Details

sample141.0ms

Algorithm

intervals

Results

68.0ms	78×	body	1280	valid
24.0ms	48×	body	640	valid
9.0ms	31×	body	320	valid
9.0ms	15×	body	2560	valid
5.0ms	70×	body	80	valid
2.0ms	14×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	9
1	9
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.8b

localize69.0ms

Local error

Found 3 expressions with local error:

0.7b	(+ x (sqrt (+ (* x x) 1.0)))
4.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b	(sqrt (+ (* x x) 1.0))

rewrite102.0ms

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:

24.0ms	(+ x (sqrt (+ (* x x) 1.0)))
45.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
27.0ms	(sqrt (+ (* x x) 1.0))

series494.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(+ x (sqrt (+ (* x x) 1.0)))
319.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
78.0ms	(sqrt (+ (* x x) 1.0))

simplify4.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5049
3	3422
2	934
1	315
0	137

prune582.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* (/ x (sqrt 1.0)) x) (/ x 1.0))
0.1b	(* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6)

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-cbrt-cube` `add-exp-log`
27×	`prod-exp` `cbrt-unprod`
16×	`pow1` `associate-r`
10×	`add-sqr-sqrt` `cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
9×	`times-frac` `pow-prod-down` `associate-*l/`
2×	`frac-times` `associate-l` `associate-r/` `-commutative` `insert-posit16` `add-log-exp`
1×	`div-inv`

Counts

2 → 73

Calls

2 calls:

79.0ms	(* (* (/ x (sqrt 1.0)) x) (/ x 1.0))
280.0ms	(* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6)

series286.0ms

Counts

2 → 6

Calls

2 calls:

138.0ms	(* (* (/ x (sqrt 1.0)) x) (/ x 1.0))
148.0ms	(* (* (* (/ x (sqrt 1.0)) x) (/ x 1.0)) -1/6)

simplify4.0s

Counts

79 → 79

Iterations

Iter	Nodes
done	5003
2	1721
1	417
0	130

prune523.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
0.1b	(* (* x x) x)
0.2b	(/ 0.125 (* (* x x) x))
12.4b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

82.0ms	(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
48.0ms	(* (* x x) x)
52.0ms	(/ 0.125 (* (* x x) x))
386.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

series496.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (/ 0.5 x) (/ 0.125 (* (* x x) x)))
52.0ms	(* (* x x) x)
69.0ms	(/ 0.125 (* (* x x) x))
226.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (* (* x x) x))))))

simplify3.6s

Counts

100 → 100

Iterations

Iter	Nodes
done	5001
2	1524
1	434
0	175

prune644.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (* (* x x) x))
14.6b	(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
21.0b	(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

10.0ms	(/ 0.0625 (pow x 5))
45.0ms	(/ 0.125 (* (* x x) x))
379.0ms	(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
783.0ms	(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series510.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 0.0625 (pow x 5))
45.0ms	(/ 0.125 (* (* x x) x))
314.0ms	(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
88.0ms	(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify3.5s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	2247
1	628
0	283

prune1.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.2b

bsearch174.0ms

Steps

Iters	Range		Point
10	1.508099977930646e-06	2590629949647.022	0.8920640501139611
10	-26711381.42537418	-6.803810524357175e-07	-1.0026376323582022

simplify14.0ms

Iterations

Iter	Nodes
done	43
1	43
0	35

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.7s	2363×	body	1280	valid
637.0ms	1540×	body	640	valid
556.0ms	785×	body	320	valid
424.0ms	774×	body	2560	valid
150.0ms	2145×	body	80	valid
50.0ms	393×	body	160	valid