Details

sample82.0ms

Algorithm

intervals

Results

28.0ms	72×	body	1280	valid
20.0ms	182×	body	80	valid
13.0ms	52×	body	640	valid
4.0ms	29×	body	320	valid
1.0ms	14×	body	160	valid

simplify8.0ms

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: 40.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
5.0b	(- (exp x) 1.0)

rewrite48.0ms

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)
11.0ms	(- (exp x) 1.0)

series86.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify2.4s

Counts

58 → 58

Iterations

Useful iterations: 3 (941.0ms)

Iter	Nodes	Cost
0	99	596
1	227	572
2	802	544
3	4675	537
done	5002	537

prune194.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (+ 1/2 (* 1/6 x))) 1)
0.0b	(+ 1/2 (* 1/6 x))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

22.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
11.0ms	(+ 1/2 (* 1/6 x))
18.0ms	(* x (+ 1/2 (* 1/6 x)))
11.0ms	(* 1/6 x)

series196.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(+ (* x (+ 1/2 (* 1/6 x))) 1)
44.0ms	(+ 1/2 (* 1/6 x))
93.0ms	(* x (+ 1/2 (* 1/6 x)))
18.0ms	(* 1/6 x)

simplify1.4s

Counts

76 → 76

Iterations

Useful iterations: 2 (354.0ms)

Iter	Nodes	Cost
0	101	708
1	310	650
2	1528	604
done	5001	604

prune183.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* x (+ 1/2 (* 1/6 x))))
0.1b	(* x (+ 1/2 (* 1/6 x)))
0.4b	(* 1/6 x)
1.0b	(log (* E (exp (* x (+ 1/2 (* 1/6 x))))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`pow1`
10×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`prod-exp`
3×	`rem-log-exp` `pow-prod-down`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `exp-sum` `log-pow` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`e-exp-1` `log-prod` `exp-prod` `exp-to-pow` `flip3-+` `flip-+` `rem-exp-log`

Counts

4 → 65

Calls

4 calls:

11.0ms	(exp (* x (+ 1/2 (* 1/6 x))))
33.0ms	(* x (+ 1/2 (* 1/6 x)))
12.0ms	(* 1/6 x)
18.0ms	(log (* E (exp (* x (+ 1/2 (* 1/6 x))))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* x (+ 1/2 (* 1/6 x))))
103.0ms	(* x (+ 1/2 (* 1/6 x)))
15.0ms	(* 1/6 x)
167.0ms	(log (* E (exp (* x (+ 1/2 (* 1/6 x))))))

simplify978.0ms

Counts

77 → 77

Iterations

Useful iterations: done (974.0ms)

Iter	Nodes	Cost
0	103	681
1	274	625
2	1345	563
done	5001	562

prune250.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 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))
5.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 183

Calls

3 calls:

194.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
206.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
73.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series187.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(/ (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)) x)
58.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
34.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

192 → 192

Iterations

Useful iterations: 2 (619.0ms)

Iter	Nodes	Cost
0	292	4572
1	768	4396
2	3896	4150
done	5000	4150

prune601.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch47.0ms

Steps

Iters	Range		Point
8	-0.03117879455470207	-2.7237372521413145e-05	-0.00013650728455141193

simplify10.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	38
1	29	38
done	29	38

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	2286×	body	1280	valid
298.0ms	1685×	body	640	valid
273.0ms	5420×	body	80	valid
98.0ms	807×	body	320	valid
32.0ms	424×	body	160	valid