Details

sample78.0ms

Algorithm

intervals

Results

28.0ms	106×	body	1280	valid
13.0ms	75×	body	640	valid
12.0ms	401×	pre	80	true
5.0ms	51×	body	320	valid
4.0ms	151×	body	80	valid
1.0ms	18×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	112
1	6	112
2	7	112
done	7	112

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.4b

localize8.0ms

Local error

Found 1 expressions with local error:

5.4b	(- (exp x) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 14

Calls

1 calls:

8.0ms

(- (exp x) 1.0)

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

(- (exp x) 1.0)

simplify1.9s

Counts

17 → 17

Iterations

Useful iterations: 3 (158.0ms)

Iter	Nodes	Cost
0	39	4032
1	83	3319
2	221	3319
3	681	3240
4	2834	3240
done	5002	3240

prune106.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

35.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
5.0ms	(* 1/6 x)

series112.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(* (* x x) (+ 1/2 (* 1/6 x)))
16.0ms	(* 1/6 x)

simplify1.6s

Counts

47 → 47

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	78	9228
1	246	7409
2	1651	7129
done	5000	7049

prune222.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (* (* (- (exp x) 1.0) (- (exp x) 1.0)) (- (exp x) 1.0)))
5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)
5.4b	(- (exp x) 1.0)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`associate-*r/`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 78

Calls

4 calls:

87.0ms	(cbrt (* (* (- (exp x) 1.0) (- (exp x) 1.0)) (- (exp x) 1.0)))
16.0ms	(- (exp x) 1.0)
15.0ms	(- (exp x) 1.0)
9.0ms	(- (exp x) 1.0)

series99.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (* (* (- (exp x) 1.0) (- (exp x) 1.0)) (- (exp x) 1.0)))
25.0ms	(- (exp x) 1.0)
28.0ms	(- (exp x) 1.0)
25.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	134	43156
1	292	33516
2	1092	33396
done	5001	31476

prune274.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(* (exp x) (exp x))
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
5.3b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`exp-prod`
16×	`times-frac`
11×	`pow1`
8×	`add-cbrt-cube` `add-log-exp`
6×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
4×	`associate-/r` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`pow2` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `div-sub` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

7.0ms	(+ (exp x) 1.0)
24.0ms	(* (exp x) (exp x))
72.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
23.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series147.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (exp x) 1.0)
24.0ms	(* (exp x) (exp x))
75.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (+ (exp x) 1.0))
33.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify2.3s

Counts

112 → 112

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	154	33454
1	427	28857
2	2842	27957
done	5001	27877

prune445.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes138.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	203
1	12	203
done	12	203

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.5s	3428×	body	1280	valid
397.0ms	2545×	body	640	valid
174.0ms	11984×	pre	80	true
137.0ms	4188×	body	80	valid
118.0ms	1238×	body	320	valid
35.0ms	585×	body	160	valid