Details

sample151.0ms

Algorithm

intervals

Results

102.0ms	188×	body	1280	valid
14.0ms	288×	body	80	valid
13.0ms	41×	body	640	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify149.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	14	8
2	26	8
3	40	8
4	49	8
5	54	8
6	63	8
7	80	8
8	95	8
9	103	8
10	111	8
done	111	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
3.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`prod-diff`
16×	`add-cube-cbrt`
11×	`associate-+l+`
9×	`add-log-exp`
5×	`fma-def`
4×	`frac-add`
3×	`flip3--` `fma-neg` `flip--` `distribute-lft-out--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `expm1-log1p-u` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 65

Calls

2 calls:

24.0ms	(- (exp x) 2.0)
119.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(- (exp x) 2.0)
83.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	124	914
1	274	729
2	709	628
3	3051	557
done	5000	554

prune247.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-r`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

5.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
12.0ms	(* 1/12 (pow x 4))

series332.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
181.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
66.0ms	(* 1/12 (pow x 4))

simplify1.3s

Counts

56 → 56

Iterations

Useful iterations: 3 (327.0ms)

Iter	Nodes	Cost
0	80	619
1	146	581
2	344	529
3	1278	526
done	5000	526

prune225.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (* (+ (exp x) 2.0) (fma (exp x) (- (exp x) 2.0) 1)) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
1.8b	(fma (exp x) (- (exp x) 2.0) 1)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube`
15×	`add-exp-log`
11×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`pow1` `associate-*l/` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `div-exp` `associate-l` `flip-+` `log1p-expm1-u`
3×	`fma-def` `associate-r`
2×	`associate-/r/` `associate-/l/` `distribute-lft-out`
1×	`+-commutative` `frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `fma-udef` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

11.0ms	(+ (exp x) 2.0)
39.0ms	(/ (* (+ (exp x) 2.0) (fma (exp x) (- (exp x) 2.0) 1)) (* (+ (exp x) 2.0) (exp x)))
62.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (exp x) (- (exp x) 2.0) 1)

series234.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (exp x) 2.0)
119.0ms	(/ (* (+ (exp x) 2.0) (fma (exp x) (- (exp x) 2.0) 1)) (* (+ (exp x) 2.0) (exp x)))
34.0ms	(* (+ (exp x) 2.0) (exp x))
72.0ms	(fma (exp x) (- (exp x) 2.0) 1)

simplify1.4s

Counts

89 → 89

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	135	1383
1	368	1209
2	1649	869
done	5002	855

prune299.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (exp x))
0.0b	(cbrt (exp x))
0.0b	(cbrt (exp x))
1.8b	(fma (exp x) (- (exp x) 2.0) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

14.0ms	(cbrt (exp x))
4.0ms	(cbrt (exp x))
4.0ms	(cbrt (exp x))
1.0ms	(fma (exp x) (- (exp x) 2.0) 1)

series461.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (exp x))
130.0ms	(cbrt (exp x))
110.0ms	(cbrt (exp x))
85.0ms	(fma (exp x) (- (exp x) 2.0) 1)

simplify2.6s

Counts

61 → 61

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	54	430
1	103	419
2	210	379
3	567	361
4	2446	343
done	5000	341

prune376.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	11	13
done	11	13

end0.0ms

sample5.0s

Algorithm

intervals

Results

3.7s	5655×	body	1280	valid
381.0ms	8061×	body	80	valid
375.0ms	1224×	body	640	valid
153.0ms	640×	body	320	valid
88.0ms	311×	body	160	valid