Details

sample102.0ms

Algorithm

intervals

Results

54.0ms	73×	body	10240	exit
22.0ms	273×	body	80	valid
4.0ms	5×	body	1280	valid
3.0ms	8×	body	320	valid
2.0ms	5×	body	640	valid
1.0ms	7×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	19
2	19
1	12
0	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (exp x))
0.0b	(- (log (+ 1 (exp x))) (* x y))
0.3b	(log (+ 1 (exp x)))

rewrite44.0ms

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-+` `insert-posit16` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `log-pow` `flip--`

Counts

3 → 48

Calls

3 calls:

5.0ms	(+ 1 (exp x))
31.0ms	(- (log (+ 1 (exp x))) (* x y))
8.0ms	(log (+ 1 (exp x)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(+ 1 (exp x))
65.0ms	(- (log (+ 1 (exp x))) (* x y))
62.0ms	(log (+ 1 (exp x)))

simplify1.6s

Counts

57 → 57

Iterations

Iter	Nodes
4	3163
3	1087
2	415
1	189
0	84

prune473.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* (cbrt (- (log (+ 1 (exp x))) (* x y))) (cbrt (- (log (+ 1 (exp x))) (* x y)))) (cbrt (- (log (+ 1 (exp x))) (* x y))))
1.0b	(cbrt (- (log (+ 1 (exp x))) (* x y)))
1.0b	(cbrt (- (log (+ 1 (exp x))) (* x y)))
1.0b	(cbrt (- (log (+ 1 (exp x))) (* x y)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
23×	`pow1`
14×	`associate-*l/`
13×	`cbrt-prod`
12×	`pow1/3`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-exp-log` `pow-prod-up` `add-cube-cbrt`
8×	`associate-*r/`
6×	`pow-plus` `associate-r`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod`
2×	`pow2` `unswap-sqr`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 104

Calls

4 calls:

104.0ms	(* (* (cbrt (- (log (+ 1 (exp x))) (* x y))) (cbrt (- (log (+ 1 (exp x))) (* x y)))) (cbrt (- (log (+ 1 (exp x))) (* x y))))
6.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))
6.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))
6.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))

series1.6s

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* (cbrt (- (log (+ 1 (exp x))) (* x y))) (cbrt (- (log (+ 1 (exp x))) (* x y)))) (cbrt (- (log (+ 1 (exp x))) (* x y))))
358.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))
416.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))
757.0ms	(cbrt (- (log (+ 1 (exp x))) (* x y)))

simplify2.9s

Counts

116 → 116

Iterations

Iter	Nodes
3	5744
2	1458
1	451
0	187

prune993.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (+ 1 (exp x)))
0.6b	(* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))
0.7b	(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
14.4b	(/ (- (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x))))) (* (* y x) (* (* y x) (* y x)))) (+ (* (* y x) (* y x)) (* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
21×	`pow1`
12×	`log-prod` `times-frac`
11×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`cube-unmult` `associate-l` `log-pow`
7×	`associate-r`
6×	`swap-sqr`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`difference-cubes` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `flip3-+` `flip-+` `distribute-lft-out`
2×	`log-div` `pow-prod-down` `prod-exp` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `pow-plus` `flip3--` `div-sub` `div-exp` `rem-log-exp` `pow-sqr` `pow-prod-up` `div-inv` `flip--`

Counts

4 → 116

Calls

4 calls:

7.0ms	(log (+ 1 (exp x)))
40.0ms	(* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))
23.0ms	(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
353.0ms	(/ (- (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x))))) (* (* y x) (* (* y x) (* y x)))) (+ (* (* y x) (* y x)) (* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(log (+ 1 (exp x)))
149.0ms	(* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))
87.0ms	(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
241.0ms	(/ (- (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x))))) (* (* y x) (* (* y x) (* y x)))) (+ (* (* y x) (* y x)) (* (log (+ 1 (exp x))) (+ (* y x) (log (+ 1 (exp x)))))))

simplify933.0ms

Counts

128 → 128

Iterations

Iter	Nodes
2	2082
1	551
0	200

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* x (+ 1/2 (* x 1/8)))
0.0b	(+ (* x (+ 1/2 (* x 1/8))) (log 2))
0.0b	(- (+ (* x (+ 1/2 (* x 1/8))) (log 2)) (* x y))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`associate-+r+` `log-prod` `associate-r` `associate-l` `insert-posit16`
2×	`distribute-rgt-in` `associate-+l+` `sum-log` `distribute-lft-in` `flip3-+` `diff-log` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip--` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

11.0ms	(* x (+ 1/2 (* x 1/8)))
10.0ms	(+ (* x (+ 1/2 (* x 1/8))) (log 2))
78.0ms	(- (+ (* x (+ 1/2 (* x 1/8))) (log 2)) (* x y))

series217.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* x (+ 1/2 (* x 1/8)))
56.0ms	(+ (* x (+ 1/2 (* x 1/8))) (log 2))
75.0ms	(- (+ (* x (+ 1/2 (* x 1/8))) (log 2)) (* x y))

simplify2.7s

Counts

64 → 64

Iterations

Iter	Nodes
3	5750
2	1038
1	301
0	109

prune522.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes216.0ms

Accuracy

91.9% (0.1b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 2.0b

bsearch48.0ms

Steps

Iters	Range		Point
7	-1.3763288755158523	-0.006947246361207331	-0.00706318010460099

simplify8.0ms

Iterations

Iter	Nodes
2	29
1	29
0	24

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	2387×	body	10240	exit
854.0ms	8436×	body	80	valid
179.0ms	262×	body	640	valid
95.0ms	98×	body	1280	valid
62.0ms	180×	body	320	valid
53.0ms	116×	body	160	valid