Details

sample45.0ms

Algorithm

intervals

Results

21.0ms	83×	body	1280	valid
6.0ms	42×	body	640	valid
5.0ms	160×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	21×	body	160	valid

simplify8.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
5.8b	(- (exp x) 1.0)

rewrite60.0ms

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:

32.0ms	(/ (- (exp x) 1.0) x)
25.0ms	(- (exp x) 1.0)

series83.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- (exp x) 1.0) x)
26.0ms	(- (exp x) 1.0)

simplify759.0ms

Counts

74 → 74

Iterations

Useful iterations: done (755.0ms)

Iter	Nodes	Cost
0	127	854
1	297	748
2	1007	667
done	5000	648

prune259.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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:

1.0ms

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

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify921.0ms

Counts

13 → 13

Iterations

Useful iterations: 3 (159.0ms)

Iter	Nodes	Cost
0	23	158
1	43	152
2	137	134
3	785	107
done	5000	107

prune59.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (fma x 1/6 1/2) 1)
0.1b	(fma x 1/6 1/2)
0.3b	(log1p (expm1 (fma x (fma x 1/6 1/2) 1)))
0.7b	(expm1 (fma x (fma x 1/6 1/2) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

1.0ms	(fma x (fma x 1/6 1/2) 1)
1.0ms	(fma x 1/6 1/2)
0.0ms	(log1p (expm1 (fma x (fma x 1/6 1/2) 1)))
1.0ms	(expm1 (fma x (fma x 1/6 1/2) 1))

series271.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma x (fma x 1/6 1/2) 1)
48.0ms	(fma x 1/6 1/2)
136.0ms	(log1p (expm1 (fma x (fma x 1/6 1/2) 1)))
46.0ms	(expm1 (fma x (fma x 1/6 1/2) 1))

simplify1.1s

Counts

54 → 54

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	63	521
1	113	479
2	316	426
3	1411	419
done	5001	410

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(+ (sqrt (exp x)) (sqrt 1.0))
0.0b	(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
5.6b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
73×	`sqrt-prod`
72×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`prod-diff`
31×	`associate-r`
28×	`times-frac`
16×	`difference-of-squares`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `add-log-exp`
7×	`pow1`
6×	`fma-def` `fma-neg`
5×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `distribute-lft-out`
3×	`exp-prod` `flip3-+` `flip-+`
2×	`frac-times` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `flip3--` `pow1/2` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip--` `div-inv`

Counts

4 → 159

Calls

4 calls:

3.0ms	(sqrt (exp x))
24.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
133.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
20.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series339.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (exp x))
58.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
208.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (/ (- (sqrt (exp x)) (sqrt 1.0)) x))
58.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify2.2s

Counts

171 → 171

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	209	2915
1	512	2368
2	2711	2062
done	5000	1843

prune482.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

98.9% (0.2b remaining)

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

bsearch51.0ms

Steps

Iters	Range		Point
10	-911936.9907706906	-4.3470241882695893e-07	-0.0001506654427850415

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	28
1	23	28
done	23	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

796.0ms	2301×	body	1280	valid
425.0ms	1666×	body	640	valid
203.0ms	5337×	body	80	valid
154.0ms	810×	body	320	valid
85.0ms	438×	body	160	valid