Details

sample115.0ms

Algorithm

intervals

Results

52.0ms	63×	body	1280	valid
26.0ms	64×	body	640	valid
11.0ms	23×	body	2560	valid
6.0ms	24×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	13×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize24.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
3.5b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.1b	(sqrt (+ (* x x) 1.0))

rewrite46.0ms

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:

18.0ms	(+ x (sqrt (+ (* x x) 1.0)))
18.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms	(sqrt (+ (* x x) 1.0))

series384.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(+ x (sqrt (+ (* x x) 1.0)))
256.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
55.0ms	(sqrt (+ (* x x) 1.0))

simplify1.6s

Counts

51 → 51

Iterations

Useful iterations: done (1.6s)

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

prune193.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite146.0ms

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:

106.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
37.0ms	(* -1/6 (/ (* x x) 1.0))

series295.0ms

Counts

2 → 6

Calls

2 calls:

250.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
44.0ms	(* -1/6 (/ (* x x) 1.0))

simplify1.4s

Counts

80 → 80

Iterations

Useful iterations: done (1.4s)

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

prune300.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

rewrite109.0ms

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:

71.0ms	(+ x (/ (pow x 3) (/ 1.0 -1/6)))
20.0ms	(/ (pow x 3) (/ 1.0 -1/6))

series153.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(+ x (/ (pow x 3) (/ 1.0 -1/6)))
44.0ms	(/ (pow x 3) (/ 1.0 -1/6))

simplify1.5s

Counts

218 → 218

Iterations

Useful iterations: done (1.5s)

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

prune524.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b	(/ 0.125 (pow x 3))
14.1b	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
51×	`times-frac`
35×	`*-un-lft-identity`
29×	`add-cube-cbrt`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`difference-of-squares`
9×	`add-exp-log`
6×	`sqr-pow`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1` `cube-mult` `unpow3`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`log-div` `distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `flip-+` `div-inv`

Counts

3 → 104

Calls

3 calls:

62.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
8.0ms	(/ 0.125 (pow x 3))
200.0ms	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

series371.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
41.0ms	(/ 0.125 (pow x 3))
200.0ms	(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

simplify966.0ms

Counts

113 → 113

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	210	1675
1	437	1478
2	1229	1404
done	5000	1394

prune330.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch96.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.9017023301953626
8	-11.923248480236845	-0.0008047768791668974	-1.002814715336328

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	54
1	38	54
done	38	54

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.8s	2305×	body	1280	valid
612.0ms	1572×	body	640	valid
473.0ms	828×	body	2560	valid
208.0ms	771×	body	320	valid
106.0ms	2130×	body	80	valid
97.0ms	394×	body	160	valid