Details

sample99.0ms

Algorithm

intervals

Results

29.0ms	330×	body	80	valid
23.0ms	42×	body	1280	valid
14.0ms	36×	body	640	valid
6.0ms	22×	body	320	valid
5.0ms	57×	body	80	overflowed
2.0ms	12×	body	160	valid

simplify536.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	307	27
4	1139	27
done	5000	27

prune14.0ms

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

localize19.0ms

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)))))

rewrite53.0ms

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))))
5.0ms	(exp (neg (* (- 1.0 eps) x)))
3.0ms	(exp (neg (* (+ 1.0 eps) x)))
20.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ 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)))
56.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify977.0ms

Counts

167 → 167

Iterations

Useful iterations: done (968.0ms)

Iter	Nodes	Cost
0	360	7789
1	1169	7198
2	3740	6612
done	5001	6609

prune371.0ms

Filtered

91 candidates to 167 candidates (-83.5%)

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

localize10.0ms

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)))

rewrite19.0ms

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)))

simplify422.0ms

Counts

72 → 72

Iterations

Useful iterations: done (420.0ms)

Iter	Nodes	Cost
0	105	699
1	261	644
2	919	575
done	5001	539

prune122.0ms

Filtered

46 candidates to 72 candidates (-56.5%)

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

localize25.0ms

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)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))

rewrite65.0ms

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:

7.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(* 0.6666666666666667 (pow x 3))
16.0ms	(- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3))
28.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))

series35.0ms

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))
15.0ms	(/ (- (pow (+ (* 0.6666666666666667 (pow x 3)) 2.0) 3) (pow (* 1.0 (pow x 2)) 3)) (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))

simplify670.0ms

Counts

168 → 168

Iterations

Useful iterations: done (661.0ms)

Iter	Nodes	Cost
0	238	6935
1	603	6667
2	2206	6391
done	5001	6389

prune879.0ms

Filtered

120 candidates to 168 candidates (-40.0%)

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

localize36.0ms

Local error

Found 4 expressions with local error:

2.5b	(sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))
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 (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))
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 (* x 0.6666666666666667)))))) (sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))

rewrite67.0ms

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:

7.0ms	(sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))
9.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
17.0ms	(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) (sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))
28.0ms	(/ (+ (* (+ (* 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 (* x 0.6666666666666667)))))) (sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667)))))))
5.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
15.0ms	(/ (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))) (sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))
24.0ms	(/ (+ (* (+ (* 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 (* x 0.6666666666666667)))))) (sqrt (+ (* (* 1.0 1.0) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ 2.0 (* (pow x 2) (+ 1.0 (* x 0.6666666666666667))))))))

simplify950.0ms

Counts

144 → 144

Iterations

Useful iterations: done (932.0ms)

Iter	Nodes	Cost
0	323	9831
1	910	9281
2	3613	8744
done	5000	8742

prune2.1s

Filtered

111 candidates to 144 candidates (-29.7%)

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

regimes133.0ms

Accuracy

95.8% (0.6b remaining)

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

bsearch98.0ms

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

926.0ms	1632×	body	1280	valid
916.0ms	10220×	body	80	valid
462.0ms	1235×	body	640	valid
179.0ms	1963×	body	80	overflowed
162.0ms	613×	body	320	valid
57.0ms	331×	body	160	valid

Details

sample99.0ms

simplify536.0ms

prune14.0ms

localize19.0ms

rewrite53.0ms

series81.0ms

simplify977.0ms

prune371.0ms

localize10.0ms

rewrite19.0ms

series12.0ms

simplify422.0ms

prune122.0ms

localize25.0ms

rewrite65.0ms

series35.0ms

simplify670.0ms

prune879.0ms

localize36.0ms

rewrite67.0ms

series55.0ms

simplify950.0ms

prune2.1s

regimes133.0ms

bsearch98.0ms

simplify5.0ms

end0.0ms

sample3.2s

Profiling