms

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1717
1	360
0	141

prune480.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (* (tan x) (tan x)) 1.0)))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
20×	`pow1` `add-cube-cbrt`
17×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`associate-l`
8×	`tan-quot`
6×	`swap-sqr` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`
2×	`pow2` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `flip3-+` `diff-log` `1-exp` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

64.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (* (tan x) (tan x)) 1.0)))
4.0ms	(- 1.0 (* (tan x) (tan x)))
20.0ms	(* (tan x) (tan x))
23.0ms	(* (tan x) (tan x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ (* (tan x) (tan x)) 1.0)))
42.0ms	(- 1.0 (* (tan x) (tan x)))
49.0ms	(* (tan x) (tan x))
38.0ms	(* (tan x) (tan x))

simplify3.3s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	2854
1	443
0	162

prune438.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `pow-unpow` `unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `add-cbrt-cube` `pow-exp` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

6.0ms	(pow (cos x) 2)
5.0ms	(pow (cos x) 2)
5.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series112.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (cos x) 2)
28.0ms	(pow (cos x) 2)
20.0ms	(pow (sin x) 2)
38.0ms	(pow (sin x) 2)

simplify981.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5004
3	2402
2	648
1	189
0	64

prune428.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

124.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (* (tan x) (tan x)) 1.0)))
11.0ms	(+ (tan x) (sqrt 1.0))
39.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (* (tan x) (tan x)) 1.0))
12.0ms	(* (tan x) (tan x))

series544.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (* (tan x) (tan x)) 1.0)))
39.0ms	(+ (tan x) (sqrt 1.0))
171.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (* (tan x) (tan x)) 1.0))
53.0ms	(* (tan x) (tan x))

simplify1.9s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	3742
1	626
0	216

prune722.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes470.0ms

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	12
1	12
0	11

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.9s	1466×	body	1280	valid
1.3s	4372×	body	80	valid
962.0ms	1241×	body	640	valid
238.0ms	592×	body	320	valid
93.0ms	329×	body	160	valid