Details

sample113.0ms

Algorithm

intervals

Results

46.0ms	98×	body	1280	valid
29.0ms	91×	body	640	valid
11.0ms	235×	body	80	valid
6.0ms	33×	body	320	valid
3.0ms	27×	body	160	valid

simplify31.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	24	8
3	30	8
4	34	8
done	34	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.1b

localize7.0ms

Local error

Found 1 expressions with local error:

7.4b	(- (exp x) (exp (- x)))

rewrite43.0ms

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:

41.0ms

(- (exp x) (exp (- x)))

series55.0ms

Counts

1 → 3

Calls

1 calls:

55.0ms

(- (exp x) (exp (- x)))

simplify2.9s

Counts

31 → 31

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	73	547
1	158	401
2	370	308
3	1377	253
done	5000	244

prune98.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

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 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))

simplify895.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	26	218
1	50	212
2	148	186
3	837	186
done	5001	186

prune49.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))) (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))))
0.7b	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
0.7b	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
0.7b	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

20.0ms	(* (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))) (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))))
1.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
2.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
2.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))

series868.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))) (cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))))
197.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
206.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))
250.0ms	(cbrt (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))))

simplify1.5s

Counts

93 → 93

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	140	2846
1	306	2672
2	783	2462
3	2252	1982
done	5000	1905

prune409.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (exp (* x -3))) (+ (+ (exp (+ x x)) 1) (exp (* x -2))))
0.0b	(+ (exp (+ x x)) 1)
0.0b	(pow (exp x) 3)
7.3b	(- (pow (exp x) 3) (exp (* x -3)))

rewrite444.0ms

Algorithm

rewrite-expression-head

Rules

109×	`*-un-lft-identity`
97×	`add-sqr-sqrt`
48×	`add-cube-cbrt`
40×	`times-frac`
36×	`prod-diff`
28×	`distribute-lft-out` `difference-of-squares`
22×	`unpow-prod-down` `cube-prod`
12×	`fma-neg` `sqr-pow`
8×	`associate-/l*` `add-log-exp`
7×	`add-cbrt-cube` `distribute-lft-out--`
6×	`add-exp-log`
5×	`pow1` `cube-mult` `unpow3` `associate-/r*`
4×	`expm1-log1p-u` `pow-pow` `fma-def` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `exp-sum` `pow-exp` `clear-num` `sum-log` `div-inv` `rem-cube-cbrt`

Counts

4 → 185

Calls

4 calls:

351.0ms	(/ (- (pow (exp x) 3) (exp (* x -3))) (+ (+ (exp (+ x x)) 1) (exp (* x -2))))
43.0ms	(+ (exp (+ x x)) 1)
4.0ms	(pow (exp x) 3)
37.0ms	(- (pow (exp x) 3) (exp (* x -3)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (- (pow (exp x) 3) (exp (* x -3))) (+ (+ (exp (+ x x)) 1) (exp (* x -2))))
16.0ms	(+ (exp (+ x x)) 1)
24.0ms	(pow (exp x) 3)
70.0ms	(- (pow (exp x) 3) (exp (* x -3)))

simplify1.8s

Counts

197 → 197

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	252	5011
1	598	4007
2	1914	3538
done	5001	3352

prune717.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	15
1	14	15
done	14	15

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	3381×	body	1280	valid
1.0s	8091×	body	80	valid
732.0ms	2417×	body	640	valid
245.0ms	1242×	body	320	valid
74.0ms	678×	body	160	valid