Details

sample86.0ms

Algorithm

intervals

Results

38.0ms	72×	body	1280	valid
17.0ms	48×	body	640	valid
10.0ms	24×	body	2560	valid
5.0ms	25×	body	320	valid
4.0ms	77×	body	80	valid
1.0ms	10×	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: 53.5b

localize9.0ms

Local error

Found 3 expressions with local error:

1.1b	(+ x (sqrt (+ (* x x) 1.0)))
1.6b	(log (+ x (sqrt (+ (* x x) 1.0))))
17.2b	(sqrt (+ (* x x) 1.0))

rewrite87.0ms

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:

25.0ms	(+ x (sqrt (+ (* x x) 1.0)))
45.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
16.0ms	(sqrt (+ (* x x) 1.0))

series341.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(+ x (sqrt (+ (* x x) 1.0)))
213.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
54.0ms	(sqrt (+ (* x x) 1.0))

simplify2.0s

Counts

51 → 51

Iterations

Useful iterations: done (2.0s)

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

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite112.0ms

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:

83.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
25.0ms	(* -1/6 (/ (* x x) 1.0))

series285.0ms

Counts

2 → 6

Calls

2 calls:

248.0ms	(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
38.0ms	(* -1/6 (/ (* x x) 1.0))

simplify1.5s

Counts

80 → 80

Iterations

Useful iterations: done (1.5s)

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

prune210.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (pow x 3))
9.5b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
17.9b	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
94×	`times-frac`
63×	`*-un-lft-identity`
46×	`add-cube-cbrt`
33×	`unpow-prod-down`
22×	`difference-of-squares`
19×	`associate-/r*`
17×	`sqr-pow`
16×	`cube-prod`
15×	`add-exp-log`
8×	`log-prod` `add-cbrt-cube`
7×	`distribute-lft-out--`
6×	`div-exp` `associate-/l*` `add-log-exp`
5×	`pow1` `log-div` `frac-sub`
4×	`cube-mult` `unpow3`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 167

Calls

4 calls:

11.0ms	(/ 0.0625 (pow x 5))
9.0ms	(/ 0.125 (pow x 3))
413.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
144.0ms	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ 0.0625 (pow x 5))
42.0ms	(/ 0.125 (pow x 3))
274.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
201.0ms	(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify1.2s

Counts

179 → 179

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	338	2966
1	679	2667
2	1858	2553
done	5000	2541

prune659.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
0.2b	(/ 0.125 (pow x 3))
8.3b	(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
36×	`times-frac`
29×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`distribute-lft-out`
6×	`log-prod`
5×	`add-cbrt-cube`
4×	`pow1` `cube-mult` `unpow3` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`log-div` `associate-+r+` `flip3-+` `frac-add` `sum-log` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `flip3--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `flip--` `div-inv`

Counts

3 → 101

Calls

3 calls:

124.0ms	(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
17.0ms	(/ 0.125 (pow x 3))
329.0ms	(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

series322.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
56.0ms	(/ 0.125 (pow x 3))
223.0ms	(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

simplify1.0s

Counts

110 → 110

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	206	1622
1	464	1404
2	1400	1332
done	5001	1328

prune294.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.5b

bsearch95.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.8999222701664713
9	-7.35943201301068	-4.403108084983288e-07	-1.004740488829904

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	56
1	44	56
done	44	56

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	2317×	body	1280	valid
933.0ms	1560×	body	640	valid
454.0ms	844×	body	2560	valid
176.0ms	784×	body	320	valid
165.0ms	394×	body	160	valid
151.0ms	2101×	body	80	valid