Details

sample85.0ms

Algorithm

intervals

Results

42.0ms	71×	body	10240	exit
14.0ms	267×	body	80	valid
4.0ms	6×	body	1280	valid
3.0ms	11×	body	640	valid
2.0ms	8×	body	320	valid
0.0ms	1×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
2	19
1	12
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.5b	(log (+ 1.0 (exp x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`log-prod`
6×	`add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `log-div` `associate--l+` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 45

Calls

3 calls:

19.0ms	(- (log (+ 1.0 (exp x))) (* x y))
10.0ms	(+ 1.0 (exp x))
9.0ms	(log (+ 1.0 (exp x)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(- (log (+ 1.0 (exp x))) (* x y))
9.0ms	(+ 1.0 (exp x))
115.0ms	(log (+ 1.0 (exp x)))

simplify1.7s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	3010
2	648
1	211
0	92

prune232.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (cbrt (+ 1.0 (exp x))))
0.7b	(+ (* (log (cbrt (+ 1.0 (exp x)))) 2) (log (cbrt (+ 1.0 (exp x)))))
1.0b	(cbrt (+ 1.0 (exp x)))
1.0b	(cbrt (+ 1.0 (exp x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`cbrt-prod`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`cbrt-div`
7×	`associate-+r+`
5×	`pow1` `flip3-+` `add-exp-log` `flip-+` `add-log-exp`
4×	`log-div` `add-cbrt-cube` `distribute-lft-out`
3×	`pow1/3`
2×	`associate-+r-` `log-pow`
1×	`+-commutative` `sum-log` `rem-log-exp`

Counts

4 → 67

Calls

4 calls:

14.0ms	(log (cbrt (+ 1.0 (exp x))))
23.0ms	(+ (* (log (cbrt (+ 1.0 (exp x)))) 2) (log (cbrt (+ 1.0 (exp x)))))
7.0ms	(cbrt (+ 1.0 (exp x)))
8.0ms	(cbrt (+ 1.0 (exp x)))

series1.0s

Counts

4 → 12

Calls

4 calls:

327.0ms	(log (cbrt (+ 1.0 (exp x))))
326.0ms	(+ (* (log (cbrt (+ 1.0 (exp x)))) 2) (log (cbrt (+ 1.0 (exp x)))))
201.0ms	(cbrt (+ 1.0 (exp x)))
192.0ms	(cbrt (+ 1.0 (exp x)))

simplify680.0ms

Counts

79 → 79

Iterations

Iter	Nodes
done	5001
2	1122
1	290
0	124

prune541.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (+ x 2.0) (* 1/2 (pow x 2)))) (* x y))
0.0b	(+ (+ x 2.0) (* 1/2 (pow x 2)))
5.4b	(log (+ (+ x 2.0) (* 1/2 (pow x 2))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

18.0ms	(* 1/2 (pow x 2))
36.0ms	(- (log (+ (+ x 2.0) (* 1/2 (pow x 2)))) (* x y))
45.0ms	(+ (+ x 2.0) (* 1/2 (pow x 2)))
37.0ms	(log (+ (+ x 2.0) (* 1/2 (pow x 2))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (pow x 2))
119.0ms	(- (log (+ (+ x 2.0) (* 1/2 (pow x 2)))) (* x y))
33.0ms	(+ (+ x 2.0) (* 1/2 (pow x 2)))
79.0ms	(log (+ (+ x 2.0) (* 1/2 (pow x 2))))

simplify891.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	1580
1	385
0	155

prune377.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize106.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
5.4b	(log (+ (* (+ (* x 0.16666666666666666) 1) (cbrt 2.0)) (* (pow x 2) (- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `log-div` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `associate-l/` `frac-add` `associate-r/`
3×	`log-prod` `flip3-+` `flip3--` `flip-+` `flip--`
2×	`pow1/3`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 52

Calls

4 calls:

11.0ms	(- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
25.0ms	(log (+ (* (+ (* x 0.16666666666666666) 1) (cbrt 2.0)) (* (pow x 2) (- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6)))))

series476.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
476.0ms	(log (+ (* (+ (* x 0.16666666666666666) 1) (cbrt 2.0)) (* (pow x 2) (- (* (cbrt 2.0) 0.09722222222222221) (* (cbrt (/ 1 (pow 2.0 5))) 1/6)))))

simplify1.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5001
2	2244
1	492
0	171

prune583.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes140.0ms

Accuracy

81.7% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 1.9b

bsearch77.0ms

Steps

Iters	Range		Point
7	-39557031.28023394	-346749.28651926527	-353769.981911287

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.4s	2545×	body	10240	exit
657.0ms	8456×	body	80	valid
159.0ms	268×	body	640	valid
119.0ms	117×	body	1280	valid
45.0ms	173×	body	320	valid
17.0ms	88×	body	160	valid