Details

sample347.0ms

Algorithm

intervals

Results

143.0ms	61×	body	2560	valid
114.0ms	82×	body	1280	valid
25.0ms	59×	body	640	valid
10.0ms	29×	body	320	valid
3.0ms	12×	body	160	valid
2.0ms	13×	body	80	valid

simplify5.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (tan x))
1.4b	(- x (sin x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

50.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series200.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (- x (sin x)) (- x (tan x)))
67.0ms	(- x (tan x))
45.0ms	(- x (sin x))

simplify143.0ms

Counts: 89 → 89

prune219.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
16.7b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
16.8b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
42×	`div-exp`
37×	`pow-to-exp` `pow-exp`
36×	`prod-exp`
18×	`unpow-prod-down`
16×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
14×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-pow` `frac-2neg` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 136

Calls

4 calls:

4.0ms	(pow (sin x) 2)
4.0ms	(pow (sin x) 2)
23.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
17.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

series185.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(pow (sin x) 2)
25.0ms	(pow (sin x) 2)
59.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
82.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

simplify43.0ms

Counts: 148 → 148

prune366.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.4b	(- x (sin x))
1.4b	(- x (sin x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

6.0ms	(- x (tan x))
5.0ms	(- x (tan x))
7.0ms	(- x (sin x))
6.0ms	(- x (sin x))

series194.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(- x (tan x))
61.0ms	(- x (tan x))
41.0ms	(- x (sin x))
35.0ms	(- x (sin x))

simplify62.0ms

Counts: 68 → 68

prune196.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
17.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

12.0ms	(* 27/2800 (pow x 4))
16.0ms	(* 9/40 (pow x 2))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series122.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* 27/2800 (pow x 4))
32.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify38.0ms

Counts: 75 → 75

prune152.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes69.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch108.0ms

Steps

Iters	Range		Point
9	1.494961173861339	216094143.84427205	2.419818388459179
9	-8327.681910469391	-0.031006959526126927	-1.5666536045569017

simplify1.0ms

end0.0ms

sample10.1s

Algorithm

intervals

Results

4.8s	1615×	body	2560	valid
3.2s	2750×	body	1280	valid
967.0ms	1869×	body	640	valid
630.0ms	907×	body	320	valid
119.0ms	525×	body	160	valid
84.0ms	334×	body	80	valid