Details

sample95.0ms

Algorithm

intervals

Results

30.0ms	85×	body	10240	exit
25.0ms	56×	body	1280	valid
14.0ms	50×	body	640	valid
7.0ms	106×	body	80	valid
7.0ms	31×	body	320	valid
2.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	11
2	11
1	10
0	5

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1))
4.1b	(- (exp x) 1)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`associate-/r*`
5×	`difference-of-sqr-1` `distribute-lft-out--`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `insert-posit16` `flip--`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `div-inv`

Counts

2 → 63

Calls

2 calls:

16.0ms	(/ (exp x) (- (exp x) 1))
9.0ms	(- (exp x) 1)

series54.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1))
24.0ms	(- (exp x) 1)

simplify2.0s

Counts

69 → 69

Iterations

Iter	Nodes
4	4327
3	1281
2	472
1	198
0	101

prune463.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 1 x) 1/2)
0.0b	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.3b	(* 1/12 x)

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`sum-log`
3×	`associate-r` `associate-l` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+` `distribute-lft-out`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

17.0ms	(+ (/ 1 x) 1/2)
24.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
9.0ms	(* 1/12 x)

series71.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ (/ 1 x) 1/2)
26.0ms	(+ (* 1/12 x) (+ (/ 1 x) 1/2))
27.0ms	(* 1/12 x)

simplify1.6s

Counts

56 → 56

Iterations

Iter	Nodes
3	2763
2	646
1	208
0	76

prune334.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ (/ 1 x) 1/2))
0.3b	(cbrt (+ (/ 1 x) 1/2))
0.3b	(cbrt (+ (/ 1 x) 1/2))
0.7b	(* (cbrt (+ (/ 1 x) 1/2)) (cbrt (+ (/ 1 x) 1/2)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
51×	`cbrt-prod`
23×	`add-sqr-sqrt`
22×	`distribute-lft-out`
18×	`cbrt-div`
15×	`add-cube-cbrt`
14×	`swap-sqr`
11×	`pow1` `div-inv`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

5.0ms	(cbrt (+ (/ 1 x) 1/2))
8.0ms	(cbrt (+ (/ 1 x) 1/2))
9.0ms	(cbrt (+ (/ 1 x) 1/2))
55.0ms	(* (cbrt (+ (/ 1 x) 1/2)) (cbrt (+ (/ 1 x) 1/2)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (+ (/ 1 x) 1/2))
65.0ms	(cbrt (+ (/ 1 x) 1/2))
65.0ms	(cbrt (+ (/ 1 x) 1/2))
84.0ms	(* (cbrt (+ (/ 1 x) 1/2)) (cbrt (+ (/ 1 x) 1/2)))

simplify3.0s

Counts

121 → 121

Iterations

Iter	Nodes
4	6493
3	1987
2	761
1	288
0	118

prune960.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1)))
4.1b	(- (exp x) 1)
4.1b	(- (exp x) 1)
4.1b	(- (exp x) 1)

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
40×	`cbrt-prod`
16×	`difference-of-squares`
14×	`swap-sqr`
12×	`cbrt-div` `add-cube-cbrt`
11×	`pow1`
10×	`associate-r` `associate-l` `add-log-exp`
9×	`flip3--` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
6×	`pow1/3` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

76.0ms	(* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1)))
16.0ms	(- (exp x) 1)
9.0ms	(- (exp x) 1)
8.0ms	(- (exp x) 1)

series211.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1)))
15.0ms	(- (exp x) 1)
15.0ms	(- (exp x) 1)
15.0ms	(- (exp x) 1)

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
4	2699
3	1124
2	519
1	239
0	120

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 21.5b

bsearch25.0ms

Steps

Iters	Range		Point
7	-0.11981472621416538	-0.0008162261515098681	-0.002288391212180564

simplify5.0ms

Iterations

Iter	Nodes
2	23
1	23
0	17

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.6s	2496×	body	10240	exit
1.1s	2304×	body	1280	valid
535.0ms	1597×	body	640	valid
198.0ms	2874×	body	80	valid
158.0ms	815×	body	320	valid
52.0ms	413×	body	160	valid