Details

sample638.0ms

Algorithm

intervals

Results

270.0ms	59×	body	2560	valid
125.0ms	91×	body	1280	valid
46.0ms	58×	body	640	valid
11.0ms	21×	body	320	valid
5.0ms	12×	body	160	valid
3.0ms	15×	body	80	valid

simplify20.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	276
1	13	276
2	17	276
3	19	276
done	19	276

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.5b	(- x (tan x))
1.6b	(- x (sin x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 110

Calls

3 calls:

29.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
8.0ms	(- x (sin x))

series232.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- x (sin x)) (- x (tan x)))
78.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify3.5s

Counts

119 → 119

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	209	49985
1	501	44919
2	1277	41275
3	4708	40985
done	5000	40935

prune649.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma -27/2800 (* (* x x) (* x x)) -1/2)
0.1b	(* (* x x) (* x x))
18.1b	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 85

Calls

3 calls:

0.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
44.0ms	(* (* x x) (* x x))
1.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

series259.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
66.0ms	(* (* x x) (* x x))
69.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify4.0s

Counts

94 → 94

Iterations

Useful iterations: 2 (244.0ms)

Iter	Nodes	Cost
0	78	14113
1	200	9431
2	616	9041
3	3347	9041
done	5003	9041

prune231.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
1.6b	(- x (sin x))
1.8b	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
18.4b	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
15×	`times-frac`
12×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `pow1` `flip3--` `fma-neg` `associate-/r/` `log1p-expm1-u` `flip--`
3×	`cbrt-prod` `associate-/r*`
2×	`sub-neg` `diff-log` `associate-*l/` `frac-add` `tan-quot` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow1/3` `div-sub` `div-exp` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

1.0ms	(cbrt x)
12.0ms	(- x (sin x))
236.0ms	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
31.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

series564.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(cbrt x)
37.0ms	(- x (sin x))
131.0ms	(/ (- x (sin x)) (+ (- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x)) (* (tan x) 0)))
131.0ms	(- (* (* (cbrt x) (cbrt x)) (cbrt x)) (tan x))

simplify3.8s

Counts

115 → 115

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	238	58879
1	592	51535
2	1516	34879
3	4835	33613
done	5000	33588

prune512.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* (* x x) 27/2800))
0.0b	(fma (* x x) (- 9/40 (* (* x x) 27/2800)) -1/2)
0.2b	(* (* x x) 27/2800)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-r` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

9.0ms	(- 9/40 (* (* x x) 27/2800))
0.0ms	(fma (* x x) (- 9/40 (* (* x x) 27/2800)) -1/2)
28.0ms	(* (* x x) 27/2800)

series225.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(- 9/40 (* (* x x) 27/2800))
79.0ms	(fma (* x x) (- 9/40 (* (* x x) 27/2800)) -1/2)
50.0ms	(* (* x x) 27/2800)

simplify3.7s

Counts

60 → 60

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	93	13954
1	233	10782
2	796	10215
3	2673	9202
done	5003	8892

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes87.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch162.0ms

Steps

Iters	Range		Point
9	0.1909160003853501	166131308.15705827	2.424239464461981
10	-27652538170.40468	-0.18371106458419734	-2.447149999215354

simplify17.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	28	1032
1	36	1032
done	36	1032

end0.0ms

sample12.9s

Algorithm

intervals

Results

5.8s	1567×	body	2560	valid
3.4s	2839×	body	1280	valid
2.2s	1839×	body	640	valid
902.0ms	930×	body	320	valid
206.0ms	470×	body	160	valid
149.0ms	355×	body	80	valid