Details

sample29.0ms

Algorithm

intervals

Results

11.0ms	67×	body	1280	valid
5.0ms	48×	body	640	valid
4.0ms	191×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 36.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

13.0ms	(/ (- (exp x) 1.0) x)
6.0ms	(- (exp x) 1.0)

series56.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: 3 (513.0ms)

Iter	Nodes	Cost
0	127	854
1	277	745
2	613	665
3	1989	637
done	5000	637

prune144.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (* x x) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

simplify1.9s

Counts

13 → 13

Iterations

Useful iterations: 3 (39.0ms)

Iter	Nodes	Cost
0	23	158
1	38	152
2	100	134
3	414	107
4	2798	107
done	5000	107

prune34.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (exp x) 1.0))
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
0.0b	(* (exp x) (exp x))
4.1b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `exp-prod`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `times-frac` `associate-r/` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `associate-/l`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 108

Calls

4 calls:

14.0ms	(* x (+ (exp x) 1.0))
24.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
8.0ms	(* (exp x) (exp x))
8.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series155.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* x (+ (exp x) 1.0))
80.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
13.0ms	(* (exp x) (exp x))
28.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify789.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (272.0ms)

Iter	Nodes	Cost
0	171	1476
1	441	1302
2	1683	1139
done	5001	1139

prune242.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(/ (- (sqrt (exp x)) (sqrt 1.0)) x)
0.0b	(* (+ (sqrt 1.0) (sqrt (exp x))) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
4.2b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
92×	`sqrt-prod`
60×	`add-cube-cbrt`
55×	`times-frac`
36×	`prod-diff`
32×	`difference-of-squares`
31×	`associate-r`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u`
3×	`exp-prod` `associate-/r*`
2×	`cbrt-undiv` `frac-times` `flip3--` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `pow1/2` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 194

Calls

4 calls:

1.0ms	(sqrt (exp x))
26.0ms	(/ (- (sqrt (exp x)) (sqrt 1.0)) x)
59.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
11.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series270.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
74.0ms	(/ (- (sqrt (exp x)) (sqrt 1.0)) x)
147.0ms	(* (+ (sqrt 1.0) (sqrt (exp x))) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
37.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify881.0ms

Counts

206 → 206

Iterations

Useful iterations: 2 (328.0ms)

Iter	Nodes	Cost
0	236	3619
1	543	2854
2	1694	2488
done	5000	2488

prune369.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes25.0ms

Accuracy

98.8% (0.3b remaining)

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

bsearch27.0ms

Steps

Iters	Range		Point
8	-0.04390830018224924	-1.7961213486546931e-06	-0.00017518926899118845

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	26	45
done	26	45

end0.0ms

sample885.0ms

Algorithm

intervals

Results

386.0ms	2235×	body	1280	valid
175.0ms	1635×	body	640	valid
110.0ms	5418×	body	80	valid
58.0ms	846×	body	320	valid
19.0ms	430×	body	160	valid