Details

sample137.0ms

Algorithm

intervals

Results

62.0ms	77×	body	1280	valid
22.0ms	45×	body	640	valid
20.0ms	27×	body	320	valid
15.0ms	27×	body	2560	valid
5.0ms	69×	body	80	valid
2.0ms	11×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	9
1	9
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize26.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ x (sqrt (+ (* x x) 1)))
4.0b	(log (+ x (sqrt (+ (* x x) 1))))
16.6b	(sqrt (+ (* x x) 1))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 45

Calls

3 calls:

21.0ms	(+ x (sqrt (+ (* x x) 1)))
22.0ms	(log (+ x (sqrt (+ (* x x) 1))))
14.0ms	(sqrt (+ (* x x) 1))

series272.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(+ x (sqrt (+ (* x x) 1)))
149.0ms	(log (+ x (sqrt (+ (* x x) 1))))
45.0ms	(sqrt (+ (* x x) 1))

simplify1.9s

Counts

54 → 54

Iterations

Iter	Nodes
4	3922
3	1654
2	660
1	271
0	121

prune468.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.2b	(* 3/40 (* (* x x) (* (* x x) x)))
0.3b	(* -1/6 (* (* x x) x))
20.1b	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1`
47×	`add-cbrt-cube` `add-exp-log`
31×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
5×	`associate-r`
4×	`insert-posit16`
3×	`*-commutative`
2×	`pow2` `pow-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `pow3` `flip-+` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

30.0ms	(* (* x x) x)
176.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
43.0ms	(* -1/6 (* (* x x) x))
59.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* x x) x)
92.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
73.0ms	(* -1/6 (* (* x x) x))
235.0ms	(+ (* -1/6 (* (* x x) x)) (* 3/40 (* (* x x) (* (* x x) x))))

simplify3.5s

Counts

109 → 109

Iterations

Iter	Nodes
3	5368
2	1138
1	368
0	127

prune889.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))
0.1b	(* (* 3/40 x) x)
0.2b	(* 3/40 x)
0.9b	(log (exp (* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
5×	`log-prod` `associate-l` `add-log-exp`
4×	`insert-posit16`
3×	`log-pow` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `exp-sum` `associate-*r/`
1×	`exp-prod` `flip3-+` `exp-to-pow` `rem-log-exp` `flip-+` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

59.0ms	(* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))
27.0ms	(* (* 3/40 x) x)
10.0ms	(* 3/40 x)
9.0ms	(log (exp (* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))))

series444.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))
40.0ms	(* (* 3/40 x) x)
26.0ms	(* 3/40 x)
189.0ms	(log (exp (* (* x (* x x)) (+ -1/6 (* (* 3/40 x) x)))))

simplify5.6s

Counts

93 → 93

Iterations

Iter	Nodes
3	7146
2	1323
1	335
0	135

prune824.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (/ 1/8 x) (* x x)) (+ x x))
0.0b	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
0.1b	(/ (/ 1/8 x) (* x x))
9.5b	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `times-frac`
19×	`add-cube-cbrt`
18×	`add-log-exp`
17×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`frac-sub`
13×	`associate-/l*`
12×	`distribute-lft-out--`
8×	`log-prod`
7×	`diff-log` `difference-of-squares`
6×	`cbrt-undiv` `log-div` `div-exp`
5×	`pow1` `flip3--` `flip--`
4×	`insert-posit16`
3×	`sub-neg` `flip3-+` `flip-+` `div-inv` `distribute-lft-out` `associate--r+`
2×	`sum-log` `prod-exp` `cbrt-unprod`
1×	`clear-num` `associate-/r*` `frac-2neg` `rem-log-exp` `log-pow` `associate--r-` `associate-/l/`

Counts

4 → 120

Calls

4 calls:

33.0ms	(- (/ (/ 1/8 x) (* x x)) (+ x x))
84.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
10.0ms	(/ (/ 1/8 x) (* x x))
71.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(- (/ (/ 1/8 x) (* x x)) (+ x x))
65.0ms	(- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x)))
42.0ms	(/ (/ 1/8 x) (* x x))
102.0ms	(log (- (/ 1/2 x) (- (/ (/ 1/8 x) (* x x)) (+ x x))))

simplify11.4s

Counts

132 → 132

Iterations

Iter	Nodes
3	8868
2	1891
1	660
0	263

prune990.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 30.6b

bsearch168.0ms

Steps

Iters	Range		Point
10	1.4996160052323843e-06	45385424.466692075	0.9616249105092439
10	-8.26555774309129e+15	-0.755072844465923	-1.056937052753612

simplify11.0ms

Iterations

Iter	Nodes
2	37
1	37
0	30

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.4s	2330×	body	1280	valid
952.0ms	1568×	body	640	valid
612.0ms	787×	body	2560	valid
286.0ms	822×	body	320	valid
207.0ms	2106×	body	80	valid
75.0ms	387×	body	160	valid