Details

sample205.0ms

Algorithm

intervals

Results

62.0ms	332×	body	80	valid
43.0ms	56×	body	10240	exit
36.0ms	50×	body	1280	valid
19.0ms	47×	body	640	valid
7.0ms	24×	body	320	valid
2.0ms	10×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	377	27
4	2267	27
done	5000	27

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
2.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
76×	`exp-neg` `frac-times`
57×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
38×	`associate-*r/`
32×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
19×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 166

Calls

4 calls:

130.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
22.0ms	(* (- 1.0 eps) x)
44.0ms	(* (+ 1.0 eps) x)
74.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series464.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
38.0ms	(* (- 1.0 eps) x)
37.0ms	(* (+ 1.0 eps) x)
316.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify773.0ms

Counts

178 → 178

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	393	7885
1	1260	7187
done	5000	6885

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
5.4b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 45

Calls

2 calls:

14.0ms	(* 0.6666666666666667 (pow x 3))
94.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series119.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(* 0.6666666666666667 (pow x 3))
65.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify687.0ms

Counts

51 → 51

Iterations

Useful iterations: done (684.0ms)

Iter	Nodes	Cost
0	84	590
1	222	548
2	908	500
done	5000	462

prune202.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
0.0b	(* (+ 1.0 eps) x)
2.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (exp (- (* (+ 1.0 eps) x))) (- (/ 1.0 eps) 1.0)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

72×	`frac-times` `frac-sub`
63×	`exp-neg`
54×	`neg-sub0` `exp-diff`
40×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
28×	`flip3-+` `flip-+`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`add-exp-log` `associate-r` `un-div-inv`
6×	`add-log-exp`
4×	`associate--r+`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `distribute-lft-out`
1×	`diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 159

Calls

4 calls:

72.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
24.0ms	(* (- 1.0 eps) x)
20.0ms	(* (+ 1.0 eps) x)
43.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (exp (- (* (+ 1.0 eps) x))) (- (/ 1.0 eps) 1.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
60.0ms	(* (- 1.0 eps) x)
34.0ms	(* (+ 1.0 eps) x)
247.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (exp (- (* (+ 1.0 eps) x))) (- (/ 1.0 eps) 1.0)))

simplify784.0ms

Counts

171 → 171

Iterations

Useful iterations: done (771.0ms)

Iter	Nodes	Cost
0	377	7431
1	1240	6746
done	5001	6602

prune609.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
0.3b	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
0.3b	(* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))
20.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

30274×	`frac-times`
24498×	`cbrt-div`
14884×	`exp-neg`
11163×	`neg-sub0` `exp-diff`
9152×	`associate-*l/`
8991×	`frac-sub`
8342×	`associate-*r/`
8167×	`flip3--` `flip--`
3721×	`un-div-inv`
2997×	`flip3-+` `flip-+`
11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity` `pow1/3`
6×	`add-exp-log` `cbrt-prod` `add-log-exp`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 9169

Calls

4 calls:

38.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
23.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
87.0ms	(* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))
1.1s	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))))

series833.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
166.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))
252.0ms	(* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))))
283.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))))

simplify11.8s

Counts

9181 → 9181

Iterations

Useful iterations: 0 (2.9s)

Iter	Nodes	Cost
0	17629	1423935
done	17629	1423935

prune2.3m

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.1b

regimes62.0ms

Accuracy

96.8% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 17.5b

bsearch182.0ms

Steps

Iters	Range		Point
10	3.960614984267581e-08	28918.939680702064	326.61229285006976

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	79
1	52	79
2	60	79
done	60	79

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.9s	1924×	body	10240	exit
1.2s	9913×	body	80	valid
1.1s	1671×	body	1280	valid
750.0ms	1259×	body	640	valid
391.0ms	316×	body	160	valid
140.0ms	647×	body	320	valid