Details

sample1.0s

Algorithm

intervals

Results

651.0ms	82×	body	1280	valid
220.0ms	57×	body	2560	valid
78.0ms	59×	body	640	valid
18.0ms	38×	body	320	valid
4.0ms	12×	body	160	valid
2.0ms	8×	body	80	valid

simplify94.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.0b	(- x (sin x))
1.0b	(- x (tan x))

rewrite78.0ms

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:

41.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (sin x))
15.0ms	(- x (tan x))

series332.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(/ (- x (sin x)) (- x (tan x)))
63.0ms	(- x (sin x))
144.0ms	(- x (tan x))

simplify2.8s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4845
2	1280
1	501
0	209

prune507.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- x (tan x))
1.0b	(- x (tan x))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 588

Calls

4 calls:

27.0ms	(/ (sin x) (- x (tan x)))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))
175.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

series488.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (sin x) (- x (tan x)))
79.0ms	(- x (tan x))
70.0ms	(- x (tan x))
264.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))

simplify2.4s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	3394
1	1403
0	617

prune2.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (* (* x x) (* x x)) -27/2800 -1/2)
0.1b	(* (* x x) (* x x))
15.1b	(fma (* x x) 9/40 (fma (* (* x x) (* x x)) -27/2800 -1/2))

rewrite61.0ms

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 (* (* x x) (* x x)) -27/2800 -1/2)
53.0ms	(* (* x x) (* x x))
1.0ms	(fma (* x x) 9/40 (fma (* (* x x) (* x x)) -27/2800 -1/2))

series298.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(fma (* (* x x) (* x x)) -27/2800 -1/2)
63.0ms	(* (* x x) (* x x))
76.0ms	(fma (* x x) 9/40 (fma (* (* x x) (* x x)) -27/2800 -1/2))

simplify3.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5004
3	3397
2	630
1	200
0	78

prune240.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes108.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch145.0ms

Steps

Iters	Range		Point
11	3.4817375791661903e-26	573579.0075499975	0.0289731118094174
10	-84463.33967257517	-3.2432757514909933e-09	-0.029114572981685117

simplify5.0ms

Iterations

Iter	Nodes
done	22
0	22

end0.0ms

sample13.6s

Algorithm

intervals

Results

6.8s	1654×	body	2560	valid
3.7s	2751×	body	1280	valid
1.7s	1866×	body	640	valid
615.0ms	459×	body	160	valid
391.0ms	925×	body	320	valid
101.0ms	345×	body	80	valid