Details

sample251.0ms

Algorithm

intervals

Results

65.0ms	131×	body	80	valid
55.0ms	53×	body	1280	valid
30.0ms	45×	body	640	valid
6.0ms	12×	body	320	valid
5.0ms	15×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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:

8.0ms	(- 1.0 (* (tan x) (tan x)))
62.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
24.0ms	(* (tan x) (tan x))
24.0ms	(* (tan x) (tan x))

series309.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (* (tan x) (tan x)))
138.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ (* (tan x) (tan x)) 1.0))
51.0ms	(* (tan x) (tan x))
77.0ms	(* (tan x) (tan x))

simplify856.0ms

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
2	1706
1	360
0	141

prune525.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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)))
0.3b	(* (tan x) (tan x))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
7×	`associate-l`
5×	`frac-times`
4×	`flip3-+` `flip3--` `tan-quot` `flip-+` `flip--` `difference-of-squares`
3×	`sub-neg` `swap-sqr` `associate-l/` `associate-r/`
2×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `sqrt-prod` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up`

Counts

4 → 89

Calls

4 calls:

14.0ms	(+ (sqrt 1.0) (tan x))
16.0ms	(- (sqrt 1.0) (tan x))
60.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
24.0ms	(* (tan x) (tan x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (sqrt 1.0) (tan x))
59.0ms	(- (sqrt 1.0) (tan x))
177.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
44.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2287
1	374
0	133

prune483.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))
0.4b	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (/ (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`pow1`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
12×	`tan-quot`
10×	`add-cbrt-cube` `add-exp-log`
9×	`swap-sqr` `associate-r` `associate-l`
6×	`add-log-exp`
4×	`times-frac` `associate-/r/` `difference-of-squares`
3×	`pow2` `frac-times` `pow-plus` `distribute-rgt-out--` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 106

Calls

4 calls:

11.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))
21.0ms	(* (tan x) (tan x))
142.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (/ (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
42.0ms	(* (tan x) (tan x))
219.0ms	(- (/ 1.0 (+ (* (tan x) (tan x)) 1.0)) (/ (* (tan x) (tan x)) (+ (* (tan x) (tan x)) 1.0)))

simplify760.0ms

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1244
1	301
0	118

prune442.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

12.0ms	(/ (* (sin x) (tan x)) (cos x))
57.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ (* (tan x) (tan x)) 1.0))
10.0ms	(* (sin x) (tan x))
12.0ms	(* (tan x) (tan x))

series418.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (* (sin x) (tan x)) (cos x))
178.0ms	(/ (- 1.0 (/ (* (sin x) (tan x)) (cos x))) (+ (* (tan x) (tan x)) 1.0))
73.0ms	(* (sin x) (tan x))
54.0ms	(* (tan x) (tan x))

simplify1.3s

Counts

121 → 121

Iterations

Iter	Nodes
done	5001
2	2680
1	487
0	190

prune490.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.5s	1457×	body	1280	valid
1.3s	4297×	body	80	valid
1.2s	1278×	body	640	valid
283.0ms	633×	body	320	valid
90.0ms	335×	body	160	valid