Details

sample59.0ms

Algorithm

intervals

Results

27.0ms	78×	body	1280	valid
8.0ms	47×	body	640	valid
5.0ms	146×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	19×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	118	6
6	453	6
7	3607	6
done	5002	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 1 expressions with local error:

4.7b	(- (exp (* a x)) 1.0)

rewrite16.0ms

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:

15.0ms

(- (exp (* a x)) 1.0)

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

(- (exp (* a x)) 1.0)

simplify2.5s

Counts

31 → 31

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	72	472
1	172	387
2	561	313
3	3046	255
done	5002	245

prune108.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/6 (pow a 3))
0.2b	(* 1/2 (pow a 2))
7.9b	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
15.8b	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `expm1-log1p-u` `cube-prod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unpow2`
1×	`cube-mult` `unpow3`

Counts

4 → 82

Calls

4 calls:

26.0ms	(* 1/6 (pow a 3))
12.0ms	(* 1/2 (pow a 2))
0.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
0.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/6 (pow a 3))
46.0ms	(* 1/2 (pow a 2))
120.0ms	(fma (pow x 2) (fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2))) (* a x))
129.0ms	(fma x (* 1/6 (pow a 3)) (* 1/2 (pow a 2)))

simplify856.0ms

Counts

94 → 94

Iterations

Useful iterations: done (852.0ms)

Iter	Nodes	Cost
0	137	1036
1	316	960
2	1249	855
done	5001	809

prune421.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(* x 1/6)
0.7b	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
0.7b	(* (* a a) (+ (* (* x 1/6) a) 1/2))
7.0b	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
12×	`associate-r`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
6×	`associate-*r/`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/`

Counts

4 → 94

Calls

4 calls:

7.0ms	(* x 1/6)
30.0ms	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
149.0ms	(* (* a a) (+ (* (* x 1/6) a) 1/2))
196.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

series365.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x 1/6)
154.0ms	(* x (+ a (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)))
77.0ms	(* (* a a) (+ (* (* x 1/6) a) 1/2))
118.0ms	(* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x)

simplify3.2s

Counts

106 → 106

Iterations

Useful iterations: 2 (910.0ms)

Iter	Nodes	Cost
0	160	1663
1	512	1474
2	3962	1271
done	5000	1271

prune590.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* a x))
0.0b	(+ (exp (* a x)) 1.0)
0.0b	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
4.6b	(- (exp (* 2 (* a x))) (* 1.0 1.0))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-def` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

16.0ms	(* 2 (* a x))
14.0ms	(+ (exp (* a x)) 1.0)
77.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
47.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

series272.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* 2 (* a x))
32.0ms	(+ (exp (* a x)) 1.0)
88.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
108.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	1938
1	444	1878
2	1807	1713
done	5001	1649

prune542.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 3.5b

regimes208.0ms

Accuracy

96.8% (0.7b remaining)

Error of 3.1b against oracle of 2.4b and baseline of 24.1b

bsearch1.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	32	52
1	43	52
done	43	52

end0.0ms

sample2.4s

Algorithm

intervals

Results

868.0ms	2735×	body	1280	valid
751.0ms	5364×	body	80	valid
288.0ms	1310×	body	640	valid
92.0ms	753×	body	320	valid
35.0ms	437×	body	160	valid