Details

sample98.0ms

Algorithm

intervals

Results

28.0ms	330×	body	80	valid
23.0ms	42×	body	1280	valid
13.0ms	36×	body	640	valid
6.0ms	22×	body	320	valid
5.0ms	57×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	307	27
4	1117	27
5	4826	27
done	5000	27

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 26.3b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b	(exp (neg (* (- 1.0 eps) x)))
0.0b	(exp (neg (* (+ 1.0 eps) x)))
2.4b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
78×	`exp-neg`
76×	`frac-times`
59×	`neg-sub0` `exp-diff`
38×	`associate-r/` `associate-l/`
30×	`flip3-+` `flip-+`
28×	`flip3--` `flip--`
19×	`un-div-inv`
12×	`exp-prod`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-cbrt-cube`
5×	`add-exp-log`
4×	`associate-l` `rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 155

Calls

4 calls:

14.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms	(exp (neg (* (- 1.0 eps) x)))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
21.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms	(exp (neg (* (- 1.0 eps) x)))
7.0ms	(exp (neg (* (+ 1.0 eps) x)))
53.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify1.0s

Counts

167 → 167

Iterations

Useful iterations: 2 (323.0ms)

Iter	Nodes	Cost
0	360	7789
1	1169	7083
2	3599	6573
done	5001	6573

prune389.0ms

Filtered

90 candidates to 167 candidates (-85.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	3	168

Merged error: 0.3b

Counts

168 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x 2)
0.3b	(* 0.6666666666666667 (pow x 3))
7.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`unpow-prod-down`
5×	`add-cbrt-cube`
4×	`pow1` `cube-prod` `unswap-sqr`
3×	`pow-unpow` `associate-l` `prod-exp` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp`
1×	`cube-mult` `sub-neg` `flip3--` `pow-pow` `unpow3` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unpow2`

Counts

3 → 63

Calls

3 calls:

2.0ms	(pow x 2)
7.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series12.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(pow x 2)
4.0ms	(* 0.6666666666666667 (pow x 3))
5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify1.8s

Counts

72 → 72

Iterations

Useful iterations: 3 (567.0ms)

Iter	Nodes	Cost
0	105	699
1	261	632
2	866	572
3	4261	525
done	5000	525

prune113.0ms

Filtered

41 candidates to 72 candidates (-75.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Merged error: 0.3b

Counts

75 → 4

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 0.6666666666666667 (pow x 3))
0.3b	(* 0.6666666666666667 (pow x 3))
11.8b	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
13.3b	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `difference-of-squares`
39×	`times-frac`
34×	`sqr-pow`
30×	`add-cube-cbrt`
24×	`associate-r`
18×	`unpow-prod-down` `cube-prod`
16×	`add-exp-log`
13×	`associate-/l*`
10×	`add-cbrt-cube`
8×	`unswap-sqr`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`difference-cubes` `distribute-lft-out--`
4×	`pow1`
3×	`associate-/r*`
2×	`cube-mult` `pow-to-exp` `flip3--` `unpow3` `pow-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 156

Calls

4 calls:

8.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(* 0.6666666666666667 (pow x 3))
16.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
30.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 0.6666666666666667 (pow x 3))
4.0ms	(* 0.6666666666666667 (pow x 3))
11.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
20.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))

simplify632.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (190.0ms)

Iter	Nodes	Cost
0	237	6935
1	603	6653
2	2195	6383
done	5000	6383

prune922.0ms

Filtered

116 candidates to 168 candidates (-44.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	168	4	172

Merged error: 0.3b

Counts

172 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))
7.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
11.7b	(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))
12.2b	(/ (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x)))))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
27×	`sqrt-prod`
24×	`flip3-+` `flip-+`
20×	`associate-*r/` `associate-/l/`
16×	`frac-add`
12×	`associate-/r*`
9×	`add-log-exp`
8×	`add-exp-log` `frac-times` `add-cbrt-cube`
6×	`sqrt-div` `associate-/l*`
5×	`pow1`
4×	`associate-*l/` `associate-/r/`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub` `associate--l+` `sum-log`

Counts

4 → 132

Calls

4 calls:

12.0ms	(sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))
9.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
24.0ms	(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))
33.0ms	(/ (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x)))))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4))))
5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
19.0ms	(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))
21.0ms	(/ (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)) (* (* 1.0 (pow x 2)) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x)))))) (sqrt (+ (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* 0.6666666666666667 x))))) (* (* 1.0 1.0) (pow x 4)))))

simplify953.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (310.0ms)

Iter	Nodes	Cost
0	323	9831
1	910	9292
2	3578	8758
done	5001	8758

prune1.9s

Filtered

109 candidates to 144 candidates (-32.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	144	4	148

Merged error: 0.3b

Counts

148 → 4

regimes134.0ms

Accuracy

95.8% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 15.6b

bsearch97.0ms

Steps

Iters	Range		Point
9	0.0012906900159990226	483.8343007553032	223.69169998523014

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	47
1	43	47
2	49	47
done	49	47

end0.0ms

sample3.2s

Algorithm

intervals

Results

895.0ms	1632×	body	1280	valid
894.0ms	10220×	body	80	valid
453.0ms	1235×	body	640	valid
175.0ms	1963×	body	80	overflowed
159.0ms	613×	body	320	valid
57.0ms	331×	body	160	valid

Details

sample98.0ms

simplify1.4s

prune9.0ms

localize18.0ms

rewrite58.0ms

series79.0ms

simplify1.0s

prune389.0ms

localize11.0ms

rewrite20.0ms

series12.0ms

simplify1.8s

prune113.0ms

localize29.0ms

rewrite69.0ms

series40.0ms

simplify632.0ms

prune922.0ms

localize34.0ms

rewrite85.0ms

series56.0ms

simplify953.0ms

prune1.9s

regimes134.0ms

bsearch97.0ms

simplify5.0ms

end0.0ms

sample3.2s

Profiling