Details

sample802.0ms

Algorithm

intervals

Results

212.0ms	51×	body	2560	valid
153.0ms	81×	body	1280	valid
95.0ms	69×	body	640	valid
84.0ms	14×	body	160	valid
18.0ms	31×	body	320	valid
2.0ms	10×	body	80	valid

simplify40.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.6b	(- x (tan x))
0.6b	(- x (sin x))

rewrite115.0ms

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:

55.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
16.0ms	(- x (sin x))

series307.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(/ (- x (sin x)) (- x (tan x)))
92.0ms	(- x (tan x))
63.0ms	(- x (sin x))

simplify1.7s

Counts: 89 → 89

prune321.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
14.8b	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
14.8b	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

rewrite87.0ms

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:

9.0ms	(pow (sin x) 2)
5.0ms	(pow (sin x) 2)
32.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
36.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sin x) 2)
25.0ms	(pow (sin x) 2)
80.0ms	(/ (pow (sin x) 2) (* (pow x 2) (cos x)))
94.0ms	(/ (pow (sin x) 2) (* (pow x 2) (pow (cos x) 2)))

simplify735.0ms

Counts: 148 → 148

prune573.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
18.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite52.0ms

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))
12.0ms	(* 9/40 (pow x 2))
24.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series158.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 27/2800 (pow x 4))
26.0ms	(* 9/40 (pow x 2))
83.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify662.0ms

Counts: 75 → 75

prune283.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
18.3b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite46.0ms

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`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

12.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
18.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* 27/2800 (pow x 4))
51.0ms	(* 9/40 (pow x 2))
184.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify608.0ms

Counts: 73 → 73

prune253.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes49.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch204.0ms

Steps

Iters	Range		Point
9	0.0024368900564104884	555.6593536559827	2.4581408457881073
10	-248837311.7084542	-0.0006576197608759923	-2.42215428873076

simplify1.9s

end0.0ms

sample13.8s

Algorithm

intervals

Results

6.4s	1642×	body	2560	valid
4.3s	2779×	body	1280	valid
1.7s	1766×	body	640	valid
629.0ms	467×	body	160	valid
404.0ms	962×	body	320	valid
71.0ms	384×	body	80	valid