Details

sample72.0ms

Algorithm

intervals

Results

14.0ms	178×	body	80	valid
10.0ms	27×	body	1280	valid
7.0ms	125×	body	80	nan
6.0ms	24×	body	640	valid
3.0ms	17×	body	320	valid
3.0ms	13×	body	640	nan
3.0ms	9×	body	1280	nan
1.0ms	10×	body	160	valid
1.0ms	6×	body	320	nan
0.0ms	4×	body	160	nan

simplify1.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
9	2335
8	741
7	343
6	223
5	123
4	75
3	41
2	29
1	19
0	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
2.6b	(- 1.0 (/ (- x y) (- 1.0 y)))
4.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
27×	`times-frac`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`distribute-lft-out--`
6×	`log-prod` `add-exp-log`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`log-div` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `log-pow` `div-inv` `associate--r-`

Counts

3 → 85

Calls

3 calls:

17.0ms	(/ (- x y) (- 1.0 y))
30.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
26.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series262.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (- x y) (- 1.0 y))
84.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
136.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify576.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1386
1	407
0	171

prune447.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.3b	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
4.7b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
13.3b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
37×	`cbrt-prod`
34×	`*-un-lft-identity`
15×	`difference-of-squares`
14×	`cbrt-div` `add-cube-cbrt`
12×	`pow1` `times-frac`
10×	`swap-sqr`
9×	`log-prod` `flip3--` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`pow1/3` `add-exp-log`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube` `unswap-sqr`
2×	`log-div` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `associate--r-`

Counts

4 → 110

Calls

4 calls:

6.0ms	(cbrt (- 1.0 y))
60.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
128.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
128.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (- 1.0 y))
160.0ms	(* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))
132.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))
78.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))

simplify987.0ms

Counts

122 → 122

Iterations

Iter	Nodes
done	5000
2	1881
1	544
0	244

prune723.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (/ x y) (/ 1.0 y)) (/ 1.0 y))
0.2b	(* (/ x y) (/ 1.0 y))
3.8b	(+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y))
4.4b	(log (+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
23×	`times-frac`
19×	`add-cube-cbrt`
17×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`frac-add`
13×	`associate-r` `associate-l`
11×	`add-log-exp`
9×	`log-div` `frac-sub`
7×	`pow1` `associate-l/` `associate-r/`
6×	`sub-div`
4×	`frac-times` `cbrt-undiv` `log-prod` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`associate-+l+` `sum-log` `sub-neg` `flip3-+` `distribute-rgt-out--` `diff-log` `flip-+` `div-inv` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `pow-prod-down` `log-pow` `*-commutative` `associate-+l-`

Counts

4 → 114

Calls

4 calls:

12.0ms	(- (* (/ x y) (/ 1.0 y)) (/ 1.0 y))
17.0ms	(* (/ x y) (/ 1.0 y))
79.0ms	(+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y))
48.0ms	(log (+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* (/ x y) (/ 1.0 y)) (/ 1.0 y))
32.0ms	(* (/ x y) (/ 1.0 y))
35.0ms	(+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y))
94.0ms	(log (+ (- (* (/ x y) (/ 1.0 y)) (/ 1.0 y)) (/ x y)))

simplify2.2s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	3455
1	630
0	236

prune645.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y)))))
2.6b	(- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))
3.7b	(log (* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))))

rewrite794.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
29×	`times-frac`
24×	`difference-of-squares`
20×	`sqrt-prod`
18×	`add-cube-cbrt`
16×	`distribute-lft-out--`
11×	`associate-r` `add-exp-log`
9×	`pow1` `flip3--` `flip--`
8×	`frac-times` `log-div` `add-cbrt-cube`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`associate-/r` `associate-l` `associate-/l`
4×	`associate-l/` `associate-r/`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `rem-log-exp` `pow-prod-down` `prod-exp` `associate-/r/` `log-pow` `distribute-lft-out` `associate-/l/`
1×	`cbrt-undiv` `log-prod` `clear-num` `frac-2neg` `diff-log` `div-sub` `div-exp` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

25.0ms	(/ (- x y) (- 1.0 y))
572.0ms	(* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y)))))
49.0ms	(- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))
140.0ms	(log (* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (- x y) (- 1.0 y))
312.0ms	(* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y)))))
148.0ms	(- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))
575.0ms	(log (* (+ (sqrt (/ (- x y) (- 1.0 y))) (sqrt 1.0)) (- (sqrt 1.0) (sqrt (/ (- x y) (- 1.0 y))))))

simplify1.4s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	2977
1	660
0	245

prune705.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes207.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 16.6b

bsearch179.0ms

Steps

Iters	Range		Point
10	61777.909360781356	5.507951260787393e+23	42220580.410328135
6	-531429590.62988466	-72632609.50044116	-80228020.28782515

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

505.0ms	209×	body	320	nan
438.0ms	5717×	body	80	valid
341.0ms	802×	body	1280	valid
269.0ms	786×	body	640	valid
264.0ms	3676×	body	80	nan
128.0ms	336×	body	1280	nan
85.0ms	467×	body	320	valid
78.0ms	369×	body	640	nan
64.0ms	228×	body	160	valid
11.0ms	118×	body	160	nan