Details

sample57.0ms

Algorithm

intervals

Results

26.0ms	81×	body	1280	valid
9.0ms	44×	body	640	valid
7.0ms	190×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	11×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	152
1	10	152
2	13	152
3	15	152
done	15	152

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.6b	(- (exp x) 1.0)

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

29.0ms	(/ (- (exp x) 1.0) x)
17.0ms	(- (exp x) 1.0)

series80.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify2.0s

Counts

58 → 58

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	99	16122
1	224	14843
2	569	14763
3	1947	14683
done	5002	14603

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
6×	`pow1` `-un-lft-identity` `add-cbrt-cube` `associate-r` `associate-l*` `add-exp-log` `add-cube-cbrt`
2×	`pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 40

Calls

2 calls:

33.0ms	(* x (+ (* 1/6 x) 1/2))
15.0ms	(* 1/6 x)

series137.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(* x (+ (* 1/6 x) 1/2))
28.0ms	(* 1/6 x)

simplify4.5s

Counts

46 → 46

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	70	7492
1	204	6296
2	646	6296
3	3635	6216
done	5019	6216

prune134.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.0 1.0) (* (exp x) 1.0))
0.0b	(* (exp x) (exp x))
0.0b	(* (exp x) (exp x))
2.5b	(- (* (exp x) (* (exp x) (exp x))) (* 1.0 (* 1.0 1.0)))

rewrite465.0ms

Algorithm

rewrite-expression-head

Rules

36×	`exp-prod`
28×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
8×	`add-cbrt-cube` `pow-prod-down` `pow-sqr` `pow-prod-up` `add-log-exp`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`add-exp-log`
2×	`pow2` `pow-plus` `cube-unmult` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`difference-cubes` `+-commutative` `sum-log` `sub-neg` `flip3-+` `distribute-rgt-out` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 93

Calls

4 calls:

6.0ms	(+ (* 1.0 1.0) (* (exp x) 1.0))
364.0ms	(* (exp x) (exp x))
24.0ms	(* (exp x) (exp x))
68.0ms	(- (* (exp x) (* (exp x) (exp x))) (* 1.0 (* 1.0 1.0)))

series128.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (* 1.0 1.0) (* (exp x) 1.0))
24.0ms	(* (exp x) (exp x))
22.0ms	(* (exp x) (exp x))
59.0ms	(- (* (exp x) (* (exp x) (exp x))) (* 1.0 (* 1.0 1.0)))

simplify3.7s

Counts

105 → 105

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	116	22433
1	314	18103
2	1196	17743
3	4319	17581
done	5015	17581

prune563.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (exp (- (exp x) 1.0))) x)
2.5b	(log (exp (- (exp x) 1.0)))
2.6b	(- (exp x) 1.0)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`log-pow`
27×	`times-frac`
25×	`exp-prod`
23×	`add-cube-cbrt`
9×	`associate-/l*`
8×	`pow1`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`log-prod` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`log-div` `sub-neg` `exp-diff` `exp-sum`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `diff-log` `div-sub` `div-exp` `rem-log-exp` `div-inv` `flip--`

Counts

3 → 86

Calls

3 calls:

93.0ms	(/ (log (exp (- (exp x) 1.0))) x)
21.0ms	(log (exp (- (exp x) 1.0)))
8.0ms	(- (exp x) 1.0)

series116.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(/ (log (exp (- (exp x) 1.0))) x)
24.0ms	(log (exp (- (exp x) 1.0)))
29.0ms	(- (exp x) 1.0)

simplify2.8s

Counts

95 → 95

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	146	36628
1	284	24593
2	680	23813
3	2204	23611
done	5024	23531

prune385.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.4b

bsearch39.0ms

Steps

Iters	Range		Point
9	-0.000626365499124896	-1.0852755758321981e-09	-0.00018422866302287845

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	23	766
1	34	766
done	34	766

end0.0ms

sample1.7s

Algorithm

intervals

Results

686.0ms	2251×	body	1280	valid
377.0ms	1677×	body	640	valid
207.0ms	5518×	body	80	valid
139.0ms	821×	body	320	valid
67.0ms	411×	body	160	valid