Details

sample77.0ms

Algorithm

intervals

Results

32.0ms	70×	body	1280	valid
13.0ms	54×	body	640	valid
9.0ms	202×	body	80	valid
4.0ms	28×	body	320	valid
1.0ms	11×	body	160	valid

simplify17.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize11.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (exp x) 1.0)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

23.0ms

(- (exp x) 1.0)

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(- (exp x) 1.0)

simplify2.1s

Counts

17 → 17

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	39	132
1	83	127
2	177	119
3	328	117
4	668	117
5	1877	117
done	5000	117

prune48.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 x) 1/2)
0.1b	(* (pow x 2) (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
3.8b	(/ (+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x) x)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log`
11×	`associate-l`
10×	`add-cbrt-cube`
9×	`times-frac`
6×	`pow1` `associate-r` `add-log-exp`
5×	`unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `cbrt-unprod` `associate-/l/` `unpow2` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `pow-to-exp` `frac-2neg` `distribute-lft-in` `div-exp` `pow-prod-down` `pow-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 89

Calls

4 calls:

8.0ms	(+ (* 1/6 x) 1/2)
34.0ms	(* (pow x 2) (+ (* 1/6 x) 1/2))
11.0ms	(* 1/6 x)
73.0ms	(/ (+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x) x)

series232.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (* 1/6 x) 1/2)
89.0ms	(* (pow x 2) (+ (* 1/6 x) 1/2))
15.0ms	(* 1/6 x)
84.0ms	(/ (+ (* (pow x 2) (+ (* 1/6 x) 1/2)) x) x)

simplify1.6s

Counts

101 → 101

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	147	1336
1	383	1255
2	1257	1136
done	5000	1127

prune367.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 72

Calls

3 calls:

10.0ms	(+ (exp x) 1.0)
229.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
59.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series83.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ (exp x) 1.0)
49.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.7s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	131	1338
1	319	1293
2	951	1179
3	3152	1035
done	5000	1035

prune235.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
0.0b	(/ 1 (+ (exp x) 1.0))
3.0b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`distribute-lft-out` `add-log-exp`
7×	`pow1`
5×	`associate-l`
4×	`div-exp` `prod-exp` `associate-/r*` `associate-/r/` `difference-of-squares`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `exp-sum` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 110

Calls

4 calls:

259.0ms	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
12.0ms	(+ (exp x) 1.0)
33.0ms	(/ 1 (+ (exp x) 1.0))
63.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series119.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- (exp (+ x x)) (* 1.0 1.0)) (/ 1 (+ (exp x) 1.0)))
9.0ms	(+ (exp x) 1.0)
39.0ms	(/ 1 (+ (exp x) 1.0))
28.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify3.4s

Counts

122 → 122

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	165	1723
1	395	1516
2	1209	1316
3	4514	1162
done	5000	1162

prune282.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.5b

bsearch55.0ms

Steps

Iters	Range		Point
9	-108.06719872485291	-1.20447477858732e-06	-0.00011882285500139608

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	50
1	44	50
done	44	50

end0.0ms

sample1.6s

Algorithm

intervals

Results

669.0ms	2262×	body	1280	valid
295.0ms	1670×	body	640	valid
237.0ms	5539×	body	80	valid
116.0ms	781×	body	320	valid
32.0ms	447×	body	160	valid