Details

sample221.0ms

Algorithm

intervals

Results

87.0ms	74×	body	10240	exit
40.0ms	55×	body	1280	valid
34.0ms	349×	body	80	valid
15.0ms	37×	body	640	valid
8.0ms	24×	body	320	valid
1.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2266
3	377
2	122
1	46
0	19

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize57.0ms

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) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(exp (- (* (- 1.0 eps) x)))
2.5b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

81×	`exp-neg` `frac-sub`
80×	`frac-times`
61×	`neg-sub0` `exp-diff`
40×	`associate-l/` `associate-r/`
31×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
20×	`un-div-inv`
18×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`associate-l`
9×	`add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-log-exp`
6×	`exp-prod` `associate-r` `add-exp-log`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr` `rem-exp-log`
1×	`distribute-lft-neg-in` `neg-mul-1` `sub-neg` `distribute-rgt-neg-in` `times-frac` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 168

Calls

4 calls:

86.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
88.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
16.0ms	(exp (- (* (- 1.0 eps) x)))
64.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
79.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
49.0ms	(exp (- (* (- 1.0 eps) x)))
313.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify633.0ms

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
1	1223
0	380

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (pow x 3) 0.6666666666666667)
6.0b	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 46

Calls

2 calls:

18.0ms	(* (pow x 3) 0.6666666666666667)
17.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

series131.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(* (pow x 3) 0.6666666666666667)
58.0ms	(+ (* (pow x 3) 0.6666666666666667) (- 2.0 (* 1.0 (* x x))))

simplify758.0ms

Counts

52 → 52

Iterations

Iter	Nodes
done	5002
2	1044
1	215
0	83

prune270.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (- (* (- 1.0 eps) x)))
5.1b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
9×	`add-sqr-sqrt` `exp-neg` `*-un-lft-identity` `frac-sub`
8×	`frac-times`
7×	`neg-sub0` `exp-prod` `exp-diff` `add-cube-cbrt`
6×	`pow1` `flip3-+` `add-cbrt-cube` `flip-+`
5×	`add-exp-log`
4×	`associate-l` `associate-l/` `associate-r/`
3×	`associate-r` `rem-exp-log`
2×	`exp-to-pow` `un-div-inv`
1×	`distribute-lft-neg-in` `neg-mul-1` `sum-log` `sub-neg` `distribute-rgt-neg-in` `flip3--` `diff-log` `div-sub` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

64.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
10.0ms	(exp (* (+ 1.0 eps) x))
14.0ms	(exp (- (* (- 1.0 eps) x)))
58.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
40.0ms	(exp (* (+ 1.0 eps) x))
52.0ms	(exp (- (* (- 1.0 eps) x)))
430.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	2211
1	445
0	174

prune582.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
0.3b	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
0.3b	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
18.6b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))))

rewrite4.6s

Algorithm

rewrite-expression-head

Rules

30117×	`frac-times`
24327×	`cbrt-div`
14808×	`exp-neg`
11106×	`neg-sub0` `exp-diff`
9105×	`associate-*l/`
8991×	`frac-sub`
8295×	`associate-*r/`
8110×	`flip3--` `flip--`
3702×	`un-div-inv`
2997×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`cbrt-prod` `pow1/3`
1×	`sub-neg` `diff-log`

Counts

4 → 9057

Calls

4 calls:

38.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
36.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
36.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
963.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))))

series870.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
171.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
160.0ms	(cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))
343.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (* (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))) (cbrt (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ eps 1.0) x)))))))

simplify9.8s

Counts

9069 → 9069

Iterations

Iter	Nodes
done	17573
0	17573

prune2.5m

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes84.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.9b

bsearch206.0ms

Steps

Iters	Range		Point
10	1.9673231826388637e-10	9645967.64350026	5.301278737300282

simplify8.0ms

Iterations

Iter	Nodes
done	63
2	63
1	55
0	37

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.0s	1879×	body	10240	exit
1.3s	9945×	body	80	valid
1.1s	1738×	body	1280	valid
462.0ms	1248×	body	640	valid
338.0ms	327×	body	160	valid
235.0ms	638×	body	320	valid