Details

sample457.0ms

Algorithm

intervals

Results

174.0ms	48×	body	2560	valid
110.0ms	97×	body	1280	valid
44.0ms	13×	body	80	valid
28.0ms	49×	body	640	valid
13.0ms	32×	body	320	valid
5.0ms	17×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.8b	(- x (tan x))
1.8b	(- x (sin x))

rewrite470.0ms

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:

42.0ms	(/ (- x (sin x)) (- x (tan x)))
11.0ms	(- x (tan x))
408.0ms	(- x (sin x))

series294.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
88.0ms	(- x (tan x))
77.0ms	(- x (sin x))

simplify2.9s

Counts

119 → 119

Iterations

Iter	Nodes
done	5000
3	4708
2	1277
1	501
0	209

prune480.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

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:

1.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
37.0ms	(* (* x x) (* x x))
0.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

series289.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(fma -27/2800 (* (* x x) (* x x)) -1/2)
68.0ms	(* (* x x) (* x x))
81.0ms	(fma 9/40 (* x x) (fma -27/2800 (* (* x x) (* x x)) -1/2))

simplify3.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5003
3	3347
2	616
1	200
0	78

prune232.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.6b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.8b	(- x (tan x))
1.8b	(- x (tan x))

rewrite254.0ms

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:

26.0ms	(/ (sin x) (- x (tan x)))
128.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series608.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (sin x) (- x (tan x)))
348.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
79.0ms	(- x (tan x))
91.0ms	(- x (tan x))

simplify2.5s

Counts

600 → 600

Iterations

Iter	Nodes
done	5000
2	3367
1	1402
0	617

prune2.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin x))
1.8b	(- (* (* x x) x) (* (sin x) (* (sin x) (sin x))))
1.8b	(- x (tan x))
33.3b	(/ (- (* (* x x) x) (* (sin x) (* (sin x) (sin x)))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
10×	`prod-diff`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes` `cube-unmult` `pow3`
4×	`expm1-log1p-u` `fma-neg` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `flip--`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `sqr-sin` `div-inv` `sin-mult` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

20.0ms	(* (sin x) (sin x))
48.0ms	(- (* (* x x) x) (* (sin x) (* (sin x) (sin x))))
10.0ms	(- x (tan x))
118.0ms	(/ (- (* (* x x) x) (* (sin x) (* (sin x) (sin x)))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin x) (sin x))
190.0ms	(- (* (* x x) x) (* (sin x) (* (sin x) (sin x))))
77.0ms	(- x (tan x))
277.0ms	(/ (- (* (* x x) x) (* (sin x) (* (sin x) (sin x)))) (+ (* x x) (+ (* (sin x) (sin x)) (* x (sin x)))))

simplify2.0s

Counts

124 → 124

Iterations

Iter	Nodes
done	5001
2	2046
1	602
0	235

prune676.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes113.0ms

Accuracy

100% (0.0b remaining)

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

bsearch123.0ms

Steps

Iters	Range		Point
6	0.0022991053059264813	0.02586244036059231	0.02458873884700214
10	-733100.9210806559	-4.034181863829644e-08	-0.026370186168873697

simplify5.0ms

Iterations

Iter	Nodes
done	22
0	22

end0.0ms

sample12.2s

Algorithm

intervals

Results

6.2s	1598×	body	2560	valid
4.0s	2738×	body	1280	valid
1.1s	1859×	body	640	valid
451.0ms	948×	body	320	valid
138.0ms	490×	body	160	valid
65.0ms	367×	body	80	valid