Details

sample76.0ms

Algorithm

intervals

Results

35.0ms	78×	body	1280	valid
15.0ms	53×	body	640	valid
8.0ms	24×	body	2560	valid
5.0ms	27×	body	320	valid
2.0ms	60×	body	80	valid
1.0ms	14×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.7b

localize10.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1.0)))
2.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b	(sqrt (+ (* x x) 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

17.0ms	(+ x (sqrt (+ (* x x) 1.0)))
17.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))

series286.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(+ x (sqrt (+ (* x x) 1.0)))
171.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
48.0ms	(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts

51 → 51

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	133	761
1	308	691
2	848	618
3	2737	602
done	5001	590

prune142.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
0.2b	(* -1/6 (/ (* x x) 1.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`associate-r`
24×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-prod`
6×	`pow1` `associate-l` `prod-exp` `cbrt-unprod`
5×	`unswap-sqr`
3×	`cbrt-undiv` `div-exp`
2×	`frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+` `div-inv` `add-log-exp`

Counts

2 → 74

Calls

2 calls:

68.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
21.0ms	(* -1/6 (/ (* x x) 1.0))

series198.0ms

Counts

2 → 6

Calls

2 calls:

173.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
25.0ms	(* -1/6 (/ (* x x) 1.0))

simplify945.0ms

Counts

80 → 80

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	162	1283
1	411	1174
2	1550	1066
done	5000	1034

prune187.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (/ (pow x 3) (/ 1.0 -1/6)))
0.1b	(/ (pow x 3) (/ 1.0 -1/6))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
137×	`*-un-lft-identity`
135×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`unpow-prod-down` `cube-prod`
15×	`add-exp-log`
14×	`cube-mult` `unpow3` `div-inv` `sqr-pow`
13×	`associate-/r*`
12×	`associate-/l*`
9×	`div-exp`
7×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`cbrt-undiv`
2×	`pow1` `pow-to-exp` `pow-exp`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `sum-log` `associate-/r/` `flip-+` `distribute-lft-out`

Counts

2 → 212

Calls

2 calls:

59.0ms	(+ x (/ (pow x 3) (/ 1.0 -1/6)))
15.0ms	(/ (pow x 3) (/ 1.0 -1/6))

series127.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(+ x (/ (pow x 3) (/ 1.0 -1/6)))
43.0ms	(/ (pow x 3) (/ 1.0 -1/6))

simplify1.0s

Counts

218 → 218

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	322	3669
1	635	2995
2	2499	2929
done	5000	2927

prune389.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* -1/6 (/ (* x x) 1.0))
0.2b	(* -1/6 (/ (* x x) 1.0))
0.2b	(* -1/6 (/ (* x x) 1.0))
24.1b	(/ (* (+ (pow (* -1/6 (/ (* x x) 1.0)) 3) 1) (/ x (sqrt 1.0))) (+ (* (* -1/6 (/ (* x x) 1.0)) (* -1/6 (/ (* x x) 1.0))) (- (* 1 1) (* (* -1/6 (/ (* x x) 1.0)) 1))))

rewrite485.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-*r/` `prod-exp` `cbrt-unprod`
10×	`pow1` `cbrt-undiv` `div-exp`
9×	`associate-l`
8×	`associate-/r/`
6×	`frac-add` `unswap-sqr`
5×	`associate-/l/`
4×	`frac-times` `associate-*l/` `div-inv` `add-log-exp`
3×	`flip3--` `flip3-+` `pow-prod-down` `associate-/r` `-commutative` `flip--` `flip-+`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 120

Calls

4 calls:

18.0ms	(* -1/6 (/ (* x x) 1.0))
18.0ms	(* -1/6 (/ (* x x) 1.0))
17.0ms	(* -1/6 (/ (* x x) 1.0))
428.0ms	(/ (* (+ (pow (* -1/6 (/ (* x x) 1.0)) 3) 1) (/ x (sqrt 1.0))) (+ (* (* -1/6 (/ (* x x) 1.0)) (* -1/6 (/ (* x x) 1.0))) (- (* 1 1) (* (* -1/6 (/ (* x x) 1.0)) 1))))

series537.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* -1/6 (/ (* x x) 1.0))
31.0ms	(* -1/6 (/ (* x x) 1.0))
25.0ms	(* -1/6 (/ (* x x) 1.0))
455.0ms	(/ (* (+ (pow (* -1/6 (/ (* x x) 1.0)) 3) 1) (/ x (sqrt 1.0))) (+ (* (* -1/6 (/ (* x x) 1.0)) (* -1/6 (/ (* x x) 1.0))) (- (* 1 1) (* (* -1/6 (/ (* x x) 1.0)) 1))))

simplify1.2s

Counts

132 → 132

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	188	3423
1	579	2833
2	2553	2275
done	5001	2269

prune648.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.4b

bsearch77.0ms

Steps

Iters	Range		Point
10	0.0001820196720056695	1126179.5725289274	0.8946210124348296
9	-76786.820650899	-0.0002772006047103471	-0.9952950592534084

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	56
1	43	56
done	43	56

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	2472×	body	1280	valid
371.0ms	1549×	body	640	valid
216.0ms	786×	body	2560	valid
106.0ms	786×	body	320	valid
66.0ms	2034×	body	80	valid
31.0ms	373×	body	160	valid