Details

sample110.0ms

Algorithm

intervals

Results

47.0ms	75×	body	1280	valid
21.0ms	57×	body	640	valid
14.0ms	26×	body	320	valid
11.0ms	24×	body	2560	valid
4.0ms	59×	body	80	valid
2.0ms	15×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	11
1	11
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize25.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1)))
2.7b	(log (+ x (sqrt (+ (* x x) 1))))
13.6b	(sqrt (+ (* x x) 1))

rewrite44.0ms

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:

19.0ms	(+ x (sqrt (+ (* x x) 1)))
11.0ms	(log (+ x (sqrt (+ (* x x) 1))))
14.0ms	(sqrt (+ (* x x) 1))

series260.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ x (sqrt (+ (* x x) 1)))
116.0ms	(log (+ x (sqrt (+ (* x x) 1))))
58.0ms	(sqrt (+ (* x x) 1))

simplify1.1s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
2	1202
1	290
0	121

prune284.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3/40 (pow x 5))
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 1/6)
16.3b	(+ (* 3/40 (pow x 5)) (- x (* (* (* x x) x) 1/6)))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1`
23×	`add-exp-log`
20×	`add-cbrt-cube`
15×	`add-sqr-sqrt`
13×	`associate-r`
12×	`prod-exp`
10×	`cbrt-unprod`
9×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt` `add-log-exp`
6×	`pow-plus` `pow-prod-up`
5×	`associate-l`
4×	`unpow-prod-down` `insert-posit16` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `associate-+r+` `sum-log` `pow-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `sub-neg` `flip3-+` `diff-log` `pow3` `pow-exp` `flip-+`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* 3/40 (pow x 5))
14.0ms	(* (* x x) x)
86.0ms	(* (* (* x x) x) 1/6)
19.0ms	(+ (* 3/40 (pow x 5)) (- x (* (* (* x x) x) 1/6)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* 3/40 (pow x 5))
60.0ms	(* (* x x) x)
47.0ms	(* (* (* x x) x) 1/6)
84.0ms	(+ (* 3/40 (pow x 5)) (- x (* (* (* x x) x) 1/6)))

simplify2.0s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2058
1	347
0	132

prune365.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1/8 (* x x)) x)
0.9b	(/ 1/8 (* x x))
14.6b	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5))) (/ 1/2 x)))
19.2b	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
63×	`times-frac`
40×	`*-un-lft-identity`
23×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
10×	`associate-/l*`
8×	`log-prod`
7×	`cbrt-undiv` `div-exp` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1` `log-div` `frac-sub`
4×	`associate-/r*` `insert-posit16`
3×	`unpow-prod-down` `flip3--` `flip--` `sqr-pow`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate-/l/`

Counts

4 → 122

Calls

4 calls:

22.0ms	(/ (/ 1/8 (* x x)) x)
12.0ms	(/ 1/8 (* x x))
124.0ms	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5))) (/ 1/2 x)))
43.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (/ 1/8 (* x x)) x)
28.0ms	(/ 1/8 (* x x))
160.0ms	(log (- (- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5))) (/ 1/2 x)))
173.0ms	(- (/ (/ 1/8 (* x x)) x) (/ 1/16 (pow x 5)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
2	3120
1	642
0	275

prune677.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))
0.1b	(* (* x x) x)
0.2b	(/ -1/8 (* (* x x) x))
11.4b	(log (+ x (+ x (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
19×	`*-un-lft-identity` `add-exp-log`
18×	`add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`distribute-lft-out`
6×	`log-prod` `pow-plus` `prod-exp` `pow-prod-up` `cbrt-unprod` `add-log-exp`
4×	`insert-posit16`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-r` `pow-prod-down` `associate-/l*`
2×	`pow2` `log-div` `flip3-+` `pow-sqr` `flip-+`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `frac-2neg` `rem-log-exp` `associate-l` `pow3` `frac-add` `log-pow` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

19.0ms	(+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))
15.0ms	(* (* x x) x)
16.0ms	(/ -1/8 (* (* x x) x))
193.0ms	(log (+ x (+ x (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (/ 1/2 x) (/ -1/8 (* (* x x) x)))
48.0ms	(* (* x x) x)
70.0ms	(/ -1/8 (* (* x x) x))
100.0ms	(log (+ x (+ x (+ (/ 1/2 x) (/ -1/8 (* (* x x) x))))))

simplify1.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	2897
1	429
0	161

prune315.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch126.0ms

Steps

Iters	Range		Point
10	4.3052657707541446e-11	1.874259372897972	0.9618552791025287
9	-209901990.47645873	-0.28008678268591264	-1.0468290506388152

simplify6.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	2308×	body	1280	valid
762.0ms	1548×	body	640	valid
532.0ms	822×	body	2560	valid
274.0ms	779×	body	320	valid
207.0ms	2129×	body	80	valid
73.0ms	414×	body	160	valid