Details

sample111.0ms

Algorithm

intervals

Results

28.0ms	46×	body	1280	valid
16.0ms	44×	body	640	valid
11.0ms	132×	body	80	valid
5.0ms	20×	body	320	valid
2.0ms	14×	body	160	valid

simplify47.0ms

Counts: 1 → 1

prune9.0ms

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))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite73.0ms

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:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(- 1.0 (* (tan x) (tan x)))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series228.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
36.0ms	(- 1.0 (* (tan x) (tan x)))
41.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify40.0ms

Counts: 117 → 117

prune271.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(- (sqrt 1.0) (tan x))
9.0ms	(+ (sqrt 1.0) (tan x))
58.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
15.0ms	(* (tan x) (tan x))

series229.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (sqrt 1.0) (tan x))
36.0ms	(+ (sqrt 1.0) (tan x))
110.0ms	(* (+ (sqrt 1.0) (tan x)) (- (sqrt 1.0) (tan x)))
38.0ms	(* (tan x) (tan x))

simplify44.0ms

Counts: 101 → 101

prune275.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

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)

rewrite21.0ms

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)
3.0ms	(pow (cos x) 2)
9.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)

series80.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (cos x) 2)
18.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
21.0ms	(pow (sin x) 2)

simplify53.0ms

Counts: 84 → 84

prune249.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
1.5b	(exp (log (pow (sin x) 2)))
15.9b	(log (pow (sin x) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`add-exp-log` `exp-sum`
6×	`pow1` `pow-unpow`
4×	`exp-prod` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `rem-log-exp` `pow-exp`
2×	`pow-pow` `log-pow`
1×	`rem-exp-log`

Counts

4 → 75

Calls

4 calls:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
6.0ms	(exp (log (pow (sin x) 2)))
4.0ms	(log (pow (sin x) 2))

series147.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin x) 2)
20.0ms	(pow (sin x) 2)
20.0ms	(exp (log (pow (sin x) 2)))
81.0ms	(log (pow (sin x) 2))

simplify71.0ms

Counts: 87 → 87

prune237.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

regimes260.0ms

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

sample3.2s

Algorithm

intervals

Results

1.6s	1496×	body	1280	valid
644.0ms	1269×	body	640	valid
523.0ms	4282×	body	80	valid
166.0ms	622×	body	320	valid
58.0ms	331×	body	160	valid