Details

sample38.0ms

Algorithm

intervals

Results

14.0ms	70×	body	1280	valid
7.0ms	59×	body	640	valid
4.0ms	161×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.9b	(- (exp x) 1.0)

rewrite50.0ms

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

Counts

2 → 52

Calls

2 calls:

35.0ms	(/ (- (exp x) 1.0) x)
12.0ms	(- (exp x) 1.0)

series75.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- (exp x) 1.0) x)
24.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 4 (1.3s)

Iter	Nodes	Cost
0	99	596
1	221	572
2	503	542
3	1095	537
4	2836	536
done	5001	536

prune199.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

23.0ms	(* x (+ 1/2 (* 1/6 x)))
12.0ms	(* 1/6 x)

series152.0ms

Counts

2 → 6

Calls

2 calls:

122.0ms	(* x (+ 1/2 (* 1/6 x)))
30.0ms	(* 1/6 x)

simplify2.5s

Counts

46 → 46

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	70	356
1	184	328
2	522	298
3	1711	298
done	5000	298

prune126.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
5.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
136×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
82×	`add-cube-cbrt`
44×	`difference-of-squares`
31×	`associate-/l*`
27×	`distribute-lft-out`
22×	`exp-sum`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`add-log-exp`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`+-commutative` `sub-neg` `diff-log` `sum-log`

Counts

4 → 195

Calls

4 calls:

229.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
152.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
17.0ms	(+ (exp x) 1.0)
97.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series180.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
50.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
15.0ms	(+ (exp x) 1.0)
38.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.1s

Counts

207 → 207

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	301	4684
1	731	4503
2	2332	4245
done	5000	3821

prune730.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (exp x) 1.0))
5.1b	(- (exp (+ x x)) (* 1.0 1.0))
5.1b	(- (exp (+ x x)) (* 1.0 1.0))
5.1b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
6×	`difference-of-squares`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `exp-sum` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 56

Calls

4 calls:

7.0ms	(cbrt (+ (exp x) 1.0))
94.0ms	(- (exp (+ x x)) (* 1.0 1.0))
72.0ms	(- (exp (+ x x)) (* 1.0 1.0))
71.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series250.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (+ (exp x) 1.0))
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.6s

Counts

68 → 68

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	90	850
1	201	811
2	551	699
3	1698	680
done	5001	673

prune297.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.4b

bsearch53.0ms

Steps

Iters	Range		Point
9	-0.002338049553438653	-8.574655782360099e-11	-0.0001245218611780339

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	77
1	37	77
done	37	77

end0.0ms

sample1.7s

Algorithm

intervals

Results

694.0ms	2297×	body	1280	valid
330.0ms	1617×	body	640	valid
272.0ms	5435×	body	80	valid
95.0ms	808×	body	320	valid
33.0ms	436×	body	160	valid