Details

sample570.0ms

Algorithm

intervals

Results

241.0ms	50×	body	2560	valid
149.0ms	85×	body	1280	valid
74.0ms	60×	body	640	valid
12.0ms	26×	body	320	valid
6.0ms	22×	body	160	valid
2.0ms	13×	body	80	valid

simplify72.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite84.0ms

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×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

30.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (tan x))
40.0ms	(- x (sin x))

series251.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(/ (- x (sin x)) (- x (tan x)))
95.0ms	(- x (tan x))
72.0ms	(- x (sin x))

simplify1.1s

Counts

119 → 119

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	209	1823
1	476	1563
2	1343	1384
done	5000	1306

prune322.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
0.1b	(* 9/40 (pow x 2))
17.1b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
23.0ms	(* 9/40 (pow x 2))
12.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series226.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(fma 27/2800 (pow x 4) 1/2)
35.0ms	(* 9/40 (pow x 2))
54.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify2.6s

Counts

67 → 67

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	106	845
1	219	700
2	588	624
3	2787	573
done	5000	572

prune224.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin x) 3)
1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- x (tan x))
33.8b	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

241×	`add-sqr-sqrt`
171×	`*-un-lft-identity`
153×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
119×	`add-cube-cbrt`
81×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3` `distribute-lft-out--`
25×	`associate-/l*`
15×	`fma-neg`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `associate-/r*` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `div-sub` `div-exp` `pow-exp` `clear-num` `div-inv` `rem-cube-cbrt`

Counts

4 → 365

Calls

4 calls:

4.0ms	(pow (sin x) 3)
49.0ms	(- (pow x 3) (pow (sin x) 3))
7.0ms	(- x (tan x))
116.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

series556.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sin x) 3)
169.0ms	(- (pow x 3) (pow (sin x) 3))
58.0ms	(- x (tan x))
297.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

simplify2.0s

Counts

377 → 377

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	411	11834
1	872	8088
2	2466	6935
done	5001	6187

prune865.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow x 3) (pow (sin x) 3))
1.9b	(- (* x x) (* (tan x) (tan x)))
16.0b	(/ (- (* x x) (* (tan x) (tan x))) (+ (tan x) x))
33.8b	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

239×	`add-sqr-sqrt`
179×	`*-un-lft-identity`
145×	`prod-diff`
135×	`unpow-prod-down` `cube-prod`
119×	`add-cube-cbrt`
91×	`times-frac`
86×	`difference-of-squares`
65×	`sqr-pow`
29×	`associate-/l*`
25×	`cube-mult` `unpow3` `distribute-lft-out--`
13×	`fma-neg`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r*`
5×	`difference-cubes` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `associate-/r/` `div-inv`
1×	`flip3-+` `flip-+`

Counts

4 → 372

Calls

4 calls:

36.0ms	(- (pow x 3) (pow (sin x) 3))
17.0ms	(- (* x x) (* (tan x) (tan x)))
54.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ (tan x) x))
143.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(- (pow x 3) (pow (sin x) 3))
134.0ms	(- (* x x) (* (tan x) (tan x)))
169.0ms	(/ (- (* x x) (* (tan x) (tan x))) (+ (tan x) x))
255.0ms	(/ (- (pow x 3) (pow (sin x) 3)) (fma x x (* (sin x) (+ x (sin x)))))

simplify2.5s

Counts

384 → 384

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	457	12473
1	1033	8846
2	3239	7686
done	5001	7684

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes99.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch84.0ms

Steps

Iters	Range		Point
9	9.85435867085541e-08	110.15968793260775	0.02674499741262323
8	-0.1517943218839364	-1.6640733670284383e-05	-0.027801200389932522

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	38
1	26	30
done	26	30

end0.0ms

sample9.9s

Algorithm

intervals

Results

4.9s	1600×	body	2560	valid
3.2s	2816×	body	1280	valid
964.0ms	1873×	body	640	valid
307.0ms	892×	body	320	valid
123.0ms	465×	body	160	valid
64.0ms	354×	body	80	valid