Details

sample67.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
16.0ms	40×	body	640	valid
11.0ms	140×	body	80	valid
5.0ms	21×	body	320	valid
2.0ms	10×	body	160	valid

simplify11.8s

Counts

1 → 1

Iterations

Iter	Nodes
9	9892
8	1985
7	571
6	236
5	102
4	50
3	29
2	22
1	18
0	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.4b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`pow1` `insert-posit16` `associate-/l*`
2×	`flip3-+` `difference-of-sqr-1` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

8.0ms	(+ 1 (exp (* -2 x)))
15.0ms	(/ 2 (+ 1 (exp (* -2 x))))
57.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series126.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1 (exp (* -2 x)))
29.0ms	(/ 2 (+ 1 (exp (* -2 x))))
81.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
4	3911
3	1437
2	615
1	266
0	120

prune639.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp (* -2 x)))
0.0b	(/ 2 (+ 1 (exp (* -2 x))))
3.4b	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
15×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out`
4×	`associate-/r*` `difference-of-squares`
3×	`pow1` `insert-posit16` `associate-/l*`
2×	`flip3-+` `difference-of-sqr-1` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3--` `diff-log` `div-exp` `div-inv` `flip--` `distribute-lft-out--`

Counts

3 → 67

Calls

3 calls:

7.0ms	(+ 1 (exp (* -2 x)))
13.0ms	(/ 2 (+ 1 (exp (* -2 x))))
66.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

series116.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(+ 1 (exp (* -2 x)))
24.0ms	(/ 2 (+ 1 (exp (* -2 x))))
79.0ms	(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

simplify2.9s

Counts

76 → 76

Iterations

Iter	Nodes
4	3911
3	1437
2	615
1	266
0	120

prune591.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2 (+ 1 (exp (* -2 x))))
0.0b	(/ (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
0.0b	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
3.4b	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

131×	`*-un-lft-identity`
100×	`times-frac`
79×	`add-sqr-sqrt`
61×	`add-cube-cbrt`
29×	`distribute-lft-out`
24×	`swap-sqr`
20×	`add-cbrt-cube` `add-exp-log`
18×	`associate-r` `associate-l`
12×	`associate-/r/` `difference-of-squares`
11×	`pow1`
9×	`associate-/l*`
8×	`associate-/r*`
6×	`cbrt-undiv` `flip3-+` `difference-of-sqr-1` `div-exp` `flip-+` `div-inv` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 191

Calls

4 calls:

20.0ms	(/ 2 (+ 1 (exp (* -2 x))))
111.0ms	(/ (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
57.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
20.0ms	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

series289.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 2 (+ 1 (exp (* -2 x))))
135.0ms	(/ (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
47.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
82.0ms	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

simplify1.0s

Counts

203 → 203

Iterations

Iter	Nodes
2	2321
1	762
0	256

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1))) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
0.0b	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
3.4b	(log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)))
3.4b	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

134×	`*-un-lft-identity`
104×	`times-frac`
82×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
42×	`log-pow`
36×	`exp-prod`
29×	`distribute-lft-out`
24×	`swap-sqr`
18×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
17×	`pow1`
14×	`difference-of-squares`
10×	`associate-/r/` `associate-/l*`
7×	`difference-of-sqr-1`
6×	`add-log-exp`
5×	`cbrt-undiv` `log-prod` `flip3-+` `div-exp` `flip-+` `div-inv`
4×	`associate-/r*` `prod-exp` `cbrt-unprod` `insert-posit16` `unswap-sqr`
2×	`log-div` `sub-neg` `exp-diff` `exp-sum`
1×	`pow2` `frac-times` `clear-num` `frac-2neg` `pow-plus` `flip3--` `diff-log` `div-sub` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

4 → 197

Calls

4 calls:

346.0ms	(/ (log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1))) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
68.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
92.0ms	(log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)))
29.0ms	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

series338.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1))) (+ (/ 2 (+ 1 (exp (* -2 x)))) 1))
33.0ms	(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
67.0ms	(log (exp (- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)))
67.0ms	(- (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) 1)

simplify938.0ms

Counts

209 → 209

Iterations

Iter	Nodes
2	2256
1	784
0	291

prune2.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes358.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch151.0ms

Steps

Iters	Range		Point
8	4.2592438902487584e-05	0.10106394179147121	0.00661692382552498
9	-3.0421098639022524	-5.8481452536585384e-08	-0.004730793410321861

simplify6.0ms

Iterations

Iter	Nodes
2	42
1	42
0	32

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1773×	body	1280	valid
656.0ms	603×	body	320	valid
612.0ms	1248×	body	640	valid
399.0ms	4033×	body	80	valid
61.0ms	343×	body	160	valid