Details

sample154.0ms

Algorithm

intervals

Results

72.0ms	61×	body	1280	valid
17.0ms	44×	body	640	valid
9.0ms	121×	body	80	valid
8.0ms	25×	body	320	valid
1.0ms	5×	body	160	valid

simplify37.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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))

rewrite75.0ms

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:

29.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
16.0ms	(* (tan x) (tan x))
19.0ms	(* (tan x) (tan x))

series332.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
61.0ms	(- 1.0 (* (tan x) (tan x)))
70.0ms	(* (tan x) (tan x))
56.0ms	(* (tan x) (tan x))

simplify632.0ms

Counts: 117 → 117

prune390.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

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)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(pow (cos x) 2)
7.0ms	(pow (cos x) 2)
7.0ms	(pow (sin x) 2)
8.0ms	(pow (sin x) 2)

series119.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
34.0ms	(pow (cos x) 2)
34.0ms	(pow (sin x) 2)
34.0ms	(pow (sin x) 2)

simplify865.0ms

Counts: 84 → 84

prune276.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
184×	`*-un-lft-identity`
172×	`add-sqr-sqrt`
94×	`add-cube-cbrt`
38×	`difference-of-squares`
30×	`associate-/r*`
26×	`distribute-lft-out`
19×	`sqrt-prod` `distribute-lft-out--`
13×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
11×	`pow1`
7×	`div-inv` `associate-/l*`
6×	`flip3--` `flip--` `add-log-exp`
4×	`tan-quot` `cbrt-undiv` `div-exp` `associate-/l/`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 224

Calls

4 calls:

62.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
12.0ms	(+ (sqrt 1.0) (tan x))
58.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
33.0ms	(* (tan x) (tan x))

series562.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))
56.0ms	(+ (sqrt 1.0) (tan x))
154.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
56.0ms	(* (tan x) (tan x))

simplify1.7s

Counts: 236 → 236

prune755.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (sqrt 1.0) (tan x))
0.2b	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
0.3b	(* (tan x) (tan x))
0.5b	(exp (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-cube-cbrt`
24×	`exp-prod`
14×	`difference-of-squares`
11×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
7×	`sqrt-prod` `distribute-lft-out--` `add-log-exp`
6×	`associate-/r*`
4×	`tan-quot` `associate-/r/`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
2×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `rem-exp-log` `distribute-lft-out` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

16.0ms	(+ (sqrt 1.0) (tan x))
80.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
32.0ms	(* (tan x) (tan x))
85.0ms	(exp (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (sqrt 1.0) (tan x))
157.0ms	(/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x)))
45.0ms	(* (tan x) (tan x))
196.0ms	(exp (/ (+ 1.0 (* (tan x) (tan x))) (- (sqrt 1.0) (tan x))))

simplify963.0ms

Counts: 127 → 127

prune533.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes264.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify909.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.0s	1539×	body	1280	valid
867.0ms	1246×	body	640	valid
787.0ms	4310×	body	80	valid
699.0ms	615×	body	320	valid
76.0ms	290×	body	160	valid