Details

sample112.0ms

Algorithm

intervals

Results

32.0ms	52×	body	1280	valid
16.0ms	42×	body	640	valid
10.0ms	134×	body	80	valid
6.0ms	20×	body	320	valid
1.0ms	8×	body	160	valid

simplify44.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 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))

rewrite77.0ms

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)))
17.0ms	(* (tan x) (tan x))
20.0ms	(* (tan x) (tan x))

series230.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
37.0ms	(- 1.0 (* (tan x) (tan x)))
42.0ms	(* (tan x) (tan x))
46.0ms	(* (tan x) (tan x))

simplify38.0ms

Counts: 117 → 117

prune257.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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--` `associate-r/` `pow-prod-down` `-commutative` `flip--`
2×	`pow2` `pow-plus` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3-+` `diff-log` `1-exp` `un-div-inv` `flip-+` `div-inv`

Counts

4 → 112

Calls

4 calls:

41.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
6.0ms	(- 1.0 (* (tan x) (tan x)))
17.0ms	(* (tan x) (tan x))
17.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* (- 1.0 (* (tan x) (tan x))) (/ 1 (+ 1.0 (* (tan x) (tan x)))))
36.0ms	(- 1.0 (* (tan x) (tan x)))
40.0ms	(* (tan x) (tan x))
36.0ms	(* (tan x) (tan x))

simplify49.0ms

Counts: 124 → 124

prune266.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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:

4.0ms	(pow (cos x) 2)
4.0ms	(pow (cos x) 2)
4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series83.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(pow (cos x) 2)
24.0ms	(pow (cos x) 2)
20.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)

simplify54.0ms

Counts: 84 → 84

prune234.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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)))))
0.3b	(+ (sqrt 1.0) (tan x))
0.3b	(* (tan x) (tan x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

11.0ms	(- (sqrt 1.0) (tan x))
77.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
10.0ms	(+ (sqrt 1.0) (tan x))
17.0ms	(* (tan x) (tan x))

series328.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt 1.0) (tan x))
210.0ms	(* (+ (sqrt 1.0) (tan x)) (/ (- (sqrt 1.0) (tan x)) (+ 1.0 (* (tan x) (tan x)))))
37.0ms	(+ (sqrt 1.0) (tan x))
36.0ms	(* (tan x) (tan x))

simplify61.0ms

Counts: 115 → 115

prune267.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes197.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	1510×	body	1280	valid
793.0ms	1259×	body	640	valid
523.0ms	577×	body	320	valid
500.0ms	4303×	body	80	valid
63.0ms	351×	body	160	valid