Details

sample55.0ms

Algorithm

intervals

Results

22.0ms	117×	body	1280	valid
8.0ms	69×	body	640	valid
5.0ms	390×	pre	80	true
3.0ms	46×	body	320	valid
2.0ms	139×	body	80	valid
1.0ms	19×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.3b

localize7.0ms

Local error

Found 1 expressions with local error:

5.2b	(- (exp x) 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

24.0ms

(- (exp x) 1.0)

series27.0ms

Counts

1 → 3

Calls

1 calls:

27.0ms

(- (exp x) 1.0)

simplify3.6s

Counts

31 → 31

Iterations

Useful iterations: 4 (1.2s)

Iter	Nodes	Cost
0	66	376
1	142	288
2	272	231
3	799	204
4	2411	175
done	5001	175

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

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:

1.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
1.0ms	(fma x 1/6 1/2)

series117.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
71.0ms	(fma x 1/6 1/2)

simplify2.0s

Counts

26 → 26

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	37	245
1	65	236
2	150	204
3	491	204
4	2422	204
done	5002	204

prune77.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (pow x 2) (fma x 1/6 1/2) x)
0.0b	(fma x 1/6 1/2)
0.0b	(pow (fma (pow x 2) (fma x 1/6 1/2) x) 3)
39.8b	(cbrt (pow (fma (pow x 2) (fma x 1/6 1/2) x) 3))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

1.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
1.0ms	(fma x 1/6 1/2)
5.0ms	(pow (fma (pow x 2) (fma x 1/6 1/2) x) 3)
5.0ms	(cbrt (pow (fma (pow x 2) (fma x 1/6 1/2) x) 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma (pow x 2) (fma x 1/6 1/2) x)
48.0ms	(fma x 1/6 1/2)
59.0ms	(pow (fma (pow x 2) (fma x 1/6 1/2) x) 3)
48.0ms	(cbrt (pow (fma (pow x 2) (fma x 1/6 1/2) x) 3))

simplify3.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (767.0ms)

Iter	Nodes	Cost
0	103	1233
1	204	1037
2	523	911
3	3190	910
done	5000	910

prune301.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
5.2b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
17×	`add-cube-cbrt`
12×	`difference-of-squares`
8×	`exp-sum`
7×	`distribute-lft-out` `add-log-exp`
5×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`fma-neg` `prod-diff` `associate-/r*`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 89

Calls

3 calls:

13.0ms	(+ 1.0 (exp x))
171.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
72.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series127.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(+ 1.0 (exp x))
78.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ 1.0 (exp x)))
39.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.9s

Counts

98 → 98

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	147	1493
1	354	1441
2	995	1308
3	3234	1293
done	5000	1287

prune259.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes24.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
done	7	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	3419×	body	1280	valid
366.0ms	2485×	body	640	valid
184.0ms	1266×	body	320	valid
171.0ms	11897×	pre	80	true
90.0ms	4074×	body	80	valid
38.0ms	653×	body	160	valid