Details

sample134.0ms

Algorithm

intervals

Results

87.0ms	177×	body	1280	valid
11.0ms	41×	body	640	valid
11.0ms	261×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.9s

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	56	8
5	62	8
6	71	8
7	88	8
8	248	8
9	788	8
10	3132	8
done	5000	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.2b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite110.0ms

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:

13.0ms	(- (exp x) 2.0)
94.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(- (exp x) 2.0)
77.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify943.0ms

Counts

71 → 71

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	124	914
1	298	735
2	1173	637
done	5002	609

prune247.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

1.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
19.0ms	(* 1/12 (pow x 4))

series142.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
50.0ms	(* 1/12 (pow x 4))

simplify4.1s

Counts

43 → 43

Iterations

Useful iterations: 3 (877.0ms)

Iter	Nodes	Cost
0	71	449
1	142	414
2	466	382
3	3334	379
done	5000	379

prune147.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* 1/12 (pow x 4)))
0.1b	(fma 1/360 (pow x 6) (log (exp (* 1/12 (pow x 4)))))
0.1b	(* 1/12 (pow x 4))
1.7b	(log (exp (* 1/12 (pow x 4))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

11.0ms	(exp (* 1/12 (pow x 4)))
1.0ms	(fma 1/360 (pow x 6) (log (exp (* 1/12 (pow x 4)))))
30.0ms	(* 1/12 (pow x 4))
4.0ms	(log (exp (* 1/12 (pow x 4))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(exp (* 1/12 (pow x 4)))
189.0ms	(fma 1/360 (pow x 6) (log (exp (* 1/12 (pow x 4)))))
74.0ms	(* 1/12 (pow x 4))
65.0ms	(log (exp (* 1/12 (pow x 4))))

simplify3.4s

Counts

77 → 77

Iterations

Useful iterations: 3 (608.0ms)

Iter	Nodes	Cost
0	97	711
1	180	611
2	489	564
3	2408	559
done	5001	559

prune274.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp x) 2.0)
0.0b	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
0.0b	(* (exp x) (+ (exp x) 2.0))
3.4b	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

10.0ms	(+ (exp x) 2.0)
20.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
56.0ms	(* (exp x) (+ (exp x) 2.0))
0.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp x) 2.0)
317.0ms	(/ (fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0)) (* (exp x) (+ (exp x) 2.0)))
37.0ms	(* (exp x) (+ (exp x) 2.0))
108.0ms	(fma (- (exp (+ x x)) (* 2.0 2.0)) (exp x) (+ (exp x) 2.0))

simplify2.0s

Counts

89 → 89

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	133	1501
1	349	1459
2	1800	1260
done	5000	1257

prune383.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

98.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.6b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	32
1	21	32
done	21	32

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.0s	5601×	body	1280	valid
913.0ms	8147×	body	80	valid
399.0ms	1244×	body	640	valid
106.0ms	660×	body	320	valid
33.0ms	327×	body	160	valid