Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	71×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	161×	body	80	valid
2.0ms	33×	body	320	valid
0.0ms	11×	body	160	valid

simplify7.0ms

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.4b	(- (exp x) 1.0)

rewrite41.0ms

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:

28.0ms	(/ (- (exp x) 1.0) x)
11.0ms	(- (exp x) 1.0)

series52.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify1.3s

Counts

74 → 74

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	127	854
1	281	745
2	612	665
3	1785	619
done	5001	605

prune133.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma 1/6 x 1/2) 1)
0.1b	(fma 1/6 x 1/2)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

0.0ms	(fma x (fma 1/6 x 1/2) 1)
0.0ms	(fma 1/6 x 1/2)

series54.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(fma x (fma 1/6 x 1/2) 1)
32.0ms	(fma 1/6 x 1/2)

simplify1.7s

Counts

26 → 26

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	33	213
1	53	204
2	114	176
3	381	175
4	1753	175
done	5001	175

prune53.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
0.0b	(* x (+ (exp x) 1.0))
3.3b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

46.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
11.0ms	(+ (exp x) 1.0)
27.0ms	(* x (+ (exp x) 1.0))
16.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series147.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
31.0ms	(* x (+ (exp x) 1.0))
28.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify662.0ms

Counts

101 → 101

Iterations

Useful iterations: done (660.0ms)

Iter	Nodes	Cost
0	147	1329
1	401	1227
2	1444	1069
done	5000	941

prune207.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
3.3b	(- (pow (exp x) 2) (* 1.0 1.0))
3.3b	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`prod-diff`
15×	`add-cube-cbrt`
13×	`log-prod`
11×	`unpow-prod-down`
10×	`exp-sum`
8×	`fma-neg` `log-pow` `add-log-exp` `difference-of-squares`
7×	`pow1` `exp-prod`
6×	`add-exp-log` `add-cbrt-cube`
5×	`unpow2` `sqr-pow`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `associate-l`
2×	`sub-neg` `flip3-+` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `log-div` `flip3--` `distribute-lft-in` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

27.0ms	(* x (+ (exp x) 1.0))
10.0ms	(+ (exp x) 1.0)
24.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
45.0ms	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* x (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
27.0ms	(- (pow (exp x) 2) (* 1.0 1.0))
24.0ms	(log (exp (- (pow (exp x) 2) (* 1.0 1.0))))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	182	1382
1	378	1225
2	965	1068
3	3237	955
done	5001	940

prune280.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes23.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 20.9b

bsearch16.0ms

Steps

Iters	Range		Point
5	-0.0002772006047103471	-9.588134368690297e-05	-0.00016816552986419862

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	36
1	25	36
done	25	36

end0.0ms

sample909.0ms

Algorithm

intervals

Results

390.0ms	2352×	body	1280	valid
172.0ms	1649×	body	640	valid
95.0ms	5259×	body	80	valid
53.0ms	818×	body	320	valid
18.0ms	412×	body	160	valid