Details

sample120.0ms

Algorithm

intervals

Results

40.0ms	58×	body	1280	valid
30.0ms	34×	body	2560	valid
22.0ms	46×	body	640	valid
7.0ms	25×	body	320	valid
6.0ms	77×	body	80	valid
3.0ms	16×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	11
1	11
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.1b

localize29.0ms

Local error

Found 3 expressions with local error:

1.3b	(+ x (sqrt (+ (* x x) 1)))
3.2b	(log (+ x (sqrt (+ (* x x) 1))))
17.7b	(sqrt (+ (* x x) 1))

rewrite45.0ms

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:

11.0ms	(+ x (sqrt (+ (* x x) 1)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1))))
17.0ms	(sqrt (+ (* x x) 1))

series256.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ x (sqrt (+ (* x x) 1)))
158.0ms	(log (+ x (sqrt (+ (* x x) 1))))
50.0ms	(sqrt (+ (* x x) 1))

simplify1.9s

Counts

54 → 54

Iterations

Iter	Nodes
4	3878
3	1588
2	647
1	272
0	121

prune522.0ms

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)
0.1b	(* (* (* x x) x) 1/6)
0.3b	(* 3/40 (* (* x x) (* (* x x) x)))
22.3b	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

rewrite484.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

14.0ms	(* (* x x) x)
59.0ms	(* (* (* x x) x) 1/6)
178.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
232.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

series254.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x x) x)
63.0ms	(* (* (* x x) x) 1/6)
55.0ms	(* 3/40 (* (* x x) (* (* x x) x)))
84.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

simplify2.7s

Counts

114 → 114

Iterations

Iter	Nodes
3	5356
2	1144
1	361
0	136

prune814.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 3/40 (* x x)) 1/6)
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
0.4b	(* 3/40 (* x x))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
5×	`associate-l`
4×	`insert-posit16`
3×	`sub-neg` `*-commutative`
2×	`pow2` `distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-*r/` `pow-sqr` `flip--` `unswap-sqr`
1×	`diff-log` `pow3`

Counts

4 → 90

Calls

4 calls:

19.0ms	(- (* 3/40 (* x x)) 1/6)
19.0ms	(* (* x x) x)
114.0ms	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
15.0ms	(* 3/40 (* x x))

series333.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (* 3/40 (* x x)) 1/6)
37.0ms	(* (* x x) x)
167.0ms	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
36.0ms	(* 3/40 (* x x))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	4260
2	1014
1	318
0	112

prune627.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ -1/16 (* (* x x) (* (* x x) x)))
0.3b	(/ 1/8 (* (* x x) x))
9.5b	(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
14.9b	(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

rewrite568.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
42×	`add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
6×	`times-frac` `frac-add` `associate-/l*`
5×	`pow1` `log-div` `log-prod`
4×	`insert-posit16` `distribute-lft-out`
2×	`associate-+l+` `clear-num` `associate-/r*` `sum-log` `frac-2neg` `flip3-+` `flip3--` `frac-sub` `flip-+` `div-inv` `flip--` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate-+l-`

Counts

4 → 97

Calls

4 calls:

67.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
26.0ms	(/ 1/8 (* (* x x) x))
201.0ms	(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
271.0ms	(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ -1/16 (* (* x x) (* (* x x) x)))
67.0ms	(/ 1/8 (* (* x x) x))
118.0ms	(log (+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x)))))
66.0ms	(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))

simplify703.0ms

Counts

109 → 109

Iterations

Iter	Nodes
2	2302
1	607
0	224

prune916.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.0b

bsearch85.0ms

Steps

Iters	Range		Point
7	0.10106394179147121	1.6697130628152668	0.9628322546007364
8	-174.255226838109	-0.11981472621416538	-1.0788943454777058

simplify7.0ms

Iterations

Iter	Nodes
2	40
1	40
0	31

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.1s	2403×	body	1280	valid
785.0ms	1500×	body	640	valid
509.0ms	821×	body	2560	valid
425.0ms	412×	body	160	valid
319.0ms	774×	body	320	valid
167.0ms	2090×	body	80	valid