Details

sample89.0ms

Algorithm

intervals

Results

40.0ms	83×	body	1280	valid
17.0ms	50×	body	640	valid
12.0ms	171×	body	80	valid
6.0ms	27×	body	320	valid
2.0ms	9×	body	160	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	18
3	18
2	15
1	13
0	5

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1) x)
2.8b	(- (exp x) 1)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/l*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `insert-posit16` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 64

Calls

2 calls:

21.0ms	(/ (- (exp x) 1) x)
8.0ms	(- (exp x) 1)

series75.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- (exp x) 1) x)
21.0ms	(- (exp x) 1)

simplify1.8s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
3	2199
2	642
1	239
0	108

prune262.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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` `insert-posit16` `add-log-exp` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

2 → 42

Calls

2 calls:

25.0ms	(* x (+ 1/2 (* 1/6 x)))
11.0ms	(* 1/6 x)

series100.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* x (+ 1/2 (* 1/6 x)))
17.0ms	(* 1/6 x)

simplify3.3s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	4217
2	733
1	205
0	72

prune160.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
0.0b	(* (exp x) (exp x))
0.0b	(* x (+ (exp x) 1))
2.8b	(- (* (exp x) (exp x)) (* 1 1))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`exp-prod` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`pow-prod-down`
4×	`times-frac` `associate-r/` `pow-sqr` `pow-prod-up` `insert-posit16` `associate-/l`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `associate-/r/` `*-commutative` `flip-+` `flip--` `unswap-sqr` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `div-inv` `distribute-lft-out`

Counts

4 → 102

Calls

4 calls:

70.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
29.0ms	(* (exp x) (exp x))
43.0ms	(* x (+ (exp x) 1))
27.0ms	(- (* (exp x) (exp x)) (* 1 1))

series235.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (* (exp x) (exp x)) (* 1 1)) (* x (+ (exp x) 1)))
24.0ms	(* (exp x) (exp x))
49.0ms	(* x (+ (exp x) 1))
39.0ms	(- (* (exp x) (exp x)) (* 1 1))

simplify1.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2373
1	468
0	157

prune385.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.0b	(* (* (exp x) (exp x)) (* (exp x) (exp x)))
0.0b	(cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x))))
2.8b	(- (cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x)))) (* 1 1))

rewrite506.0ms

Algorithm

rewrite-expression-head

Rules

150×	`exp-prod`
122×	`pow1`
79×	`pow-prod-up`
61×	`add-sqr-sqrt`
59×	`*-un-lft-identity` `pow-sqr`
58×	`add-cube-cbrt`
54×	`pow-prod-down`
19×	`pow-plus`
18×	`add-cbrt-cube`
14×	`pow2`
9×	`prod-exp` `cbrt-unprod`
8×	`add-exp-log`
6×	`add-log-exp`
4×	`swap-sqr` `associate-r` `associate-l` `insert-posit16`
2×	`*-commutative` `unswap-sqr`
1×	`cbrt-prod` `sub-neg` `flip3--` `pow1/3` `diff-log` `pow3` `rem-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 158

Calls

4 calls:

21.0ms	(* (exp x) (exp x))
73.0ms	(* (* (exp x) (exp x)) (* (exp x) (exp x)))
297.0ms	(cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x))))
109.0ms	(- (cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x)))) (* 1 1))

series104.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (exp x) (exp x))
33.0ms	(* (* (exp x) (exp x)) (* (exp x) (exp x)))
25.0ms	(cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x))))
31.0ms	(- (cbrt (* (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (exp x) (exp x)))) (* 1 1))

simplify3.3s

Counts

170 → 170

Iterations

Iter	Nodes
done	5001
3	3967
2	1446
1	416
0	144

prune471.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch53.0ms

Steps

Iters	Range		Point
9	-34.11472770615283	-3.67231414207575e-08	-0.00021841426619390923

simplify7.0ms

Iterations

Iter	Nodes
done	36
2	36
1	35
0	25

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2233×	body	1280	valid
427.0ms	1648×	body	640	valid
321.0ms	5494×	body	80	valid
138.0ms	818×	body	320	valid
101.0ms	430×	body	160	valid