Details

sample109.0ms

Algorithm

intervals

Results

51.0ms	114×	body	1280	valid
19.0ms	73×	body	640	valid
12.0ms	279×	body	80	valid
7.0ms	40×	body	320	valid
2.0ms	19×	body	160	valid

simplify36.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	36
6	36
5	35
4	33
3	30
2	24
1	14
0	7

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.4b

localize15.0ms

Local error

Found 1 expressions with local error:

5.7b	(- (exp x) (exp (- x)))

rewrite42.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

41.0ms

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

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

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

simplify3.3s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
4	4704
3	1166
2	418
1	170
0	73

prune107.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

0.0ms	(fma 1/3 (* x x) 2)
0.0ms	(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
6.0ms	(* x (fma 1/3 (* x x) 2))

series286.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(fma 1/3 (* x x) 2)
94.0ms	(fma (pow x 5) 1/60 (* x (fma 1/3 (* x x) 2)))
132.0ms	(* x (fma 1/3 (* x x) 2))

simplify2.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5025
3	1864
2	390
1	143
0	66

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (* 1/3 (* x x))) (* x 2))
0.0b	(fma (pow x 5) 1/60 (+ (* x (* 1/3 (* x x))) (* x 2)))
0.1b	(* x (* 1/3 (* x x)))
0.2b	(* 1/3 (* x x))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-r` `*-commutative`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

45.0ms	(+ (* x (* 1/3 (* x x))) (* x 2))
0.0ms	(fma (pow x 5) 1/60 (+ (* x (* 1/3 (* x x))) (* x 2)))
32.0ms	(* x (* 1/3 (* x x)))
30.0ms	(* 1/3 (* x x))

series333.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (* x (* 1/3 (* x x))) (* x 2))
102.0ms	(fma (pow x 5) 1/60 (+ (* x (* 1/3 (* x x))) (* x 2)))
53.0ms	(* x (* 1/3 (* x x)))
28.0ms	(* 1/3 (* x x))

simplify1.5s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1118
1	282
0	102

prune424.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp x))
0.0b	(exp (* 3 x))
0.0b	(exp (* 3 x))
6.1b	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
10×	`add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `exp-prod` `add-exp-log` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-flip`
3×	`associate-/r` `fma-neg` `associate-/l` `difference-of-squares`
2×	`exp-to-pow` `div-exp` `distribute-lft-out--` `rem-exp-log`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `flip--` `inv-pow`

Counts

4 → 121

Calls

4 calls:

12.0ms	(/ 1 (exp x))
6.0ms	(exp (* 3 x))
6.0ms	(exp (* 3 x))
35.0ms	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

series106.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ 1 (exp x))
10.0ms	(exp (* 3 x))
11.0ms	(exp (* 3 x))
71.0ms	(- (exp (* 3 x)) (/ 1 (exp (* 3 x))))

simplify2.7s

Counts

133 → 133

Iterations

Iter	Nodes
done	5002
3	2485
2	907
1	475
0	213

prune719.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.6b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	18
1	18
0	14

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.3s	3396×	body	1280	valid
782.0ms	2501×	body	640	valid
353.0ms	8274×	body	80	valid
267.0ms	1215×	body	320	valid
70.0ms	631×	body	160	valid